# Full Text: Thanks for Nothing: Gratitude, Model Revisability, and the Practice of Realizing Emptiness

> Extracted from `thanks-for-nothing-v0.11.0-manuscript.pdf`

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COMPUTATIONAL MODELS · CONCEPTUAL INQUIRY · REPRODUCIBLE RESEARCH
Thanks for Nothing
Gratitude, Model Revisability, and the Practice of Realizing Emptiness
A source-grounded study of gratitude, absence and revisable representations. Synthetic experiments clarify enabling
operations; human gratitude and realization require separate evidence.
Conceptual cover illustration generated with AI; not a scientific result.
Daniel Ari Friedman
Active Inference Institute
ORCID: 0000-0001-6232-9096
daniel@activeinference.institute
Code and reproducibility materials: https://github.com/docxology/thanks_for_nothing
DOI: 10.5281/zenodo.23402517
Research manuscript, version 0.11.0 2026-10-22
Paper: CC BY 4.0 ; original code: MIT. Third-party rights remain separate.

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CONCEPTUAL GRAPHICAL ABSTRACT
What can ‘nothing’ mean?
Evidence, availability, counterfactual value and revisability answer different questions.
Appreciation does not make them interchangeable.
Recorded absence
What did a functioning channel observe?
A recorded absence can be evidence when the channel
discriminates between possible states.
A no-event record differs from missing data and from a claim that nothing exists.
Missing observation
Was a usable record available?
The missing-record sentinel supplies no observation likelihood in
the declared implementation.
Ignoring missingness requires assumptions; other missingness processes can be
informative.
Counterfactual appreciation
Against which alternative is an outcome valued?
An uneventful outcome can acquire value relative to an avoided
harm without supplying favorable evidence.
The valuation-only control preserves belief updates and predictive losses by
construction.
Revisable representations
Can a useful distinction be examined and conditionally retained?
The finite counterpart tests access, retention and revision; it does
not measure realization of emptiness.
Non-reification concerns how a representation is held, beyond recording an
absence.
An enabling chain, not an attainment scale
Appreciate
examinability
Choose and
pay
Gain
effective
access
Compare
evidence
Retain or
revise
Assess
independently
Symbols: s is latent state, o observation, p prior and q posterior. In the value illustration, r is reference-
event probability, c its cost and C_actual the actual cost. T extual traditions remain situated comparisons,
not equivalent doctrines; see the atlas and edition notes.
Conceptual proposal →  finite enabling operations →  a separate human research obligation.
s 0 q
q(s ∣o = 0)
s q?
q(s) = p(s)
Reference Actual
ΔV
V = r c − Cactual
Conditional use
Evidence: Recorded absence Missingness Counterfactual value Revisability

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EXPERIMENTAL GRAPHICAL ABSTRACT
From mechanisms to bounded claims
Source reconstruction, corrected comparisons and new extensions remain separate. Recall cohort:
5120 independent agent-world units in 5 declared strata.
Recall and independent prediction
Matched exposure and replay dose separate positive selection from
learning and independent prediction.
Optimism shifts and predictive accuracy differ; effects depend on the world and
comparator.
Recorded absence and counterfactual value
A no-event token can update belief; the missing-record rule supplies
no likelihood.
Valuing an avoided harm changes assigned value without creating favorable evidence.
Native attention and learned-channel transfer
Native GNN/pymdp runs distinguish agent and process; transfer
bridges remain separate.
The source supplies before-only gaze. A favorable attention shift need not improve
prediction.
Enacted inquiry and effective access
Paid activity, effective access and evidence-based retention or
revision are distinct operations.
Blocked access can incur cost without revision; exact enumeration retains adverse
selections.
Adaptive scene sampling
Complete query-conditioned GNN channels expose a context-
dependent access advantage.
Already-open and uniform controls do not establish a further inquiry-specific benefit.
Joint scene and encoding inquiry
Spatial and contingency queries test joint inference over the scene
and its encoding.
Equivalent laws remain unidentified; excluded support stays unavailable; the
reference anchor is stipulated.
Execution and evidence remain inspectable
GNN
declarations
Parsed graphs
and tensors
Actual
numerical
consumers
Independent
controls
Paired and
joint
uncertainty
Reproducible
artifacts
Glyphs unpack the admitted likelihood: s or z is hidden, o observed and q a known query. Dimensions come
from executed GNN. The world glyph is one declared stratum; complete models and controls follow.
Synthetic model evidence does not establish human gratitude, clinical benefit, contemplative
realization or philosophical equivalence.
s[2] o[3]
A: 3 x 2
s[2] o[2]
A: 2 x 2
s[13] o[3]
A: 3 x 13
s[3] o[2]
A: 2 x 3
z[3] o[3]
q[3]
A: 3 x 9
z[9] o[9]
q[16]
A: 9 x 144
Evidence: Recall Absence Transfer Enacted inquiry Scene sampling Scene/encoding

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GNN / BAYESIAN MODEL CARD
From declarations to executed models
A time-unrolled POMDP view, parsed dependencies and the complete consumer inventory.
BAYESIAN TIME SLICE / conditional on the selected action
A observation | state
B next state | state, action
D initial-state prior
C log outcome preferences
Shaded: observations. Open: latent states and
the conditioned action. D initializes the first
state; C guides native policy selection, outside
this conditional DAG.
P(s0 : T, o0 : T ∣u0 : T − 1, A, B, D) = D(s0)
T
∏
t = 0
A(ot ∣st)
T − 1
∏
t = 0
B(st + 1 ∣st, ut)
DECLARATION GRAPH / source structure, not an instantaneous causal DAG
26 declarations; 2 topology groups. Complete
query graph shown. B advances time; q and z
define the joint basis. Full models are linked
below.
The Bayesian diagram defines the tensor
semantics. Finite consumers add their own
declared task laws; a shared backend label does
not establish native execution.
AUTHORING INPUTS / complete executed instances in the linked cards
Declaration / consumer A B C D SHA
analysis
Protocol carrier 1 x 1 1 x 1 x 1 1 1 93ac17
gratitude
Finite learner 3 x 2 2 x 2 x 1 3 2 a2945f
nothingness
Finite comparators 2 x 2 2 x 2 x 1 2 2 5cfa88
attention_positive
Native GNN / pymdp 3 x 13 13 x 13 x 13 3 13 1d47aa
attention_negative
Native GNN / pymdp 3 x 13 13 x 13 x 13 3 13 2b5411
emptiness_practice
Finite inquiry 2 x 3 3 x 3 x 1 2 3 e27328
gaze
Finite scene inquiry 3 x 3 3 x 3 x 1 3 3 2a370a
boundary_gaze
Finite joint inquiry 9 x 9 9 x 9 x 1 9 9 4d0b48
A: observation x state; B: next x previous x action. SHA: source-digest prefix only. Full tensors, settings,
annotations, native graphs, dependency revisions and evidence digests are in the linked complete card.
Scope: finite synthetic software models. These graphs do not establish human gratitude,
contemplative realization, clinical efficacy or philosophical equivalence.
st st + 1
ot ot + 1
ut
B
A A
s
A B D q z
o u
C
Evidence: Model inventory Methods Limits Complete cards

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Contents
Abstract 2
1 Introduction 2
1.1 Nothing as evidence, missingness, value and revisability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Emptiness and appreciation: a situated dialogue across traditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Methods 8
2.1 Reconstructing sources and admitting executable models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Separating recall, recorded absence and counterfactual value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Testing the chain from appreciation to effective inquiry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Transferring learned channels to active scene sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 Joining scene evidence with questions about its encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.6 Defining estimands and testing uncertainty procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Results 12
3.1 Positive recall changes optimism without a general predictive benefit . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Effective access permits revision and appropriate retention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3 Access advantages do not establish an inquiry-specific gaze benefit . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4 Learning an encoding differs from using it for prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 Discussion 20
4.1 Gratitude for the possibility of examining one’s own constructions . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.2 What gaze, confidence and first-person reports can establish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3 From finite mechanisms to an identifiable human research program . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.4 Conclusion: appreciate, examine and remain able to revise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Supplementary information 23
S1. Conceptual distinctions and the scholarship behind them . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
S2. Declared models, executable interfaces and independent controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
S3. Experimental design, estimands and uncertainty procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
S4. Complete results, including adverse and unavailable estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
S5. Mechanistic interpretation and competing explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
S6. What these models do and do not identify . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
S7. Human research: manipulations, measurements and recovery checks . . . . . . . . . . . . . . . . . . . . . . . . . . 80
S8. Source custody, operating diagnostics and complete interval tables . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
S9. Model settings injected from admitted declarations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
S10. Textual editions, translation choices and comparison limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
References 97
1

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Abstract
Gratitude can concern a benefit received, a harm that did not occur, or the conditions that make one’s own assumptions exam-
inable. We develop the proposal that appreciating these conditions can orient practice toward realizing emptiness: examining
how distinctions arise, relinquishing their assumed intrinsic necessity, and retaining their conditional usefulness. The argu-
ment distinguishes an observed absence, a missing observation, counterfactual valuation and non-reification, and places their
differences in dialogue with explicitly situated philosophical and scriptural sources. We reconstruct Fisher, Sandved Smith and
Hohwy’s gratitude and gaze notebooks, then separate faithful reconstruction from corrected experiments and new mechanisms.
GNN-declared paired recall experiments use 5120 independent agent-world units, matched environmental exposure and replay
dose, normalized likelihoods, and independent predictive assessment. Pinned Realizing Emptiness interfaces supply structural
admission and finite mathematical comparators. An enacted inquiry model separates appreciation, costly activity, access to al-
ternatives and evidence-responsive retention or revision; explicit learning-to-gaze and joint scene/encoding experiments examine
transfer and identifiability. Exact count enumeration, mathematical nulls, paired controls and joint bootstrap inference make
the resulting software claims independently checkable.
Selective positive recall reduces the declared optimism summary, while its predictive consequences depend on the world mix-
ture and the specified transfer bridge. Counterfactual absence valuation preserves inference by construction. Accessible inquiry
can revise a contradicted restriction and retain a useful one; activity without access instead incurs costs while preserving rigid
forecasts. Exact analysis exposes rare adverse selections absent from seeded realizations. The original gaze code reproduces the
pre-intervention occupancy but contains no implemented after intervention. Our active-scene extension finds a context-dependent
access advantage without an additional inquiry-specific predictive advantage. Joint scene/encoding inquiry distinguishes learn-
ing an encoding from combining it with scene evidence: observationally equivalent labels remain unidentifiable, and excluded
hypotheses cannot be recovered. Known-answer fixtures also retain skew-related undercoverage and unavailable rare-event esti-
mates rather than treating replication size as a remedy for every inferential failure. The contribution is a reproducible account
of enabling operations and their limits, together with a falsifiable human research program that separates inquiry value from
patience, anticipated good news and instrumental information demand. Synthetic model results establish neither human grat-
itude nor contemplative realization or clinical benefit. Code, declared models and reproducibility materials are available at
github.com/docxology/thanks_for_nothing.
1 Introduction
A functioning channel can record no event (observed absence), whereas an unavailable record leaves an outcome unobserved
(missing observation). An actual outcome can also be valued against a specified alternative (counterfactual value). The Realizing
Emptiness proposal introduces a further task: examining a useful distinction’s assumed intrinsic necessity and practicing its
conditional use (non-reification). These operations motivate different questions about gratitude for avoided harm and for the
conditions that enable inquiry. Their practical and mathematical consequences organize this study.
Computational models provide a way to specify those consequences without assuming that their state variables are direct
measurements of lived experience. Fisher, Sandved Smith, and Hohwy propose that gratitude practice can be represented as
deliberate precision allocation to positive observations, followed by learning that changes world beliefs and an optimism-task
readout ( Fisher et al. 2025 ). Their preprint also presents a modified Yarbus attention task as a proof of concept. A subsequent
journal abstract describes the same broad research program ( Fisher et al. 2026 ). We inspect the archived preprint in full and
the journal publication at abstract level; detailed reconstruction claims concern the preprint and its associated notebooks, not
an assumed identical journal full text.
The proposal is useful because it connects an everyday practice to explicit operations on inference and learning. It also makes the
limits of that connection visible. Increasing the probability assigned to a favorable state is not the same as improving predictive
accuracy. An optimism score is not a direct measure of well-being. Rehearsing an event is not collecting an independent
observation, and changing a likelihood parameter by hand is not showing that the parameter was learned and transferred to
another task. Those distinctions determine which claims a reproducible extension can support.
We ask what follows from a declared finite model when positive-event selection, replay dose, environmental exposure, inference,
and evaluation are separated. We then ask whether appreciation of an absence can be represented without converting an unob-
served or hypothetical event into favorable evidence. Finally, we develop the more demanding proposal that gratitude can orient
an agent toward examining its own model-making. The title “Thanks for Nothing” holds these questions together: appreciation
of contingent benefits and avoided harms, and appreciation of the opportunity to realize that conceptual constructions need not
be intrinsically or compulsorily established.
The work has three levels of analysis. Source reconstruction preserves the numerical behavior of supplied notebooks and docu-
ments differences between that behavior and a normalized generative-model interpretation. Corrected experiments hold environ-
mental exposures fixed across conditions, normalize likelihoods, match replay dose, and evaluate frozen models on independent
observations. New extensions distinguish observed absence from missingness, assign counterfactual value without changing be-
liefs, and enact a repeated inquiry policy over alternative representations. Keeping these levels separate prevents a correction
from being reported as a faithful replication, or our proposed practice extension from being attributed to the original gratitude
paper.
The resulting contribution is methodological and conceptual. A finite simulation can reveal how an intervention changes the
model that was implemented, expose failures of an estimator under a known null, and make otherwise ambiguous uses of “absence”
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explicit. Whether those operations characterize human gratitude remains an empirical question requiring construct validation,
comparison activities, and outcomes beyond the simulation’s own favored readout.
The paper contributes an explicit appreciation–inquiry proposal, a modular finite counterpart imported through pinned GNN and
Realizing Emptiness interfaces, and complementary evaluations through exhaustive evidence decisions, paired repeated-policy
experiments and active scene sampling. It reconstructs both source notebooks, connects corrected learning to gaze through a
declared likelihood embedding, and distinguishes structural access from information-seeking policy. The corrected recall study
constrains favorable interpretations of selective rehearsal. Supplementary methods retain estimator failures and complete interval
comparisons.
The psychological interpretation is a further research obligation. Construct validity concerns the testable relations supporting an
interpretation, rather than the name attached to an operation ( Cronbach and Meehl 1955 ). Calling a preference gratitude or a
family change insight therefore cannot supply the missing evidence. Our contribution makes proposed operations discriminable;
the validation account explains what would be needed to connect them to human constructs.
1.1 Nothing as evidence, missingness, value and revisability
We use 4 stable terms, identified in Figure 1 and repeated in the task and result figures. They classify different questions rather
than stages of an achievement scale. Here, observed absence concerns evidence; missing observation concerns availability; coun-
terfactual value concerns evaluation relative to a reference; and non-reification concerns the status accorded to a representation.
Concept Operation in this project Evidential boundary
A: Observed absence Update with the no-event likelihood. Detection and exposure assumptions
matter.
B: Missing observation Retain the prior under our missingness
rule.
State-dependent missingness needs its
own model.
C: Counterfactual value Assign value without adding an
observation.
Reference-dependent value is not new
evidence.
D: Non-reification Examine its conditions; retain or revise
its use.
Finite revisability does not measure
realizing emptiness.
The distinctions also organize the scholarship. Goh and colleagues study contrastive silences within structured auditory contexts,
rather than every possible absence ( Goh et al. 2023 ). Missingness has a different inferential role: ignoring its mechanism requires
explicit assumptions and an inferential target ( Seaman et al. 2013 ). Our no-update sentinel is a declared modeling choice, not
a consequence of calling a value missing.
Counterfactual thinking can influence affect and action through different routes, including contrast with an alternative or as-
similation toward an imagined event ( Epstude and Roese 2008 ). Mental subtraction of an existing benefit is therefore a useful
comparison for appreciation, while remaining distinct from detecting an absent harm or establishing gratitude ( Koo et al. 2008 ).
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Figure 1: Different questions require different meanings of nothing. The 4 panels distinguish evidence, availability, reference-
dependent value and the status of a representation. A: Observed absence records 𝑜 = 0 through a functioning detector; B: Missing
observation has no observation; C: Counterfactual value compares expected reference harm with actual cost. D: Non-reification
redraws a self/world boundary while preserving useful dependencies. These are symbolic operations, with no sampled estimates
or confidence intervals. Realizing Emptiness motivates examining assumed necessity; the diagram supplies neither a realization
score nor evidence that appreciation causes inquiry.
1.2 Emptiness and appreciation: a situated dialogue across traditions
1.2.1 What is absent, what remains and what depends on conditions
Saṃyutta Nikāya (SN, the Connected or Grouped Discourses) and Majjhima Nikāya (MN, the Middle-length Discourses) are
collections of early Buddhist scripture in the Pali Sutta Piṭaka. Their numbers identify discourses, not scientific measures. In
Kaccayanagotta Sutta: To Kaccayana Gotta (on Right View) , SN 12.15, the Buddha is presented as teaching conditioned arising
and cessation while rejecting opposed extremes. Ṭhānissaro Bhikkhu’s translation says:
‘Everything exists’: That is one extreme.
The discourse also rejects the opposing assertion of universal non-existence ( Thanissaro Bhikkhu 1997b , discourse paragraph
beginning with the two extremes). In Cula-suññata Sutta: The Lesser Discourse on Emptiness , MN 121, the same translator
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distinguishes what is absent from what remains:
Whatever remains, he discerns as present: ‘There is this. ’
That passage occurs at the end of the wilderness-perception sequence; the later Release section examines refined concentration as
conditioned and subject to cessation ( Thanissaro Bhikkhu 1997a ). Both quotations use the catalogued Access to Insight editions.
These are translated textual arguments to interpret, not empirical evidence for a Bayesian model or a numerical definition of
realization. The textual supplement identifies the editions and translation-sensitive qualifications.
A further discourse specifies the object of the negation. In Suñña Sutta: Empty , SN 35.85, sensory and mental domains are
described as empty of self or what pertains to self ( Thanissaro Bhikkhu 1997c ). That qualification differs from claiming that no
event occurred or that no observation was recorded. It constrains our interpretation of non-reification without making the finite
support comparison a realization criterion.
The Mahāyāna Heart Sutra supplies a different textual setting. In Thich Nhat Hanh’s explicitly revised English rendering, the
first address to Sariputra reads:
this Body itself is Emptiness and Emptiness itself is this Body.
The wording is specific to this contemporary translation, whose accompanying explanation identifies deliberate changes intended
to avoid nihilistic interpretations ( Thich Nhat Hanh 2014 ). Its paired formulation makes it difficult to treat emptiness as a
separate object that abolishes embodied phenomena. It also cautions against treating a variable named empty as an adequate
philosophical account. This is a comparison between differently situated texts, not a claim that the early discourses and all
Mahāyāna traditions articulate an identical doctrine. The edition notes distinguish the translated passage from its translator’s
explanatory argument.
1.2.2 Using distinctions without treating them as intrinsically necessary
The raft simile in Alagaddupama Sutta: The Water-Snake Simile , MN 22, distinguishes relying on a useful means of crossing
from continuing to carry it afterward ( Thanissaro Bhikkhu 2004 , The Raft Simile). This motivates a question about appropriate
reliance rather than indiscriminate rejection. Our retention controls test the narrower computational question of whether a
working predictive family remains useful; the discourse’s liberative purpose is not reduced to predictive loss.
Lutz and colleagues distinguish object orientation, meta-awareness and dereification within a provisional phenomenological
framework ( Lutz et al. 2015 ). Noticing a construction and ceasing to take it as intrinsically necessary are therefore different
hypotheses. Philosophical non-reification also requires identifying what is negated. Garfield and Thakchöe distinguish the
rejection of intrinsic nature from the status of conventional phenomena, while comparing interpretations that differ on that
status (Garfield and Thakchöe 2011 ). Our Realizing Emptiness connection concerns examining assumed necessity while retaining
conditional usefulness. The finite model makes an enabling operation explicit; the complete philosophical comparisons and
construct boundaries remain in the scholarship supplement .
Nāgārjuna’s Mūlamadhyamakakārikā (MMK) gives this caution a more specific philosophical basis. In our descriptive paraphrase
of the inspected Sanskrit witness, the verse on dependent arising connects dependent arising, emptiness and dependent designation
in its account of the middle way; the preceding discussion distinguishes two truths and makes reliance on convention necessary
for teaching the ultimate ( Nagarjuna 2020 , MMK 24.18 and 24.8–10). This is our paraphrase, not a quotation from an English
translation. Resolving the pronouns in the dependent-arising verse and determining what dependent designation entails require
interpretation, for which the differing accounts discussed by Garfield and Thakchöe remain relevant (Garfield and Thakchöe 2011 ).
The comparison therefore concerns how distinctions are held and used. It does not identify conventional truth with held-out
predictive accuracy or make successful model selection a criterion of realization.
1.2.3 F rom gratitude to benefactors toward appreciation of enabling conditions
Our constructive proposal is gratitude for the conditions that permit examination, for an insight that changes how a distinction
is held, and for the continuing possibility of revision. Appreciation can precede inquiry, follow it, or support its continua-
tion. Those are different temporal relations. The Kataññu discourses in the Aṅguttara Nikāya (AN, the Numerical Discourses)
connect gratitude with benefactors and ethical repayment, including parental care ( Thanissaro Bhikkhu 2002 ). Appreciation
of impersonal inquiry conditions is our constructive extension, rather than a translation of that benefactor-centered account.
Sandved-Smith and colleagues’ account of examining an assumed self/world separation motivates the computational bridge
(Sandved-Smith et al. 2026 ). The model implements access to alternatives and conditional use of a representation; it does not
establish that appreciation produces contemplative realization.
The capacities that permit appreciation can themselves become its object. Epictetus considers perception and understanding
within an argument for divine providence ( Epictetus 1887, I.6 , pp. 19–21). A Jewish liturgical comparison appears in the
Babylonian Talmud: the blessing on opening one’s eyes includes “Blessed…Who gives sight to the blind. ” The wording follows the
annotated William Davidson English edition ( Berakhot, n.d. , Berakhot 60b:5). Both passages make an ordinary capacity salient
without requiring a newly acquired possession. Their providential and liturgical meanings remain distinct from our declared
value for examinability. In a human study, appreciation of a capacity, attribution to a benefactor and willingness to use that
capacity would require separate assessment.
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1.2.4 Useful hollowness, nonattached action and responsibility
The Daodejing offers a direct comparison for the usefulness of an unfilled condition. James Legge’s translation states:
Clay is fashioned into vessels; but it is on their empty hollowness, that their use depends.
The surrounding wheel, vessel and room examples relate constructed form to what its unfilled space enables ( Laozi 2008 , ch. 11).
Appreciating a useful hollow therefore need not mean preferring less structure everywhere. The arrangement matters to the use.
This helps articulate a functional question about absence while leaving Daoist wu, wuwei and Buddhist śūnyatā distinct. Chan’s
discussion also cautions against reducing wuwei to mere inactivity ( Chan 2025, secs. 6–7 ). Neither the vessel example nor our
inference-preserving valuation condition establishes a shared ancient gratitude technique.
Action without a demand for a particular result supplies another comparison. Swami Mukundananda translates the Bhagavadgītā
as follows:
You have a right to perform your prescribed duties, but you are not entitled to the fruits of your actions.
The same verse ends by rejecting attachment to inaction ( Swami Mukundananda, n.d.-a, chap. 2 , verse 47). Its duty-oriented
and theological setting matters: nonattachment to fruits is not a definition of Bayesian uncertainty or Buddhist emptiness. For
our proposal, it sharpens the distinction between valuing an opportunity to inquire and insisting that inquiry confirm a welcome
answer. An inquiry policy may choose a costly examination whose evidence supports retention, revision or an unfavorable
forecast. Evaluating these outcomes independently makes that distinction experimentally consequential without representing the
model as an enactment of the Gītā.
The Gītā also resists reducing response to an internal feeling. In the verses on sacrificial cooperation, Mukundananda’s translation
places received gifts within a sacrificial relation involving humans and divine participants; enjoying gifts without return offerings is
censured (Swami Mukundananda, n.d.-b, 3.10–13 ). Read alongside the earlier verse on duty and its fruits, these verses distinguish
relinquishing entitlement to results from relinquishing responsibility to act. Their yajña is not generic ecological interdependence
or a computational exchange rule. The comparison instead asks what follows recognition of a benefit: possession of a favorable
attitude, a costly practice, an obligation to another, or some combination. Our finite inquiry policy addresses only the relation
between valuing access, paying a cost and using available evidence; it implements neither sacrifice nor interpersonal repayment.
1.2.5 Contentment and humility without relinquishing reciprocal obligations
Appreciation need not take a new acquisition as its threshold. Ben Zoma’s answer about wealth in Avot, in Joshua Kulp’s
translation, is: “Who is rich? He who rejoices in his lot” ( Kulp, n.d.-b, 4:1 ). The saying invokes a psalm on labor’s fruit and
the enjoyment of labor’s fruit; its setting includes learning, self-command and honoring others. It redescribes wealth through a
relation to what is available rather than an increment in possessions. Rejoicing is not automatically gratitude to a benefactor,
and the selected clause supplies no addressee. Nor does appreciation of an existing lot justify deprivation or injustice. This
witness helps separate contentment, gratitude and the counterfactual valuation of an avoided harm before attempting to measure
any of them.
Guru Nanak’s Japji Sahib supplies a distinct theological comparison. Sant Singh Khalsa renders the conclusion of the second
pauri: “O Nanak! One who understands His Command, does not speak in ego. ” Walking in divine Will in the preceding pauri
supplies immediate practical context in the Sri Guru Granth Sahib (Guru Nanak, n.d. , ang 1, pauris 1–2). Understanding hukam
here qualifies self-assertion within an order one does not author. It is not an explicit instruction to feel gratitude, and neither
hukam nor haumai can simply be replaced by natural law or a Bayesian self-model. Its relevance to our question is responsiveness
without claiming authorship or mastery, rather than a vacant object to be celebrated. The text’s Creator, grace and practical
orientation remain part of that comparison.
A comparison should also admit an ethically relevant case without an explicit grateful response. In the Analects, Zigong asks for
a rule of lifelong practice, and the answer specifies shu, reciprocity: “What you do not want done to yourself, do not do to others. ”
The inspected Legge edition and Eno’s teaching translation give the exchange different chapter numbers ( Confucius 2002, XV.23 ;
2015, 15.24 ). Here a consequential absence is the unwanted imposition one refrains from making. Reciprocity constrains one’s
conduct; it does not wait for another person to repay a benefit. This ethical comparator supplies neither an emptiness doctrine
nor a gratitude exercise. Keeping it in the comparison tests whether the phrase Thanks for Nothing can invite a useful question
while leaving a passage’s different answer intact.
1.2.6 Thanksgiving amid adversity: attending to the addressee
Theistic traditions bring the addressee and obligations of appreciation into focus. The First Letter to the Thessalonians , in the
New Revised Standard Version Updated Edition, instructs:
give thanks in all circumstances, for this is the will of God in Christ Jesus for you.
The wording situates thanksgiving in circumstances and a relationship to God ( New Revised Standard Version Updated Edition
2021, 5:18). Thanksgiving need not await a favorable outcome, but this sentence does not by itself say that every harmful event is
a benefit. That distinction matters when interpreting appreciation of an avoided harm: favorable evaluation of a counterfactual
difference cannot establish how someone should respond to an actual loss.
The cited paragraph of Mishnah Berakhot, in Joshua Kulp’s translation, requires blessing for evil as for good ( Kulp, n.d.-a, 9:5 ).
The later Talmudic discussion preserves different formulas for good and bad tidings ( Berakhot, n.d. , Berakhot 60b:7). Blessing
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across circumstances therefore does not erase the distinction between those circumstances. The comparison poses a question
about the response and its divine addressee, rather than converting adverse evidence into favorable evidence. Blessing, gratitude,
praise and acceptance can be related within a practice while remaining different candidate constructs for research.
In Mustafa Khattab’s The Clear Quran , a divine proclamation reads, “If you are grateful, I will certainly give you more. ” The
verse also warns against ingratitude; its surrounding account recalls deliverance and God’s independence from human gratitude
(Khattab, n.d.-a , Sūrat Ibrāhīm 14:6–8). This religious relation cannot be replaced by a numerical optimism preference. Nor is the
promise a quantified experimental law that appreciation produces wealth, predictive accuracy or clinical benefit. A comparison
attentive to shukr asks about recognition, response and accountability, while preserving the theological setting of the translated
passage.
The beneficiary and addressee of gratitude need not have symmetrical needs. In the same translator’s rendering, a verse in
Sūrat Luqmān directs gratitude to Allah while locating its good in the grateful person and affirming divine self-sufficiency
(Khattab, n.d.-b, 31:12 ). This complements, rather than first introduces, the qualification already present in Sūrat Ibrāhīm
(Khattab, n.d.-a, 14:8 ). Gratitude is not represented as supplying something God lacks, yet obligation and accountability remain.
That is a different relation from the Gītā’s return offerings, the Analects’ restraint and Avot’s rejoicing in one’s lot. Calling all of
them positive valuation would conceal who responds, to whom, through what practice and for what reason. Those distinctions
would need to enter a human study’s instructions and measures rather than being inferred from a common favorable score.
1.2.7 Apophatic language and the limits of computational comparison
Christian apophatic theology provides a further comparison concerning the limits of predication. In C. E. Rolt’s translation of
Mystical Theology, Pseudo-Dionysius writes of the Cause: “It transcends all affirmation by being the perfect and unique Cause
of all things”; the same final sentence also places it beyond negation ( Pseudo-Dionysius the Areopagite, n.d., V ). This concerns
a transcendent divine Cause, not the same object of negation as Madhyamaka’s critique of intrinsic nature. Its relation between
praise and the removal of predicates ( Pseudo-Dionysius the Areopagite, n.d., II ) nevertheless shows why appreciating something
and claiming to describe it exhaustively are separable operations. Removing a predicate in this theological argument is not
equivalent to deleting a hypothesis from a statistical model.
These comparisons refine the research questions through their differences. A useful absence concerns what an arrangement
enables; nonattachment concerns one’s relation to action and its fruits; thanksgiving and blessing raise questions of addressee
and obligation; non-reification concerns the status accorded to a distinction. None licenses replacing another tradition’s terms
with a shared latent variable called wisdom. Our constructive bridge is narrower: appreciate the conditions of examination,
act without requiring a preferred finding, and keep useful distinctions conditionally available. The comparative crosswalk ,
textual scope notes and prospective empirical design distinguish this proposal from historical identity, doctrinal consensus and
demonstrated human effects.
1.2.8 Reading the atlas as a comparison of textual witnesses
Figure 2 places these witnesses beside one another under two questions: what is absent or relinquished, and what appreciation
or response is articulated? Its cells are our interpretive summaries, not quotations or measurements. The selection follows the
manuscript’s questions and the availability of verified named witnesses; it is not a census of world traditions, a geographical
distribution or a proposed historical lineage. Separate Buddhist and Christian rows retain different textual problems within
those broad labels. A passage that does not specify gratitude is marked accordingly in the companion, rather than being used
to claim that its tradition lacks gratitude. Translator, locator, source link and interpretive limit travel with each row in the
searchable source companion ; the textual supplement and comparative crosswalk retain the surrounding argument.
The atlas exposes a limit of the computational bridge as well as a motivation for it. A vessel’s hollow, a relinquished entitlement,
a withheld imposition and a divine Cause beyond predicates are different candidates for what nothing could mean. The ensuing
response can be discernment, duty, rejoicing, blessing, restraint or praise. Our model asks only whether valuing the opportunity
for examination can support costly inquiry while independent evidence governs retention or revision. The texts neither implement
nor validate that mechanism. Their contribution is to discipline its interpretation and suggest distinctions a future empirical
study would have to preserve.
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Figure 2: Distinct textual responses to absence and relinquishment. Selected named textual witnesses are aligned by what is
absent or relinquished and what appreciation or response follows. Read each row from the named witness and passage locator to
the two interpretive summaries. Alternating shading guides row tracking and encodes no grouping or rank. Separate Buddhist
and Christian rows retain different textual settings; the source companion gives translators, links, addressees, practices and limits.
This is an editorially selected qualitative comparison, with no sampled estimates, shared scale, ranking or confidence intervals.
Gratitude is not explicit in every passage. These witnesses neither exhaust their traditions nor establish doctrinal equivalence,
historical influence or validation of the finite computational model.
2 Methods
2.1 Reconstructing sources and admitting executable models
We preserve the supplied gratitude and modified Yarbus notebooks, reconstruct their available numerical behavior, and distin-
guish those reconstructions from corrected comparisons and new mechanisms. Every new categorical model and experimental
design is admitted through packaged Generalized Notation Notation (GNN) declarations. The imported GNN version is 4.1.0
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and the Realizing Emptiness version is 3.0.0, with exact commits and executing-module digests retained in the provenance record.
A current-upstream check is documented separately; reproducible execution continues to use immutable pins.
The experimental overview separates each question, controlled manipulation, independent assessment and decisive limitation.
The detailed task illustrations define the unknowns, observations, available actions and assessment targets. The diagrammed
agents are finite models. Painting regions and locations are authored registration choices; the models do not infer scene semantics
from pixels. The full formal methods retain every equation, likelihood, prior, policy, access intervention and independent oracle.
The task crosswalk gives the same overview as a searchable table and preserves the concrete detector, timeline and query
diagrams.
The imported interfaces have bounded responsibilities. GNN supplies the actual parser and admission of the declared categorical
arrays; Realizing Emptiness supplies structural admission and finite numerical operations. We separately check those operations
against mathematical controls whose targets do not move with the experimental parameters. This separates a dependency being
called from its output being correct for the stated task. It also leaves the interpretation open to scrutiny: admitting a candidate
family is a software operation, whereas identifying that family with a person’s self/world representation would require additional
evidence. The interface account and model-role notation specify these boundaries before the experimental comparisons.
Checking a model family is also distinct from updating within it. Gelman and Shalizi argue for a cycle in which discrepancies
can motivate changing the model, beyond posterior calculation inside an assumed family ( Gelman and Shalizi 2013 ). Here
independent controls test specified software and finite-model implications; they do not constitute an empirical check of a human
gratitude theory. The implemented access gate exposes authored alternatives, while constructing a better candidate family
remains outside the model.
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Figure 3: What each experiment changes, scores and can rule out. Read each row from its question through the controlled
comparison to its assessment and decisive limitation. Recall, absence/value, enacted inquiry, learned gaze transfer, active scene
sampling and joint scene/encoding inquiry are separate experiments. Budgets and independent-unit descriptions come from
the admitted designs; a new observation, a replayed event and a structural question have different roles. This is a design map,
not an effect-size display; the main Results and complete supplementary tables report the estimates and uncertainty. The
comparison column identifies software controls that constrain interpretation. No row measures human gratitude, eye movements
or contemplative realization.
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2.2 Separating recall, recorded absence and counterfactual value
The graphical-model inventory connects parsed GNN nodes and edges to admitted tensor dimensions and the actual numerical
consumers. Shared graphical syntax does not imply shared execution or empirical interpretation.
The corrected recall study contains 5120 independent agent-world units: 1024 replicates in each of 5 fixed world strata. Each
unit receives the same environmental exposures under 4 paired conditions. Selected positive recall is compared with no recall,
dose-matched random recall and valuation without new belief learning. Training, replay, optimism-task readout and independent
predictive assessment remain separate. Binary Brier loss and observation log loss are evaluated alongside the source-inspired
optimism summary.
Each comparator addresses a different explanation. No recall supplies the ordinary-learning reference; random recall matches
the amount of replay while changing its selection rule. The valuation-only condition changes the assigned value of an uneventful
outcome without supplying a new observation or changing the learning path. Sharing environmental exposure within a unit
prevents a different history of good and bad events from explaining the contrast. Assessment uses new observations after
learning is frozen, so further exposure, a favorable readout and better prediction cannot be counted as the same outcome. The
paired-exposure protocol describes the shared histories and random streams, while the scoring definitions distinguish latent-state
Brier loss, observation log loss and the optimism task.
The absence experiment separates observed absence from missing observation: a functioning detector’s no-event outcome is
distinct from an unavailable record. We assign counterfactual value through a separate reference calculation. Thus a record can
change a posterior because the channel discriminates states, while a value can change because the chosen comparison changes.
Neither operation licenses treating an unavailable event as observed favorable evidence. The absence model states the detector
likelihood, missing-record convention and reference-value calculation separately.
2.3 Testing the chain from appreciation to effective inquiry
The practice experiment supplies a finite enabling counterpart to non-reification and uses 512 independent paired replicates per
context and 12 windows. A policy can value examination, pay its cost and gain access to alternative predictive families; a sham
can incur the activity cost without that access. Evidence determines conditional retention or revision, followed by 512 new
assessment observations per window. Stationary and reversal contexts distinguish a restriction that remains useful from one that
becomes inadequate. The open family is selected only when its evidence exceeds that of the restricted family; a tie retains the
restriction. The selected forecast then faces assessment data that did not select it. The enacted-policy model and Figure 13
make the action, access, evidence and assessment stages explicit. Prediction and expenditure remain separate outcomes.
This separation also informs the prospective measurement plan. Process-evaluation guidance distinguishes implementation,
mechanisms of impact and context ( Moore et al. 2015 ). Logging an activity alone therefore leaves its delivery and consequences
unresolved. In this finite model, activity and informative access are distinct recorded quantities; their mapping to human
measures remains a proposal. The process-measurement argument specifies that analogy and its limits.
Figure 10 retains the detailed mappings and distinct units in the technical supplement.
2.4 Transferring learned channels to active scene sampling
The source gaze code provides before-condition reconstruction only. New learned-channel transfer maps frozen recall channels
to scene sampling through explicitly declared bridges. The active scene task uses 13 registered locations and 48 decisions per
episode, with 512 paired replicates per context. Already-open utility and uniform sampling are active comparators; access to a
larger candidate menu is distinguished from a preference for information.
Transfer is an authored hypothesis about how tasks are connected. The likelihood bridge transports the learned observation
channel; the alternative readout bridge uses a different projection of the same learning result. Holding the learned channels
fixed makes their downstream consequences comparable without presenting either bridge as empirically identified. Scene-wide
predictive loss is evaluated separately from occupancy of positively labeled locations and from movement cost. The transfer
construction specifies both bridges, and the active-inquiry model distinguishes opening the candidate menu from changing how
queries are selected.
2.5 Joining scene evidence with questions about its encoding
The intersection supplies a further finite counterpart to non-reification by joining an unknown scene with an unknown predictive
encoding. A policy chooses a spatial query or a nonspatial action-response question. The diagnostic regime contains encoding
information in the joint action-response relation even though the separate marginals are uniform. The label-only regime removes
that information. All 6 policies share the same potential query outcomes within each independent unit. Restricted support and
a yoked sham test specific failure modes.
Figure 12 in the supplement specifies query budgets, conditional channels, and separate assessment targets.
The intersection contains 9216 independent paired units in 18 fixed cells, generating 55296 policy episodes with 24 dependent
decisions each. The anchored prediction target stipulates a reference-frame intervention; it is not ordinary future prediction
under an unchanged process. The sham follows the integrated policy’s query schedule but discards action identity and ignores
the schedule likelihood. Its null is conditional on that updater, not proof that no information is available to any observer.
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The common decision budget makes the competition between evidence routes visible. Spending a decision on an encoding question
leaves fewer spatial observations, and learning the encoding alone need not identify the scene. We therefore retain separate scores
for encoding judgments, the current scene and prediction under the stipulated reference intervention. Allocation and expenditure
explain what a policy did without replacing those assessment targets. The joint observation law and reference-target definition
state which information each route can supply and why the anchor is necessary.
2.6 Defining estimands and testing uncertainty procedures
Complete paired units are resampled within fixed strata; decisions, windows and policy conditions do not enlarge the independent
sample. The recall family has 8 primary contrasts. Gaze and intersection analyses are separate exploratory families of 58 and
84 members. Joint rectangles use 16383 shared bootstrap maxima and retain a conditional 99% Monte Carlo quantile bracket.
Proved constants, stochastic estimates and unavailable sample constants receive different statuses. Known-answer skew and
rare-event controls retain undercoverage and unavailability.
The target is an equally weighted mean over declared world strata, not a population effect for people or naturally occurring
environments. Changing the world weights changes that target, even when every within-world result is held fixed. Within each
stratum, resampling preserves the paired outcomes and their shared exposures. This follows the simulation-study distinction
between the generating mechanism, estimand, method and performance measure ( Morris et al. 2019 ). The weighting analysis
treats alternative mixtures as sensitivity scenarios, while the joint-resampling methods preserve dependence across contrasts
rather than combining separate intervals after the fact.
Independent replication and resampling answer different precision questions. More simulated agents reduce Monte Carlo error
for a declared generating process; more bootstrap draws refine the conditional numerical approximation to an interval. Neither
supplies additional human observations. We therefore report Figure 14 with an explicit standard-error calculation, rather than
treating a visually stable trajectory as proof of precision ( Koehler et al. 2009 ). The simulation-design scope separates this
diagnostic from sensitivity across model settings.
An interval procedure can also fail to return an interval. Under our explicit rule that any zero-variance bootstrap resample
makes studentization unavailable, additional resamples can reveal more such failures. We derive an exact finite Bernoulli
availability benchmark and compare it with Figure 40 . A vailability, coverage across all experiments and coverage among
available intervals answer different questions; excluding failures from the denominator can conceal the practical limitation
(Morris et al. 2019, secs. 3.4, 5.1 ).
Uncertainty has more than one source. Replicate variation concerns the simulated units; the Monte Carlo bracket concerns
estimation of the bootstrap critical value conditional on those units. Neither addresses uncertainty over the authored model
family or its human interpretation. A mathematical identity can establish an exact null, but an accidentally constant finite
sample cannot justify inventing a stochastic interval. The interval and decision rules , intersection uncertainty and known-answer
operating checks retain these distinctions, including cases in which a nominal confidence procedure performs poorly.
Supplementary statistical methods specify pointwise intervals, fixed-stratum weighting, sign-flip assumptions, multiplicity and
the representable-translation regression. Complete interval tables retain every reported comparison. A generated variable ledger
binds each changing manuscript value to its producer; model settings and numerical findings are injected into both narrative
and captions. Mathematical identities, scripture identifiers, historical source locators and bibliographic years are fixed references,
not fitted model variables.
3 Results
Each main result pairs the cognitive situation with selected readouts. The supplement retains the complete comparisons, bar
charts, trajectories and operating checks. Schematic nodes and arrows describe the declared computational task, rather than
observed psychological or contemplative processes.
3.1 Positive recall changes optimism without a general predictive benefit
The source adapters expose implementation-sensitive labels, likelihood normalization and aliased snapshots. Corrected positive
recall reduces the stipulated optimism summary. Its predictive consequences vary across the fixed world grid and the chosen
comparison. Absence valuation leaves belief updates and predictive losses unchanged by construction. These findings concern
the implemented operations, not a human well-being outcome.
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Figure 4: Selective replay changes a readout without guaranteeing better prediction. Shared environmental exposure is held
fixed within each paired unit; positive and random replay have matched doses, and frozen models face separate new tests. Panel
a shows exposure, replay and independent assessment. Panels b (optimism) and c (Brier loss) show positive recall minus no
recall (circles, solid) or matched random recall (squares, dashed) at each fixed world probability. Zero denotes no paired contrast.
Both vertical axes multiply native differences by 1000; their scales differ. Whiskers are pointwise analytic 95% intervals over
1024 independent paired units per world; connections guide comparison across the fixed grid. Negative Brier differences favor
positive recall; an optimism change is not a well-being effect. World-specific intervals are exploratory; pooled tests and every
interval method remain supplementary.
Optimism-task change. Estimates and interval bounds are multiplied by 1000.
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Contrast Mean Bootstrap t 95% interval Holm p; MC decision
Positive - None -2.270 [-2.278, -2.262] 0.00098; reject
Random - None -0.017 [-0.031, -0.004] 0.23535; retain
Absence - None 0.000 Unavailable 1.00000; retain
Positive - Random -2.253 [-2.267, -2.239] 0.00098; reject
Brier-loss change. Estimates and interval bounds are multiplied by 1000.
Contrast Mean Bootstrap t 95% interval Holm p; MC decision
Positive - None 0.171 [0.135, 0.207] 0.44312; retain
Random - None 2.177 [2.125, 2.229] 0.00098; reject
Absence - None 0.000 Unavailable 1.00000; retain
Positive - Random -2.005 [-2.066, -1.946] 0.00098; reject
The contrast with random recall is central to interpretation. A change relative to no recall can reflect additional replay as
well as its positive selection; the dose-matched comparison asks what positive selection adds under the same exposure. Neither
comparison makes the optimism readout an independent definition of benefit. The table’s Brier contrast concerns probability
prediction, whereas the optimism contrast concerns the task’s authored readout. Their different signs and world dependence
must therefore be read as different properties of the model, not averaged into a single favorable verdict.
Figure 20 shows why the fixed-grid average is incomplete. Figure 21 describes heterogeneity within each world, and Figure 22
shows how a different weighting changes the aggregate target. Those spreads and sensitivity ranges are not confidence intervals
for a human effect. The complete recall results retain the interval procedures, while the source reconstruction distinguishes
implementation findings from the corrected experiment.
The valuation-only null answers a separate semantic question. Assigned counterfactual value can vary while the paired beliefs
and predictive losses remain exactly unchanged. Conversely, the absence detector can change beliefs when its recorded no-event
outcome is informative. Figure 23 and Figure 24 display these distinct operations. The null validates their separation in this
implementation; it does not show that appreciation and belief are independent in people.
3.2 Effective access permits revision and appropriate retention
Costly activity helps only when it makes a relevant alternative available. In reversal contexts the inquiry policy can select a
predictor excluded by the restricted family; sham and blocked access preserve rigid forecasts while charging activity costs. A
useful working restriction can be retained or reused. The exhaustive count calculation also identifies rare adverse selections that
a finite seeded sample can miss.
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Figure 5: Access, rather than activity alone, permits evidence-responsive revision. The agent values an opportunity to examine
a working family, chooses costly activity, may gain access, and selects a predictor before seeing new assessment outcomes. Panel
a identifies these stages. Panel b compares reversal-process probabilities with frozen mean forecasts; panel c shows each policy’s
held-out log loss minus rigid prediction, with zero denoting equal loss. Sham and blocked access preserve rigid forecasts while
charging activity costs. Loss whiskers are pointwise analytic 95% intervals over 512 independent paired replicate averages, each
averaging 12 windows. Forecast curves are descriptive means. Negative log-loss differences favor the policy, in nats per outcome;
costs are separate. The model can retain a useful restriction, and no stage measures realization.
The stationary context gives retention a substantive role. When the restricted family already supplies an adequate forecast,
greater access need not produce a predictive gain, and the activity charge can remain. In the reversal context, access permits
evidence-responsive use of an alternative and later return to a useful restriction. Figure 16 shows those different consequences;
Figure 17 shows why choosing an activity cannot stand in for gaining effective access. The no-preference comparator further
separates the declared value of examinability from inquiry driven by previous instrumental gain.
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The exhaustive analysis qualifies any interpretation based only on the seeded trajectories. It evaluates the possible calibration
counts under the declared process, including rare counts at which the open family is selected adversely. A seeded stationary
null can therefore coexist with a nonzero exact probability of an unhelpful selection. The exact-decision result and Figure 15
distinguish conditional selection from how often the relevant evidence occurs. The figure repeats each count distribution on linear
and logarithmic axes so rare events remain visible alongside the modal evidence. Its selection probability describes how often
the rule chooses the open family under a specified process, conditional on effective inquiry; it is not a posterior probability that
this family is true. These results establish a property of this finite candidate menu, not that a larger menu or another process
would behave similarly.
Together these findings establish a conditional enabling mechanism. They do not identify the declared opportunity value as
human gratitude, nor make every relaxation beneficial. Complete practice results retain the costs and policy contrasts; the
complete practice interval table retains all interval procedures, including unavailable studentized intervals. Success requires
effective access and appropriate evidence use, with independent prediction and cost kept visible.
3.3 Access advantages do not establish an inquiry-specific gaze benefit
The preserved source code reproduces published before occupancy and contains no after-practice intervention. The new transfer
experiments link actual learned channels to a separate scene task, where a change in positive-location sampling can coexist with
worse prediction. Already-open policies improve reversal prediction relative to an excluded candidate, but the direct comparisons
do not establish an additional predictive advantage specific to inquiry.
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Figure 6: Looking differently and predicting better are separate tests. An agent samples declared scene sites and updates a
finite belief; learned-likelihood transfer and active inquiry are evaluated as distinct experiments. Panel a shows the sites and
sampling loop. Panel b uses the likelihood bridge to compare positive-site policy changes with no recall, in percentage points.
Panel c shows open-inquiry log loss minus already-open utility or uniform sampling, in nats per outcome; negative values favor
inquiry. The panels have different endpoints and scales. Transfer whiskers are pointwise analytic 95% intervals over complete
paired agents. Active-scene circles show analytic bounds; diamonds use the full exploratory 58-contrast joint rectangle over
complete replicate averages. The dashed bridge is an alternative readout projection. Intervals spanning zero do not establish an
inquiry-specific advantage, and registered model sites are not measured eye tracking.
The source and transfer findings answer different questions. Figure 25 concerns the executable before condition; no reconstructed
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after effect is available from that code. Figure 27 instead reports a new experiment whose learned channels and bridge are explicit.
Its positive-location change and predictive-loss change use different units and can point toward different judgments of success.
The alternative bridge provides a sensitivity analysis of that connection rather than another independent replication of the source
claim.
The active-scene comparison then asks whether an access advantage also identifies an information-seeking advantage. Opening
a previously excluded candidate can improve forecasts in a reversal context even when the sampling rule is uniform or guided
by utility alone. Figure 29 shows the consequences separately. The direct inquiry-versus-already-open contrasts are needed
before attributing an additional predictive gain to the information preference. Their bounds do not establish such a gain in the
admitted design; this is a bounded lack of evidence, not a general equivalence theorem for inquiry policies.
The full gaze record retains both bridges and all paired comparisons. Figure 30 keeps the 58-member exploratory family together,
and Figure 31 shows why nominal confidence is not a universal guarantee. Skew-related undercoverage and unavailable rare-event
regions remain reported results. The complete joint table preserves each estimate’s status rather than dropping unfavorable or
uninformative cases from the display.
A practical-equivalence claim would require justified, prospectively specified bounds and an analysis that can exclude effects
outside them ( Lakens 2017 ). No such test is claimed here. The equivalence boundary separates these inconclusive stochastic
comparisons from the model’s proved identities.
3.4 Learning an encoding differs from using it for prediction
The joint experiment separates learning an encoding from using it with scene evidence. Label-equivalent encodings remain
observationally indistinguishable. Restricted zero support prevents recovery of an excluded encoding even when a distinguishing
channel exists. The matched-query sham and boundary-only policy retain their exact conditional identities; adverse nonzero
offsets remain visible.
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Figure 7: Learning an encoding is different from using it for reference prediction. Spatial observations and paired randomized-
action responses update a joint belief over scene and encoding under one 24-decision budget. Panel a separates evidence routes
and targets. Panels b and c show policy-minus-visual-only differences for the preselected H2 case: anchored excess log loss and
encoding Brier loss, respectively. Zero denotes equal loss; the endpoints have separate scales. Bounds come from the complete
84-member exploratory family, with 512 independent paired replicates per fixed scene stratum. Circles are stochastic estimates,
squares proved constants and crosses unavailable intervals. Negative differences favor the named policy. Encoding improvement
alone does not establish reference transfer; adverse restricted-policy offsets and exact sham values remain visible.
The diagnostic channel explains why the response record matters. An action and a response can each be marginally uninformative
while their relation identifies the encoding. Erasing the action identity removes that route for the specified updater. In the label-
only regime, by contrast, the encodings have the same observation law, so more sampling cannot distinguish them. Figure 33
makes this difference visible; Figure 34 shows how spatial observations and encoding questions share the budget. Neither a query
count nor low posterior uncertainty alone establishes that the relevant distinction has been learned.
Learning an encoding is also different from using it for the anchored prediction. A boundary-only policy can improve its encoding
judgment while lacking scene evidence needed for the reference target. Conversely, an excluded encoding remains unavailable
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to a restricted prior even when an informative channel exists. Figure 32 retains encoding and anchored losses side by side, and
Figure 35 keeps behavioral descriptions separate from those scores. Direct integrated-versus-uniform anchored comparisons do
not establish an additional predictive advantage in this design.
The 84-member family contains 30 proved constants and retains all remaining stochastic or unavailable estimates. Complete
joint bounds preserve the exact offsets and uncertainty statuses. Figure 36 characterizes precision within the declared design; it
cannot turn observationally equivalent encodings into identifiable ones. The separate native boundary checks establish specified
QRF and Gaussian properties. Figure 37 distinguishes failure of marginal-threshold blanket recovery from recovery using the
known full covariance; neither is evidence of a measured human metacognitive boundary.
4 Discussion
4.1 Gratitude for the possibility of examining one’s own constructions
The stronger proposal is that appreciation can support the practice of examining what seems compulsory in one’s way of
construing experience. Gratitude for an opportunity to inquire need not demand a favorable conclusion. A practice can reveal
that a distinction is contingent while preserving its everyday usefulness; it can also reveal that a particular alternative does not
help. This orientation differs from collecting agreeable evidence. It values the possibility of revising the terms in which evidence
is understood, while continuing to answer to consequences.
The finite extension makes this proposal more demanding than a verbal endorsement. Preference must affect action; action must
actually provide access; accessible comparison must consume evidence; and a selected working representation must face indepen-
dent observations. The sham and no-access nulls show where the chain can break. Their role is not to devalue aspiration, but
to prevent its presence from being counted as an enacted mechanism. The no-preference condition also shows why instrumental
inquiry and appreciation for its possibility need separate identification. Here the latter is declared, not inferred from simulated
behavior or validated as human gratitude.
Useful self/world models can persist after their assumed necessity is questioned ( Sandved-Smith et al. 2026 ). Our model reflects
that point by allowing a restricted working family to be retained or reused when its evidence is better. Returning to useful
distinctions need not reinstate the rule that alternatives are inadmissible: future inquiry remains available. This is the substantive
difference between a representation that is employed and a restriction that cannot be examined. The finite family switch supplies
a constrained analogy; it does not exhaust the source’s physical or contemplative claims.
Practice also has a temporal structure. A moment of insight would not remove changing conditions or the need to examine
future constructions. The repeated reversal design therefore asks about continued revisability rather than a one-way progression
through named attainments. Its costs matter as well. More inquiry can be predictively useful while consuming resources; if an
adequate model already works, the charge can remain without a predictive gain. Our separate cost column makes that possibility
visible instead of declaring every relaxation beneficial.
This positive proposal requires more than being thankful that a harm did not occur. The object of appreciation can be an
enabling relationship, a discrepancy, an opportunity to question an assumed boundary, or the continued possibility of revision.
Appreciation following an insight is another possibility. Neither causal direction is measured by this model. Lutz and colleagues’
framework permits meta-awareness without dereification ( Lutz et al. 2015 ); our accessible candidate menu therefore supplies a
testable enabling condition rather than a sufficient realization criterion.
4.2 What gaze, confidence and first-person reports can establish
Natural gaze depends on tasks, learning and changing information requirements ( Tatler et al. 2011 ). A fixed painting partition
therefore needs an explicit task description, not an implied natural-vision interpretation. Võ and colleagues additionally distin-
guish recorded fixation locations from retrospective knowledge of those locations ( Võ et al. 2016 ). Their task-specific findings
motivate measuring monitoring independently rather than inferring it from a scanpath.
The joint model implements selection of evidence about a supplied encoding. It does not learn the representation language or a
metacognitive architecture. Nelson and Narens’ monitoring/control distinction and Fleming and Lau’s separation of confidence
bias, sensitivity and efficiency remain central to empirical translation ( Nelson and Narens 1990 ; Fleming and Lau 2014 ). A
person could look differently without understanding the boundary differently, or report insight without improved independent
monitoring.
These distinctions require different observations in a human task. Mean confidence concerns a response tendency; sensitivity
concerns how well confidence distinguishes correct from incorrect judgments; efficiency concerns metacognitive performance
relative to the available first-order performance ( Fleming and Lau 2014 ). A change in one cannot be substituted for evidence of
another. Likewise, looking longer at an informative region does not by itself establish awareness of why that region matters. The
model’s encoding Brier score evaluates an explicitly defined first-order probability judgment, not a measurement of metacognitive
efficiency or dereification.
An empirical bridge would therefore retain the actual action-response pairs, independent scene predictions and confidence reports,
rather than interpreting a changed scanpath retrospectively as insight. It would also test whether any apparent advantage depends
on the stipulated reference anchor and whether an observer can use information in an adaptive query schedule that the software
sham ignores. The extended gaze interpretation explains the conceptual limits, and the coupled human-task proposal specifies
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the distinct measurements and comparator requirements. The useful contribution is a task in which evidence routes can be
separated and challenged; the task does not settle the meaning of a lived realization.
First-person descriptions would supply another evidential stream. In a visual-task study, trained participants’ reports organized
trial groups for behavioral and EEG analysis ( Lutz et al. 2002 ). Such reports could constrain our empirical interpretation
alongside predictions and confidence, without making either a report or a score a sufficient criterion of realization.
4.3 From finite mechanisms to an identifiable human research program
The models assume finite authored candidate menus, known likelihoods, explicit access gates and declared costs. The
scene/encoding target also requires a stipulated anchor. Useful prediction, informative questions, low entropy and flexible
switching are different achievements; none is a sufficient measure of contemplative realization. Larger simulated samples
characterize Monte Carlo precision within these assumptions and cannot resolve observation-equivalent models.
The gratitude literature makes comparator choice consequential beyond the simulation. The inspected preregistered meta-analysis
reports small aggregate gains, but its comparison with positively valenced activities does not establish a significant advantage or
equivalence (Choi et al. 2025 ). Its country-based cultural proxy and English-language search also constrain generalization. Our
matched replay and exposure controls address a narrower computational question: what a selection rule does under a declared
process. They do not isolate human gratitude from positive reflection, engagement, social attribution or expectancy. The
comparator synthesis retains those study-specific qualifications alongside favorable findings and disputed optimism measurements.
A human study would separately manipulate appreciation, access to alternatives, instrumental information and delay or effort. It
would record scene predictions, encoding judgments, confidence, inquiry choices and eye movements, with an independent transfer
target. Practice instructions and the interpretation of process measures must be specified rather than treating all contemplative
activities as one intervention ( Van Dam et al. 2018 ). Patience, anticipated good news, expectancy and compliance remain rival
mechanisms. The preserved empirical-design supplement gives the interaction estimand, identification problem, manipulation
checks, alternative explanations and model-recovery requirements.
Practice specificity matters for the proposed causal chain. Dahl and colleagues distinguish attentional, constructive and decon-
structive practice families and their proposed mechanisms ( Dahl et al. 2015 ). An instruction to appreciate an enabling condition
therefore cannot be assumed to recruit the same processes as attentional training or inquiry into an assumed self/world bound-
ary. The empirical proposal would need to specify what participants actually do, how they recognize an alternative, and what
counts as appropriate retention as well as revision. The inquiry-rival analysis separates valuing examinability from seeking useful
information, anticipating good news or tolerating delay.
Fitting the software policy to behavior would introduce another identification problem. Different combinations of declared
value, cost and action precision can produce the same initial choices; exact replay of those choices does not identify their
psychological cause. Parameter recovery and model recovery address different questions, and both must be evaluated before
assigning substantive meanings to fitted parameters ( Wilson and Collins 2019 ). Equation (5) shows the confounding in this
model; the prospective inquiry study specifies independent manipulations and recovery checks that would be needed to move
beyond it. A menu member winning a comparison still need not explain the behavior adequately.
Relative model ranking also needs an adequacy check: simulations should reproduce the behavioral pattern they purport to
explain ( Palminteri et al. 2017 ). Our exact oracles and adverse controls create opportunities to reject specified mechanisms,
but a successful finite demonstration cannot substitute for that human test. The validation account separates reconstruction,
numerical verification, model criticism and construct interpretation.
4.3.1 Generalization beyond the declared experiment
Generalization would require a declared target beyond the tested sample. Yarkoni’s argument concerns variation over stimuli,
tasks and settings as well as participants ( Yarkoni 2022). For this proposal, instructions, social attribution and the contexts
in which retention or revision is useful belong in that target. More paired simulations improve conditional precision without
sampling those human differences.
The detailed interpretive argument and all source-access qualifications remain in the discussion supplement and scope limits .
This is a targeted scholarly synthesis, not a systematic review. The software supports finite-model claims; human gratitude,
lived realization, clinical benefit and philosophical equivalence require distinct evidence.
4.4 Conclusion: appreciate, examine and remain able to revise
“Thanks for Nothing” names more than relief that no harm occurred. It proposes appreciation for the conditions that make one’s
own constructions examinable, and an orientation toward practicing realization of emptiness while retaining useful representations.
The executable counterpart distinguishes the value of inquiry, its cost, chosen activity, effective access, evidence-based revision
and independent consequences. Its semantic nulls prevent aspiration from being mistaken for enactment, while its retention
controls prevent indiscriminate relaxation from being counted as progress.
The gratitude-recall experiments remain a complementary constraint: positive selection did not yield a general optimism or
predictive-performance benefit, and statistical conclusions depended on world composition and distributional assumptions. To-
gether, the constructions support a clear research program: appreciate without inventing favorable evidence, inquire without
assuming the preferred answer, retain distinctions where useful, and remain able to revise them. The numerical results establish
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finite conditional mechanisms. Whether this orientation supports human gratitude or realization requires the separate conceptual,
phenomenological and empirical work the manuscript specifies.
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Supplementary information
The technical record preserves the original formal methods, complete numerical results, source diagnostics and extended inter-
pretation. Stable equation and section identifiers link these details to the IMRAD argument. Changing settings and estimates
are hydrated from their producers.
S1. Conceptual distinctions and the scholarship behind them
Appreciating the conditions of inquiry
Our central proposal concerns the object and direction of appreciation. One can appreciate the conditions that permit examina-
tion: a teacher, a conversation, a stable interval, a difficult discrepancy, or the availability of an alternative description. Those
conditions need not already feel pleasant or confirm a favorable self-image. Gratitude, on this proposal, can support the willing-
ness to look more carefully at how experience is being organized. Preferring opportunities for such examination is distinct from
preferring that a flattering hypothesis turn out true. Practice makes that preference consequential through repeated allocation
of time and attention, with costs and the possibility of finding that a familiar distinction remains useful.
Sandved-Smith and colleagues’ There is no self-evidence supplies the conceptual bridge ( Sandved-Smith et al. 2026 ). Their
account treats the assumed necessity of a self/world separation as a structural commitment that can become available to inquiry.
Their discussion of opacification concerns bringing model-making into view; dependent-origination inquiry concerns the conditions
on which a designation depends ( Sandved-Smith et al. 2026, secs. 4.1–4.3 , pp. 12–15). The proposed shift is not the destruction
of every representation. Useful models can continue to operate while the claim that a particular division must organize every
possible situation is relinquished. We take this as a reason to model access to alternatives and ongoing conditional use, rather
than to reward indiscriminate uncertainty.
This gives the proposed relationship a direction: appreciation of enabling conditions can motivate practice; practice can expose a
previously unexamined restriction; evidence can then support retention, revision or renewed inquiry. A gratifying thought alone
does not perform these operations. Likewise, simply asserting that distinctions are empty does not show that a restriction has
become examinable. Gratitude may also arise after an inquiry, as appreciation of newly visible possibilities, but that feedback
is a future empirical hypothesis. The implemented feedback below concerns observed model-evidence gain only, not a simulated
emotional response.
The practical target remains realization of emptiness, not appreciation of a metaphysical thing called nothing. The finite
counterpart operationalizes one proposed enabling mechanism—revisability of a structural commitment—while leaving the lived
realization and the philosophical adequacy of the computational interpretation open. This distinction permits a substantive
positive proposal without treating a software score as its completion.
Dahl, Lutz and Davidson propose distinct attentional, constructive and deconstructive practice families ( Dahl et al. 2015 ). Their
framework separates meta-awareness, reappraisal and self-inquiry while retaining ethical, interpersonal and cultural context.
In our synthesis, appreciation can prepare or motivate examination without itself constituting deconstructive insight. This
distinction prevents a single practice score from standing in for every proposed link.
Social gratitude and broader appreciation
Relational evidence supplies a different target from a favorable numerical value. Algoe, Haidt and Gable’s naturalistic gift-
giving study associated perceived benefactor responsiveness, gratitude and later relationship ratings ( Algoe et al. 2008 ). Only
its abstract was inspected here. That social association does not identify causal mediation or a benefactor-free appreciation
mechanism; the existing relational theory and intervention comparisons therefore retain separate roles.
Gratitude is not a unitary computational primitive. An influential moral account emphasizes recognizing another person’s bene-
ficial action, motivating prosocial behavior and reinforcing generosity ( McCullough et al. 2001 ). A relational theory emphasizes
finding and maintaining responsive partners ( Algoe 2012 ). Broader accounts include habitual appreciation of positive aspects
of life ( Wood et al. 2010 ). A model of favorable and unfavorable states can represent a stipulated appreciation operation while
omitting benefactor recognition, reciprocity, obligation and interpersonal interpretation. The absence of a benefactor is therefore
a substantive construct boundary, not a naming detail.
This boundary also affects measurement. He and colleagues compared writing about a significant other, writing about health and
no writing; highly correlated gratitude and appreciation word ratings did not establish that the constructs were interchangeable
(He et al. 2022 ). Their selected indebtedness comparison must be read alongside a nonsignificant omnibus test and uncontrolled
writing time and length. Yu and colleagues distinguish recipient benefit from benefactor cost in social gratitude ( Yu et al. 2018 ).
These findings motivate separate measures of appreciation, gratitude, relief and obligation. They do not license calling the
present counterfactual value a validated gratitude score.
Bartlett and DeSteno’s interpersonal experiments found greater costly helping following gratitude induction than neutral or
amusement conditions; source attribution constrained its incidental extension to strangers ( Bartlett and DeSteno 2006 ). These
results motivate separating action and social interpretation from pleasant affect. They do not test contemplation or establish
that benefactor-free appreciation motivates inquiry.
Gratitude may also affect the costs a person will tolerate. In DeSteno and colleagues’ randomized autobiographical-recall
study, a planned gratitude-versus-pooled-comparators contrast favored greater patience in incentivized intertemporal choice
(DeSteno et al. 2014 ). The inspected accepted manuscript concerns 75 young adults, an immediate task and that planned
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contrast; it does not establish enduring adherence or every separate pairwise effect. For the present proposal, patience is both
a plausible bridge to sustained practice and a rival explanation: greater willingness to wait does not identify a greater value of
examinability.
What intervention comparisons identify
Comparison activity determines the explanation a study can address. Cunha and colleagues’ randomized writing trial had
substantial attrition, and its neutral-event activity often included positive material ( Cunha et al. 2019 ). A post-test positive-
affect advantage therefore does not imply superiority on every outcome or at follow-up. A guided internet intervention against a
wait list addresses a different comparison, which does not isolate gratitude from guidance and expectancy ( Heckendorf et al. 2019 ).
Favorable diary associations add another design rather than settling the mechanism ( Hartanto et al. 2023 ).
Meta-analyses and reviews emphasize comparator-dependent conclusions, generally small effects and the importance of positive
or psychologically active controls ( Davis et al. 2016 ; Cregg and Cheavens 2021 ; Kerry et al. 2023 ). The inspected Kerry review
is itself bounded by restrictive inclusion and a single-researcher search. A newer preregistered synthesis reports small aggregate
gains and between-country variability, providing a counterweight to a uniformly skeptical account without validating a specific
computational mechanism ( Choi et al. 2025 ). Its full text reports no significant advantage over positively valenced activities;
that imprecise comparison does not establish equivalence. Country is a proxy for culture, and the English-language search limits
generalization. Matching replay dose and exogenous exposure in our model isolates a selection rule under a declared process. It
does not isolate human gratitude from expectancy, task engagement, social meaning or demand characteristics.
Optimism is a further, distinct target. Daily-life findings identify overlapping but distinguishable associations of gratitude and
optimism (Newman et al. 2021 ). Belief-updating tasks motivate the source readout, but their specificity and measurement remain
contested (Garrett et al. 2014 ; Hobbs et al. 2022 ). Shah and colleagues argue that apparent updating asymmetries can arise from
statistical task properties; Garrett and colleagues dispute aspects of that analysis ( Shah et al. 2016 ; Garrett and Sharot 2017 ).
This disagreement motivates estimator controls and independent predictive scores rather than treating a favorable task score as
construct validation.
Absence, mental subtraction and relief
An observed absence can be perceptually structured: the inspected silence experiments concern contrastive auditory silences
within structured sound ( Goh et al. 2023 ). Their discussion leaves absolute silence as a further question and qualifies analogies
to other modalities. These results do not test a failed recorder. An imagined alternative is different again. Koo and colleagues
asked participants to imagine that an existing positive event had not occurred ( Koo et al. 2008 ). Their affect and relationship
outcomes should not be summarized as uniformly gratitude-specific: the first two studies did not show significant differences on
the direct event-gratitude item. Mental subtraction of an actual benefit is not the same manipulation as detecting an uneventful
interval, establishing that a harm was prevented, or assigning an externally chosen hazard reference.
Epstude and Roese’s functional account further separates content-specific pathways, which can supply information for action,
from content-neutral pathways through affect, motivation and processing style ( Epstude and Roese 2008 ). The emotional con-
sequence depends on how the alternative is used: comparison with a worse possibility can produce favorable contrast, whereas
vividly imagining it can produce assimilation. This is a reason to measure the process and its outcome separately. Our counter-
factual value condition implements a reference calculation with a designed belief null; the review does not establish that human
counterfactual thinking preserves beliefs or that its affective consequence is necessarily gratitude.
Counterfactual gambling feedback ( Coricelli et al. 2005 ) and conditioned pain relief ( Seymour et al. 2005 ) concern still other
contrasts. The common reference dependence makes them relevant comparisons, but does not identify relief, gratitude and
appreciation as one latent mechanism. Our valuation-only condition is deliberately narrower: it asks whether the software can
assign a counterfactual value while preserving its evidence update. Human reflection could change recall, attention or hazard
beliefs as well; the designed null is an experimental contrast to test, not a prediction imported from those studies.
Emptiness and the continued use of representations
The main-text introduction identifies the Buddhist collections and named discourses and supplies short, edition-specific quota-
tions. Those textual readings constrain interpretations that equate emptiness with total non-existence or a blank numerical state.
The distinction between what is absent and what remains, and the discourse’s treatment of refined concentration as conditioned,
matter to the interpretation ( Thanissaro Bhikkhu 1997b , 1997a). This is philosophical source interpretation, not a claim that
the text describes Bayesian computation.
Garfield’s translation and commentary and his work on cross-cultural interpretation supply further philosophical context
(Garfield 1995 , 2001). Our access to those books is limited to verified publisher identity and synopsis, not verse-by-verse
analysis. The inspected emptiness preprint develops a specific physics and active-inference account; it does not settle
every philosophical interpretation ( Sandved-Smith et al. 2026 ). Its emphasis on continuing revision after a structural
change ( Sandved-Smith et al. 2026, secs. 5.1–5.3 ) motivates repeated opportunities to examine a working model. Its broader
policy-scope discussion ( Sandved-Smith et al. 2026, secs. 6.1–6.2 ) motivates a normative question about whose consequences
matter. We keep that normative question distinct from prediction: a wider action-influence scope is not, by itself, a measure of
compassion.
We use non-reification as a modeling discipline: a chosen representation can function without being treated as the only admissible
description. Consistent label permutation checks a prerequisite representational invariant, while the new practice experiment
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tests the consequential availability of a genuinely different predictive candidate. Neither renaming states nor increasing entropy
is counted as realization. In particular, a distinction that predicts well should be retainable. Valuing examinability is therefore
compatible with precise, useful everyday inference.
Garfield and Thakchöe’s chapter gives the object of negation a precise role ( Garfield and Thakchöe 2011, 73–87 ). Negating intrin-
sic nature and negating conventional phenomena have different implications; emptiness itself must not simply replace intrinsic
nature as another intrinsic essence. Their comparison of Tsongkhapa and Gorampa also shows why preserving conventional
efficacy does not settle every Madhyamaka interpretation. The chapter presents that disagreement without adjudicating it. We
use the limited analogy of withholding intrinsic status from a useful construction, rather than claiming that every tradition
equates emptiness with representational flexibility. The source catalog distinguishes the cited print edition from its earlier online
publication and preserves both publication dates.
This sharpens the positive practice proposal. Gratitude can concern the contingent conditions that enable investigation and the
continuing possibility of using distinctions without making them compulsory. Practicing inquiry includes attending to how a
distinction is established, acting to examine its consequences, and remaining able to retain or revise its application. Our software
executes a finite portion of this proposal. Its assessment concerns prediction, access and cost; the philosophical and experiential
claims require arguments and observations beyond that execution.
F rom conceptual distinctions to model tests
Distinction Implemented comparison Evidence still needed
Replay content versus activity dose Positive versus matched random recall Human controls matching expectancy
and engagement
Detected absence versus missing record Absence likelihood versus missingness
sentinel
Detection reliability and
recording-failure manipulations
Counterfactual value versus new
evidence
Separate valuation with a designed
belief null
Joint valuation, belief, relief and
gratitude measures
Model policy versus gaze Declared learned-channel transfer and
paired scene-risk controls
Empirical transfer and independent gaze
prediction
Scene content versus its encoding Coupled scene/contingency queries,
erasure and label-equivalence controls
Measured gaze, action-pair access and
experimentally instantiated reference
transfer
Confidence versus metacognitive
sensitivity
Posterior uncertainty and proper
prediction scores kept separate
First-order judgments, corresponding
confidence and sensitivity/efficiency
estimands
Motivation versus access Preference and costly activity versus an
effective access gate
Separate social attribution, engagement
and metacognitive process measures
Access versus enacted revision A vailable repertoire versus
evidence-selected working family
Noticing and using alternatives, with
curiosity and compliance controls
Useful representation versus compulsory
restriction
Exact prior comparison and held-out
prediction after reversals
Behavioral model comparison and
alternative explanations of flexibility
Representation versus realization Label invariance as a prerequisite, not
the endpoint
Philosophical argument and
phenomenological and empirical work
This mapping is our synthesis of the inspected literature, not a combined claim established by any cited study. The source catalog
records whether each item was inspected in targeted full-text sections, at abstract level or through bibliographic metadata. The
review is targeted, not a systematic search.
V alidation, model criticism and generalization
Different checks warrant different conclusions. Reconstructing a source tests fidelity to an artifact; independent mathematical
controls test a specified implementation; behavioral validation tests a model’s explanatory claims. Cronbach and Meehl’s
construct-validity argument adds a further obligation: an interpretation must participate in testable relations, and adverse
evidence may require reconsidering the measure, theory or design ( Cronbach and Meehl 1955 ). Our terms appreciation and
examinability identify proposed operations, not validated human constructs.
Relative fit cannot settle adequacy. Palminteri and colleagues recommend simulation-based tests of the behavioral effect a
model is meant to explain, alongside discrimination and recovery ( Palminteri et al. 2017 ). Gelman and Shalizi distinguish
posterior calculation from checking model implications and using discrepancies to revise a family ( Gelman and Shalizi 2013 ).
Our candidate-menu controls implement narrower checks. They neither generate a new representation language nor establish
that the selected family describes a person. Likewise, mathematical revisability supplies no independent philosophical proof of
non-reification.
The target of a generalization must also match what the design addresses. Yarkoni includes tasks, stimuli and settings among
relevant sources of variation ( Yarkoni 2022). Our fixed worlds and authored scene partition therefore define a conditional
computational target. Their weighted average is not an estimate over human cultural or contemplative settings. The textual
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comparison serves a different purpose again: its named editions discipline interpretation, without turning selected passages into
sampled evidence about populations. The empirical program must establish its own target and measurement plan.
T extual witnesses, useful absence and gratitude
The ancient comparisons sharpen the object of appreciation and the purpose of inquiry. They do not provide inter-
changeable definitions of nothing. In the Kataññu discourses, gratitude concerns received care and its ethical repayment
(Thanissaro Bhikkhu 2002 ). Extending appreciation to a detector, an opportunity to examine assumptions or an impersonal
enabling condition changes that interpersonal structure. A future human study must therefore establish which construct is
elicited, rather than validating it by a scriptural label.
The Daodejing, in James Legge’s inspected digital edition titled The Tao Teh King , describes the use of a wheel, vessel and
room through the relation between their constructed form and unfilled space ( Laozi 2008 , ch. 11). This offers a comparison
for appreciating enabling conditions. The useful hollow of a vessel is neither an unavailable record nor, by itself, evidence of
freedom from reification. Chan distinguishes divergent interpretations of wu and relates wuwei to ethical and political questions;
he explicitly resists reducing it to total inactivity ( Chan 2025, secs. 6–7 ). We therefore retain the transliterated terms rather
than treating nonbeing, nonaction and Buddhist emptiness as synonyms.
Epictetus makes the capacities for perception and understanding objects of gratitude within an argument for divine providence
(Epictetus 1887, I.6 , pp. 19–21). That comparison gives appreciation for cognitive capacities a concrete historical counterpart,
while its providential commitment differs from our account of contingent inquiry conditions. The declared opportunity-value
parameter neither measures Stoic gratitude nor imports that metaphysics.
Textual comparison Question sharpened here Computational use Inference not licensed
Kataññu discourses
(Thanissaro Bhikkhu 2002 )
Who or what is appreciated,
and why?
Separate benefaction from
declared opportunity value
Impersonal appreciation is
canonically identical to
interpersonal gratitude
Raft simile ( Thanissaro
Bhikkhu 2004 )
When is reliance useful, and
when is relinquishment
appropriate?
Retain useful working
representations while keeping
alternatives examinable
A family switch is liberation
Suñña discourse ( Thanissaro
Bhikkhu 1997c )
Empty of what? Specify the object of a
non-reification analogy
No event, no data and
non-self have the same
meaning
Daodejing (Laozi 2008 ; Chan
2025)
What can an unfilled or
unasserted condition enable?
Keep functional absence and
its value distinct
Wu, wuwei and Buddhist
emptiness are equivalent
Epictetus ( Epictetus 1887 ) Can the capacities for inquiry
themselves be appreciated?
Make the proposed object of
appreciation explicit
A numerical inquiry
preference establishes
gratitude or providence
Heart Sutra (Thich Nhat
Hanh 2014 )
How does a specified
rendering relate emptiness
and embodied phenomena?
Question a reified
interpretation of an
empty-state label
All Buddhist textual
traditions supply the same
realization criterion
Bhagavadgītā (Swami
Mukundananda, n.d.-a )
What differs between acting
and claiming entitlement to
its fruits?
Separate inquiry value from a
demand for favorable
evidence
Nonattachment means
inaction or an uninformative
posterior
Thanksgiving and blessing
(New Revised Standard
Version Updated Edition 2021;
Kulp, n.d.-a ; Berakhot, n.d. ;
Khattab, n.d.-a )
To whom is appreciation
directed, and what response
is required?
Distinguish addressee,
circumstance and evaluative
response
Harm becomes favorable
evidence, or a religious
promise becomes an efficacy
estimate
Mystical Theology
(Pseudo-Dionysius the
Areopagite, n.d. )
How can praise coexist with
limits on predication?
Distinguish appreciation from
exhaustive conceptual
description
Apophatic theology and
Madhyamaka negate the
same object
MMK (Nagarjuna 2020 ) How do dependent
designation and conventional
discourse bear on emptiness?
Keep a useful distinction’s
status open to examination
Conventional truth is
held-out accuracy
Gītā offerings ( Swami
Mukundananda, n.d.-b )
What response is owed for
received gifts?
Distinguish valuing a benefit
from undertaking a practice
The model implements yajña
or divine reciprocity
Avot (Kulp, n.d.-b ) Must appreciation await an
additional possession?
Separate existing-lot
contentment from a new
reward
Contentment automatically
measures gratitude or
justifies deprivation
Japji (Guru Nanak, n.d. ) What changes when one
understands an order one
does not author?
Ask about responsiveness
without assuming mastery
Hukam and haumai are a
likelihood law and a
self-model
Analects (Confucius 2002 ,
2015)
Can a response consist in
withholding an unwanted
imposition?
Retain a relevant ethical
comparator without inventing
gratitude
Shu is repayment, emptiness
or gratitude practice
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Textual comparison Question sharpened here Computational use Inference not licensed
Qur’an on gratitude’s
beneficiary ( Khattab, n.d.-b )
Who benefits, and does the
addressee need repayment?
Distinguish beneficiary,
addressee and obligation
Divine self-sufficiency is
absence or an empirical
utility function
These are deliberately asymmetric comparisons. Early Buddhist translated discourses, later philosophical accounts of emptiness,
Daoist interpretive traditions and Stoic providential reasoning have different questions and aims. The proposed model borrows
no authority for an empirical effect from their age. Its contribution is to expose a limited sequence of choices and consequences
that a subsequent empirical design can challenge.
S2. Declared models, executable interfaces and independent controls
Parsed graphical structure and execution roles
Figure 8 is generated from the actual pinned GNN parser’s variables and connections, rather than a separately authored edge
list. Every cataloged model is also rendered by GNN’s native network renderer. Admission checks native graph statistics against
parsed topology and compares retained pixels with a fresh isolated native render, in addition to binding image digests and
the numerical record’s source identity. The inventory in Figure 9 focuses on complete runtime families, with dimensions and
instance counts from the admitted arrays and execution catalog. The opening model card separately lists authoring inputs and
distinguishes native attention execution, finite numerical consumers and the neutral analysis-protocol carrier. A declared backend
identifies a supported representation; it does not by itself prove that a particular numerical backend executed an experiment.
These graphs express declaration dependencies. The state–transition cycle is not an instantaneous causal DAG, and the shared
syntax does not identify a psychological mechanism. Passive preferences remain inactive where the finite consumer does not
select actions. The analysis carrier’s neutral tensors carry settings rather than a new model of a person. The software checks
reject stale model identities, altered topology and missing native renders before accepting the publication products.
The opening Bayesian model card unrolls the categorical tensor definition across time, conditional on selected actions; it does not
reinterpret the declaration cycle as an instantaneous causal network. Its inventory distinguishes the same numerical consumers
shown here. The accompanying complete model cards preserve all admitted arrays and scientific settings, original declaration
annotations, native graph assets, dependency revisions and exact consumer digests. Finite task-specific likelihoods and policies
remain defined by their own declared settings and methods rather than inferred from the common tensor syntax.
The executable model set also includes complete standalone GNN instances for exogenous worlds and observation schedules, news
readouts, the fixed attention process, transfer embedding and alternative prior supports. Scene and joint-inquiry declarations
expand all query-conditioned channels into a controlled categorical model whose state combines the known query with the
latent candidate basis. Its transition sets the next query while retaining the candidate; numerical consumers recover conditional
likelihoods from the admitted GNN array. Diagnostic and label-only laws are separate complete models. Each instance is
preserved and read back through real GNN admission before use, with originating declaration versions, consumer identities and
evidence digests retained. Fitted agent channels remain learned data under the declared family. Historical notebook behavior
and independent mathematical oracles retain their separate evidential roles.
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Figure 8: Graph structure comes from the executed GNN declarations. The graph exposes the admitted StateSpaceBlock
variables and Connections edges. Only declarations with identical parsed nodes and edges share a panel. Complete executable
instances expose known-query and latent-basis variables as well as their joint state. Arrows retain the declared direction; native
per-model GNN renders and topology statistics accompany the publication view. This is a declaration dependency graph, not
an estimated causal DAG or an uncertainty interval. The state–transition cycle is not an instantaneous causal claim. A common
graph syntax does not imply common psychological meaning, action selection or numerical execution. The tensor and consumer
inventory distinguishes those roles.
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Figure 9: Complete runtime GNN families expose the full declared state space. Each row binds a complete executable family
to admitted dimensions and numerical evidence. Instances share a row only when family and dimensions agree; their parameter
values can differ. The front-matter model card separately lists the authoring inputs, including native attention models and the
analysis carrier. A is observation by state; B is next state by previous state by action; C contains observation preferences; D is
the state prior. R denotes restricted prior support. Dimensions and instance counts are injected from admitted tensors and the
execution catalog. Shapes describe finite model structure, not sample size or empirical uncertainty. These local finite consumers
use GNN-admitted arrays; native GNN/pymdp execution is separately recorded for attention. The generic GNN backend label
does not establish that a native policy executor ran every experiment. Passive preferences and neutral protocol tensors do not
acquire a scientific role from appearing in the graph.
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Figure 10: From each meaning of nothing to its implemented operation. The rows connect the shared vocabulary to distinct
inputs, model operations and assessment targets. A: Observed absence and B: Missing observation show posterior probabilities
and KL information in bits. C: Counterfactual value places the fixture’s reference value in cost units beside the corrected
study’s maximum paired belief difference. D: Non-reification links costly access to independent prediction. These are exact
fixture readouts or declared settings, with no sampling intervals; values in different units are not a common effect size. The first
rows test numerical semantics. The non-reification row is a finite enabling counterpart to Realizing Emptiness, rather than a
realization score.
Experimental questions and independent assessment
The crosswalk below is generated from the same typed task registry as the main overview. It separates what changes, what is
assessed and which control constrains the interpretation.
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Experimental question
Manipulation / matched
input Assessment Control / limit
Recall: does selected replay
improve prediction?
Positive vs random replay;
same exposure and matched
replay dose.
1024 paired units/world;
frozen Brier and optimism
tests.
Value-only control:
unchanged beliefs and
predictive losses.
Absence: no event, no record,
or a different value?
Functioning detector vs
missing record; actual vs
reference cost.
Posterior change in bits;
separate counterfactual cost
value.
No record adds no evidence
under the declared rule.
Practice: does chosen activity
provide usable access?
Value and cost affect activity;
24 calibration observations.
512 new outcomes/window;
512 paired units/context.
Sham or blocked access:
activity can cost without
revising.
Transfer: what follows from a
learned likelihood?
Freeze learned channels;
compare likelihood and
readout bridges.
5120 complete paired agents;
attention and scene loss
separately.
A favorable attention shift
need not improve prediction.
Scene inquiry: access or the
sampling policy?
Restricted vs open; utility vs
inquiry vs uniform; 48
decisions.
512 paired units/context;
scene loss and movement
cost.
Already-open comparators
test an inquiry-specific
increment.
Boundary inquiry: can the
inferred frame be used?
Spatial vs action-response
queries; one 24-decision
budget.
512 paired units/cell;
encoding and reference losses.
Label-only, excluded support
and matched-query erasure
controls.
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Figure 11: Concrete settings behind the experimental comparisons. The panels introduce paired recall, a detector with an
absent or unavailable record, costly access to predictive alternatives, and discrete scene sampling. Training and replay durations,
assessment sizes, costs, locations and decision budgets are generated from the executed records. In the scene, circles, triangles
and squares identify positive, negative and neutral registered sites; R and O denote restricted and open candidate families. The
timelines and icons describe the protocol and carry no inferential intervals. The scene is a schematic registration; its pixels do
not generate observations. Counterfactual value does not update beliefs, and activity does not guarantee access.
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Figure 12: Two evidence routes answer different questions about the same scene. Scene content Z and encoding H jointly
determine appearance W; an encoding question returns a randomized action and its conditional response. The middle probe uses
reliability 0.8. Spatial samples and 3 question types share 24 decisions. Separate scores assess the encoding and prediction under
the declared H=0 reference intervention. All boxes describe an admitted protocol, not an estimated effect; arrows denote data
dependencies. Neither evidence route alone identifies the full reference target in the diagnostic setting. The pinned Realizing
Emptiness mathematical fixtures are separate checks, not extra observations or participants.
GNN declarations and executable upstream interfaces
Packaged Generalized Notation Notation declarations supply the categorical tensors and experimental parameters. The project
imports the pinned GNN implementation and the Realizing Emptiness model-admission interface rather than maintaining a
parallel parser. Admission checks finite entries, nonnegative probabilities, normalized likelihood and transition columns, and the
expected dimensions. Each result retains the hash of its model declaration. The admitted design serialized with the results records
the seed, phase lengths, observations per day, replay limit and precision, learning and forgetting rates, concentration, assessment
sizes, and resampling budgets; these values are the numerical specification for replay. Realizing Emptiness also supplies finite KL
and information-ordering comparators and a binomial interval routine. These imports are software dependencies with bounded
mathematical roles; their use does not transfer empirical or philosophical validation to this project.
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## Page 38

The learning model has 2 hidden states, labeled going well or going poorly, and a 3-category observation alphabet, labeled positive,
neutral, and negative. Labels identify an operational coding scheme. They do not independently establish an event’s value to
a person. Environmental states are sampled with a fixed stratum-specific probability of going well, followed by observations
from the declared environmental likelihood. This produces a stationary artificial world within a stratum. The agent’s transition
model is separately declared and need not equal the environment’s state frequency. Environmental luckiness is therefore a design
parameter, not a diagnosis or a personality measure. The practice extension uses a different, valence-neutral binary channel; its
predictions are never labeled happiness or safety.
The imported Realizing Emptiness 3.0.0 source is commit pinned ( Friedman 2026). We use its BoundaryScreen, QRFDeployment
and SeparationPrior.admissible interfaces to validate a common screen and admit a restricted repertoire; FreeEnergyTerms
computes actual KL complexity and expected log likelihood; BMRComparison supplies the difference algebra. The package also
executes practice_protocol_map() and build_ongoing_revision_audit() and retains their receipt and executing-module
hashes. The upstream practice mapping supplies a vocabulary, not an applied intervention engine: its GNN deltas remain
metadata. The upstream revision diagnostic selects and scores the same windows. Our enacted, costly policy and independent
assessment are new mechanisms in this project, not improvements silently attributed upstream.
Notation and distinct modeling roles
The recall, absence and practice models share categorical machinery but have different scientific roles. The following notation
keeps state inference, family comparison and action choice distinct.
Symbol Meaning and units
𝑜, 𝑠 Observed category and hidden state in the recall/absence
models
𝑎𝑜𝑠, 𝐴𝑜𝑠 Likelihood pseudocount and normalized observation
probability
𝑝𝑡, 𝑞𝑡, 𝛽 Prior, posterior and generalized-Bayes observation precision
𝜌𝑓 , 𝜂 Per-update forgetting multiplier and learning increment
𝑚 and 𝑗 ∈ {𝑅, 𝑂} Predictive candidate and restricted/open working family
𝑛𝑡𝑜, 𝑍𝑡𝑗, 𝐹𝑡𝑗 Calibration count, sequence evidence and free energy in nats
𝜌𝑒, 𝑐, 𝜆𝑔, 𝛽𝑎 Examinability value, activity cost, gain-to-utility weight and
practice choice precision
𝑔𝑡−1, ̂ 𝑝, 𝐿 Previously observed gain, frozen forecast and assessment log
loss
ℎ, 𝑟, 𝐻, 𝑅 Fixed world stratum, paired replicate and their counts
𝐸, 𝑎, 𝑥𝑎, 𝑟(𝑎) Learned-state embedding, scene location, unit-square
coordinate and its region
𝜂𝐻, 𝜆𝐼, 𝜅 Scene ambiguity weight, information weight and movement
charge
𝛾𝑇 , 𝛾𝐴 Transfer-policy and active-scene choice precisions, respectively
Observation precision 𝛽, choice precision 𝛽𝑎 and upstream structural-prior precision have different roles. No common scalar
called precision is treated as a measure of realization. The forgetting multiplier 𝜌𝑓 is unrelated to examinability value 𝜌𝑒.
An enacted policy for examinable representations
The central practice experiment asks whether valuing the availability of inquiry can sustain a practice that makes a structural
restriction revisable. It implements a finite counterpart of an enabling mechanism for realizing emptiness; it does not encode
realization as a hidden state or an optimization target. The 3 declared deployments share a 3-channel screen. Sector assignments
distinguish deployments using only self and env from the deployment using sensation, action and context. The imported
separation-prior interface admits 2 deployments when enforced and the complete menu when relaxed. These labels are opera-
tional assignments, not measurements of a person’s self/world experience. Distinct predictive likelihoods make the alternative
consequential; mere relabeling remains a negative control.
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## Page 39

Figure 13: A proposed human motivation and an executed software mechanism. The diagram asks which links are needed
for appreciating examinability to support useful inquiry. Solid arrows connect declared value, costly activity, effective access,
evidence-based retention or revision, and prediction on new outcomes. Named software controls and prospective behavioral rivals
identify ways these links can fail. The dashed appreciation-to-preference link is an unmeasured proposal; the diagram contains
no effect estimates or confidence intervals. Future access remains possible after a working-family choice. Activity, an open menu
and a favorable score are each insufficient as a measure of realization.
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## Page 40

Declaration Value / role
Candidate channel-zero probabilities 0.85, 0.55, 0.15
Restricted / open prior (0.5, 0.5, 0) / (0.333333, 0.333333, 0.333333)
Transition / observation preference Identity / neutral
Stationary context Channel-zero probability 0.85 for 12 windows
Reversal context 0.85 for 4 windows; 0.15 for 4 windows; 0.85 for 4 windows
Replicates / observations 512 per context; 24 calibration and 512 held-out per window
Examinability value / cost 0.4 / 0.2 declared utility units
Action precision / previous-gain weight 6 / 1 utility unit per nat
Access probability when available 1; no-access and sham controls block effective access
Resampling 4095 bootstrap draws over replicate averages
These values are declared in emptiness_practice.gnn.md; the generated audit retains the exact admitted design and source
hash. The upstream structural-prior precision of 2 is passed as validation metadata, not converted into a hand-added free-energy
penalty. This extension does not claim a continuous precision-ablation result.
Let 𝑚 index the candidates, 𝐴𝑜𝑚 their declared channel likelihoods, and 𝑛𝑡𝑜 the calibration counts in window 𝑡. For each
candidate prior 𝑝𝑗(𝑚), with 𝑗 ∈ {𝑅, 𝑂}denoting restricted and open, define
ℓ𝑡𝑚 = ∑
𝑜
𝑛𝑡𝑜 ln 𝐴𝑜𝑚, 𝑞 𝑡𝑗(𝑚) = 𝑝𝑗(𝑚)exp ℓ𝑡𝑚
∑𝑚′ 𝑝𝑗(𝑚′)exp ℓ𝑡𝑚′
. (1)
Both posteriors are recomputed on the same calibration observations. The imported distribution-derived free-energy decompo-
sition, evaluated consistently in nats with base=e, is
𝐹𝑡𝑗 = 𝐷 KL[𝑞𝑡𝑗‖𝑝𝑗] − ∑
𝑚
𝑞𝑡𝑗(𝑚)ℓ𝑡𝑚 = − ln ∑
𝑚
𝑝𝑗(𝑚)exp ℓ𝑡𝑚. (2)
Here 𝑍𝑡𝑗 is the prior-weighted likelihood of the ordered calibration sequence. Its logarithm is evaluated with a support-aware
shift and an independent scalar evidence sum. Native KL-minus-accuracy components remain in the receipt, but the strict
decision uses the scalar log evidence ratio; subtracting rounded components can spuriously break an exact tie. Equation (2)
is exact for these finite posteriors, not a fitted psychological law. The comparison retains Δ𝐹𝑡 = 𝐹 𝑡𝑂 − 𝐹𝑡𝑅, its accuracy and
complexity components, and both forecasts. An accessible inquiry selects the open working family only if ln (𝑍𝑡𝑂/𝑍𝑡𝑅) > 0;
otherwise it retains or returns to the restricted working family. A tie retains the restriction. We import BMRComparison for its
difference algebra, while recomputing both posteriors: relaxing a zero-support restriction is not an application of the analytic
posterior-reuse BMR identity. No gain is manufactured by simply deleting a scalar cost.
Valuing an opportunity is represented separately from selecting a model. Before the current window’s comparison is made
available to the policy, chosen inquiry 𝑎𝑡 ∈ {0, 1}has probability
𝑃 (𝑎𝑡 = 1 ∣ 𝑔 𝑡−1) =logistic[𝛽𝑎 (𝜌𝑒 − 𝑐 + 𝜆𝑔𝑔𝑡−1)] . (3)
Here 𝜌𝑒 values examinability, 𝑐 charges activity, and 𝜆𝑔 maps previously observed evidence gain into utility. Initially 𝑔−1 = 0.
After a genuinely accessible inquiry, 𝑔𝑡 = max(0,ln(𝑍𝑡𝑂/𝑍𝑡𝑅)); otherwise the previous observed gain is retained. Equation
(3) receives neither current-window counterfactual gain nor held-out outcomes. This explicit cost addresses a boundary in the
emptiness source, whose model-reduction discussion assumes that metacognitive access has already become available and sets
aside its acquisition costs ( Sandved-Smith et al. 2026, sec. 4.3 , footnote 7, p. 15).
5 conditions distinguish the mechanism. Rigid never chooses inquiry. Inquiry values examinability and can access alternatives.
No preference sets 𝜌𝑒 = 0 while retaining costly stochastic and instrumentally reinforced inquiry; it is not a zero-activity
control. Sham can value and choose activity but exposes no alternative repertoire. No access likewise retains preference and
activity while blocking metacognitive access. A chosen activity always incurs its declared cost, even when access fails. These
semantic interventions specify what would have to differ in an empirical comparison; their activity names do not establish that
human practices are matched.
All conditions receive the same calibration and held-out observation arrays and common action/access random numbers within
a replicate. Separate random streams generate calibration and assessment conditional on the exogenous context schedule. A
working-family choice persists between inquiries; within each window every agent refits its posterior from the declared prior for
that family on the current calibration batch. The reset is an explicit episodic design choice, not cumulative lifetime learning.
The frozen forecast is then
̂ 𝑝𝑡𝑗(𝑜) = ∑
𝑚
𝐴𝑜𝑚𝑞𝑡𝑗(𝑚), 𝐿 𝑡𝑗 = − 1
𝑁𝐻
𝑁𝐻
∑
ℎ=1
ln ̂ 𝑝𝑡𝑗(𝑜𝐻
𝑡ℎ). (4)
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## Page 41

Equation (4) is evaluated on observations that never select the family or update its posterior. Counterfactual comparisons are
retained in the research receipt even for rigid or blocked agents, but are not supplied to those agents’ policies. The inferential unit
is the independent paired replicate: losses are averaged over its windows before taking policy-minus-rigid contrasts. Analytic,
percentile and studentized interval records are retained; the main table presents analytic pointwise 95% intervals and the
supplement retains all retained families. This exploratory extension is separate from the original 8 primary contrasts and does
not create a second significance-testing family.
Known-answer controls require useful restrictions to survive favorable evidence, contradictory evidence to permit revision, equal
likelihoods to produce no strict preference, invalid channels to fail, consistent candidate permutations to preserve forecasts, and
sham/no-access forecasts to remain identical to rigid forecasts. The policy receipt is checked against only previously observed
gain. No gate requires superior predictive loss: opportunity value, epistemic benefit and incurred cost remain distinct quantities.
The candidate menu deliberately omits a low-probability channel from the restricted family, so reversal is a constructed resolving
case, not evidence that relaxation is universally beneficial.
Access and control also have a computational phenomenology distinct from task success. Sandved-Smith and colleagues
model perceptual, attentional and meta-awareness levels, separating the ability to access a cognitive state from controlling
it ( Sandved-Smith et al. 2021 ). Our binary access gate is an authored simplification, not an implementation of that hierarchical
architecture. Neither exposing an alternative in software nor observing a changed response establishes a participant’s reflective
awareness.
The action policy is a stipulated logistic choice rule with reinforcement from previously observed evidence gain. It is not expected-
free-energy planning over future observations. Its utility units, action precision and gain weight must be interpreted together.
Initially, choice depends on the product 𝛽𝑎(𝜌𝑒 −𝑐): equal increases in opportunity value and cost leave that probability unchanged.
These fixed design parameters are consumed by the simulator; they have not been independently identified from behavior.
The identification limit extends beyond the initial choice. Conditional on a fixed gain history, the entire logistic policy depends
on only two combinations:
𝜂0 = 𝛽𝑎(𝜌𝑒 − 𝑐), 𝜂 1 = 𝛽𝑎𝜆𝑔,
(𝛽𝑎, 𝜌𝑒, 𝑐, 𝜆𝑔) ⟼ (𝛽𝑎/𝑘, 𝑘𝜌 𝑒 + 𝑑, 𝑘𝑐 + 𝑑, 𝑘𝜆 𝑔), 𝑘 > 0. (5)
For admissible nonnegative values and costs, this transformation preserves every conditional choice probability. Choices alone
therefore cannot identify all four original parameters. Independently varied or measured costs, an explicit utility scale and
parameter-recovery checks are necessary before interpreting a fitted preference as gratitude. Observed expenditure can supply
information beyond choices; the invariance does not claim that differently charged activities have identical costs.
Exact evidence decisions and conditional operating characteristics
The finite family comparison admits a derivation independent of its software decomposition. Let ℛ be the retained candidate
set, let 𝑤 = ∑𝑚∈ℛ 𝑝𝑂(𝑚)with 0 < 𝑤 < 1 , and let 𝑝𝑅 and 𝑝𝑋 be the open prior conditioned on ℛ and its complement. For
positive likelihoods, marginal evidence satisfies
𝑍𝑂 = 𝑤𝑍𝑅 + (1 − 𝑤)𝑍𝑋, ln 𝑍𝑂
𝑍𝑅
= ln[𝑤 + (1 − 𝑤)𝑍𝑋
𝑍𝑅
] . (6)
Thus the open family wins exactly when 𝑍𝑋 > 𝑍𝑅. Enlarging support is not automatically rewarded: the evidence of the added
candidates must exceed the retained family’s average evidence. The same-data evidence comparison remains conditional on the
declared candidate menu and priors; it does not establish the menu’s absolute adequacy ( Wilson and Collins 2019 ). Nor is it
the posterior-reuse identity for Bayesian model reduction: a candidate with zero restricted prior mass requires a new posterior
fit when admitted.
In the admitted candidate menu, 𝑤 = 2
3 . Writing 𝐿𝑚(𝑘) = 𝐴𝑘
0𝑚𝐴𝑛−𝑘
1𝑚 , the rule becomes 2𝐿3(𝑘) > 𝐿1(𝑘) + 𝐿2(𝑘). The coefficients
follow from the admitted open prior and its conditional restriction. The binomial coefficient is absent from each ordered-sequence
likelihood and cancels in a comparison of count likelihoods. It must be included when assigning probability to a count under the
process. If 𝒦𝑂 contains the winning counts, then
𝑃𝑝(select open ∣ effective inquiry) = ∑
𝑘∈𝒦𝑂
(𝑛
𝑘)𝑝𝑘(1 − 𝑝)𝑛−𝑘. (7)
The implemented oracle enumerates all 𝑛 + 1counts and checks native decisions and forecasts against rational products and sums.
Decimal strings of the admitted GNN tensor entries define its rational coefficients; open and conditional restricted priors are
normalized exactly. The rational count masses sum to one. Logarithms and predictive losses remain numerical evaluations and
retain an explicit error check against the native path. This exhaustive finite check replaces sampling error for this calculation,
not uncertainty about whether the model represents people.
Let 𝑓𝑅(𝑘)be the restricted channel-zero forecast and 𝑓𝑆(𝑘)the forecast after the evidence-selected family is fitted. With
ℓ(𝑝, 𝑓) = −𝑝ln 𝑓 − (1 − 𝑝)ln(1 − 𝑓), the conditional expected predictive contrast is
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## Page 42

Δℒ(𝑝) =
𝑛
∑
𝑘=0
(𝑛
𝑘)𝑝𝑘(1 − 𝑝)𝑛−𝑘 [ℓ(𝑝, 𝑓𝑆(𝑘)) − ℓ(𝑝, 𝑓𝑅(𝑘))] . (8)
A negative value favors evidence selection relative to restriction. Both predictors use the same calibration count; the loss
expectation concerns a new observation from the declared process. Selection probabilities and this expected loss are conditional
on an effective inquiry. They do not integrate the repeated policy’s action probability, availability, history or cost. The repeated
experiment evaluates those additional mechanisms separately.
An observed zero in repeated simulations does not establish impossibility. Zero-numerator bounds require an explicitly defined
event and independent trials with a common event probability ( Hanley and Lippman-Hand 1983 ). For an adaptive trajectory, an
event such as any revision over the entire trajectory has the complete independent replicate as its trial; correlated windows cannot
inflate that denominator. The exact conditional count oracle answers a separate question under its admitted finite channel. It
can retain a rare positive selection probability even when a repeated experiment happens to observe no corresponding event.
Recall inference, normalization and learning
Let 𝑎𝑜𝑠 > 0 denote the agent’s likelihood pseudocounts. The expected observation probabilities are normalized separately for
each hidden state:
𝐴𝑜𝑠 = 𝑎𝑜𝑠
∑𝑜′ 𝑎𝑜′𝑠
. (9)
For prior 𝑝𝑡(𝑠), observed category 𝑜𝑡, and precision 𝛽 > 0, the implemented generalized-Bayes update is
𝑞𝑡(𝑠) =
𝑝𝑡(𝑠)𝐴𝛽
𝑜𝑡 𝑠
∑𝑠′ 𝑝𝑡(𝑠′)𝐴𝛽
𝑜𝑡 𝑠′
. (10)
The operation powers the likelihood values for the observed category. It does not first renormalize every likelihood column
after exponentiation. Ordinary online inference uses unit precision; replay uses the declared positive precision. An unsupported
observation or invalid probability array raises an error. A missing observation, represented separately from any categorical
outcome, returns a copy of the prior. This last behavior is an explicit missingness convention, not a theorem that missingness is
always uninformative.
Learning applies forgetting and a belief-weighted increment:
𝑎𝑜𝑠 ← 𝜌 𝑓 𝑎𝑜𝑠 + 𝜂 1{𝑜 = 𝑜𝑡}𝑞𝑡(𝑠), 0 < 𝜌 𝑓 ≤ 1, 𝜂 > 0. (11)
The first observation of each day uses the declared initial prior; subsequent online observations use the transition prediction
from the preceding posterior. Initial counts are the declared likelihood multiplied by a prior-concentration parameter. Thus
probability shape and accumulated concentration remain distinct. The POMDP and process-theory literature provides the
general lineage for this construction ( Friston et al. 2017 ; Sajid et al. 2021 ; Smith et al. 2022 ), but the particular update and
replay choices above define this experiment.
At day’s end, positive recall samples existing positive observations without replacement, up to the declared recall limit. When
fewer positive observations occurred, the replay dose is smaller; the algorithm does not invent favorable experiences. Random
recall samples the same number of time points from all observations of that day. Selected indices are processed in temporal order.
Both replay conditions use the stored prior from the original time point together with the current learned likelihood. Replay
adds another pseudocount update: it is deliberate reweighting of existing experience, not replacement of the original update
and not acquisition of independent evidence. Because forgetting is applied per update, sensitivity to forgetting must also be
interpreted in relation to replay dose.
Absence observations and counterfactual valuation
The separate absence model includes an observation category explicitly designated as absence. When its likelihood differs between
hidden states, observing that category changes the posterior. In contrast, the missing-observation sentinel preserves the prior
under the implemented convention. An uninformative likelihood provides a third case: an actual observation occurs, but it does
not distinguish states. KL divergence from the prior records the magnitude of updating; the imported routine expresses this
comparison in bits. These distinctions prevent “nothing was measured” from silently becoming “harm was absent. ” Missing-data
methods provide context for the need to state observation assumptions ( RUBIN 1976 ).
Counterfactual value is defined separately as
𝑉cf = ℎref𝑐harm − 𝑐actual. (12)
The reference hazard and harm cost are declared inputs, not estimates recovered from the absence itself. In the main study,
absence appreciation uses the intervention-phase frequency of the neutral category multiplied by reference hazard and harm cost.
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## Page 43

Treating that category as an uneventful interval is a new coding decision, not a claim that every neutral experience is absence
of harm. A nonzero value therefore expresses evaluation relative to a reference scenario; it does not prove that an actual harm
was prevented.
Controls set reference hazard or harm cost to zero, supply uninformative observations, reject invalid probabilities, and permute
hidden-state labels with their corresponding probabilities. Label permutation should preserve predictions. This is a finite
representational consistency requirement, offered as one modest operational aspect of non-reification. It is not a comprehensive
model of conceptual flexibility. An imported Blackwell Bayes-risk comparison supplies an additional, separate information-
ordering control; it must not be mistaken for a theorem that the main gratitude experiment measures philosophical insight.
F rom learned likelihoods to scene sampling
The gaze extension begins with the exact numerical class in the preserved modified Yarbus notebook. Its 13 locations belong to 5
positive, 5 negative and 3 neutral states, with observations ordered positive, neutral, negative. The source comparison alternates
its positive and negative likelihood templates for 5 pairs of 1000 states under a single seed of 42. Its state occupancy includes
the initial neutral location. We reproduce that draw order rather than seed each profile separately. The notebook contains no
gratitude import, parameter learning or before/after intervention. Its cached bars also disagree with its code. Consequently,
agreement with the published before bars is a reconstruction result; a new intervention cannot be presented as reproduction of
the paper’s after bars.
Task-directed scene viewing supplies relevant background ( Yarbus 1967; Castelhano et al. 2009 ). The latter experiment manip-
ulated viewing instructions, not gratitude or contemplative practice. Likewise, active-inference models can formalize context-
sensitive sampling (Mirza et al. 2019 ) without establishing that our valence partition is a perceptual fact. Our regional categories
and coordinates are stipulated. We inspect Yarbus’s publisher chapter metadata/abstract, Castelhano and colleagues’ full article,
and Mirza and colleagues’ targeted full-text model sections; no claim of reading the restricted Yarbus chapter is made.
We retain each corrected agent’s normalized likelihood before and after intervention, frozen before assessment. A declared
column-stochastic embedding 𝐸 ∈ ℝ 2×13 assigns each scene location a distribution over the learned latent states. Each column
is nonnegative and normalized; its weights come from the preserved GNN transfer_state_map. The primary bridge is
𝐴scene
𝑖,𝑐,𝑡 = 𝐴learned
𝑖,𝑐,𝑡 𝐸, 𝜋 𝑖,𝑐,𝑡(𝑎) ∝exp{𝛾𝑇 [𝐶⊤𝐴scene
𝑖,𝑐,𝑡 (∶, 𝑎) − 𝜂𝐻𝐻(𝐴scene
𝑖,𝑐,𝑡 (∶, 𝑎))]} , (13)
where 𝑡 denotes pre/post intervention, 𝑖 a paired agent and 𝑐 its condition. The GNN declaration sets 𝛾𝑇 = 1.5, 𝜂𝐻 = 0.5
and 𝐶 = (2, 0, −2). This source-like policy is stationary within an assessment: the entropy penalty is not called information
gain. The subscript distinguishes this weight from the recall learning increment 𝜂. Preferences and the common external scene
process remain fixed. Pre/post sampled paths share 127 action uniforms after an initial neutral location, giving 128 states per
path. Both expected positive-location policy mass and whole-scene predictive loss are retained. Environmental feedback does
not update these transferred channels.
A separate sensitivity bridge mixes the fixed source-like positive/negative templates using the independently assessed world-well
readout as the mixing weight. It tests a different mapping and consumes assessment information; it is not parameter transfer.
The direct bridge is tested for invariance to perturbing that readout. Both mechanisms retain the same agent identities and
exposure hashes, and their results are reported separately. The map 𝐸, mixture assumption and unchanged scene process are
new hypotheses. Neither bridge is claimed to be the authors’ missing after implementation.
Active visual inquiry with revisable structural support
The second gaze extension uses 3 candidate scene representations. The imported Realizing Emptiness admission supplies the
restricted prior 𝑅, which excludes candidates incompatible with the enforced separation, and the open prior 𝑂, which admits
the complete menu. The GNN gaze specification declares 3 regional observation channels, a canonical positive-region 𝐴 tensor,
identity transitions within an episode, preferences, geometric coordinates, policy weights, contexts and paired contrasts. Strict
admission checks their compatibility with the imported structural family. Native distribution-derived free-energy evaluation is
compared with an independent exact evidence sum after every update.
Let 𝑚 index candidates, 𝑎 locations and 𝑟(𝑎)their region. For posterior 𝑞𝑡(𝑚), the predictive channel is 𝑝𝑡(𝑜 ∣ 𝑎) = ∑𝑚 𝐴𝑟(𝑎)(𝑜 ∣
𝑚)𝑞𝑡(𝑚). Expected information gain is enumerated exactly:
𝐼𝑡(𝑎) = 𝐻[𝑝𝑡(𝑜 ∣ 𝑎)] − ∑
𝑚
𝑞𝑡(𝑚)𝐻[𝐴𝑟(𝑎)(𝑜 ∣ 𝑚)] = ∑
𝑜
𝑝𝑡(𝑜 ∣ 𝑎) 𝐷KL(𝑞𝑡(𝑚 ∣ 𝑜, 𝑎)‖𝑞𝑡(𝑚)) . (14)
Independent posterior-KL and known-answer tests check Equation (14) . Identical candidate channels and a known candidate
yield zero information gain. The authored one-step policy separates expected observation value, information gain and movement:
𝜋𝑡(𝑎) ∝exp{𝛾𝐴 [∑
𝑜
𝐶𝑜𝑝𝑡(𝑜 ∣ 𝑎) + 𝜆𝐼𝐼𝑡(𝑎) − 𝜅‖𝑥𝑎 − 𝑥𝑎𝑡−1
‖2]} . (15)
The declaration sets 𝛾𝐴 = 4 , 𝜆𝐼 = 4 and 𝜅 = 0.2 in a unit-square geometry. The information weight 𝜆𝐼 is separate from the
practice gain weight 𝜆𝑔. Utility-only controls set it to zero; a uniform open control samples all 13 locations equally. These
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## Page 44

weighted terms define the experiment; we do not claim equivalence to a complete expected-free-energy planner or multi-step
optimal policy. Observations are drawn from a shared external regional channel, and the posterior changes only through the
selected observations. A zero prior cannot acquire an omitted candidate by ordinary within-family Bayesian updating.
Whole-scene risk prevents an agent from choosing its own favorable evaluation set. Before every observation, we score the
predictive distribution against the known synthetic process at every location:
𝐿𝑡 = − 1
13
13
∑
𝑎=1
∑
𝑜
𝑝∗(𝑜 ∣ 𝑎)log 𝑝𝑡(𝑜 ∣ 𝑎). (16)
This is exact population cross-entropy under the declared process, not a held-out human sample or measured calibration. Episode
means average this prequential quantity across 48 sampled locations. Stationary windows use candidate sequence (0, 0, 0)and
reversal windows (0, 2, 0). Each episode resets its admitted prior; candidate identity is stable within the episode. Thus this
experiment tests repeated opportunities for structural access under different contexts, not persistent learning of a changing
context across windows.
6 conditions separate open access, inquiry and activity: restricted utility, open utility, open inquiry, restricted inquiry, a behav-
iorally exact restricted sham, and uniform open sampling. Potential action uniforms and time-by-region outcome uniforms are
shared across policies. Opening support does not force inquiry, and choosing inquiry cannot recover a candidate that remains
excluded. The imported practice model elsewhere makes access itself an enacted decision; this gaze extension conditions on
access in order to isolate the sampling consequences.
Scanpaths use the 13 admitted coordinates, normalized to the unit frame and registered to the complete portrait. The licensed
museum photograph of Munch’s The Scream is credited in each figure ( Munch 1893 ). Straight segments connect sampled
locations; circle and square mark the first and last displayed locations. This registration is newly declared, not recovery of the
source montage. The painting supplies no pixels to inference, and no gaze coordinates, dwell times or affective ratings were
measured. Context changes the synthetic regional channels while the background image remains fixed.
F rom scene gaze to inquiry into its boundary
A scene can be inspected while its framing assumptions remain unexamined. Conversely, an agent can ask how its observations
depend on an action without learning which scene it is viewing. Our intersection experiment makes these complementary
operations explicit. It imports the admitted gaze channels and Realizing Emptiness support, then adds a separately declared
variable for a predictive boundary/reference encoding. This is joint finite structural inquiry. Calling its question selection
metacognitive gaze is an operational metaphor, not a claim that ordinary inference has become human meta-awareness.
Nelson and Narens distinguish monitoring of an object-level process from control that changes that process
(Nelson and Narens 1990 ). Their framework motivates recording an encoding posterior separately from the policy that
selects evidence. Sandved-Smith and colleagues implement a deeper precision-control and meta-awareness architecture while
explicitly setting aside selective epistemic foraging ( Sandved-Smith et al. 2021 ). Our 9-state model is a simpler, different
construction. Neither its posterior entropy nor its confidence is a measure of metacognitive sensitivity or efficiency in the sense
reviewed by Fleming and Lau ( Fleming and Lau 2014 ).
Let 𝑍 denote a reference scene and 𝐻 a boundary/reference encoding, each with 3 values. Under the admitted independent
uniform prior, the diagnostic regime displays appearance 𝑊 :
𝑝(𝑍 = 𝑧, 𝐻 = ℎ) =1
9, 𝑊 = 𝑇 ℎ(𝑍) = (𝑍 + 𝐻)mod 3. (17)
The 13 visual queries use the existing regional channels conditional on 𝑊 . They can identify appearance without identifying 𝐻.
Marginalizing the uniform 𝑍 leaves the same visual likelihood for each encoding; this result depends on the admitted prior and
cyclic maps, not on a general principle that vision cannot inform a boundary. The restricted condition replaces only the 𝐻 prior
by the actual upstream-admitted support (0.5, 0.5, 0).
A boundary question instead reveals a paired randomized action 𝑣 and response 𝑟. The action is uniform and independent.
Query 𝑗 has declared reliability 𝜌𝑗:
𝑝𝑗(𝑣, 𝑟 ∣ ℎ) =1
3 [𝜌𝑗1{𝑟 = (𝑣 + ℎ)mod 3} +1 − 𝜌𝑗
2 1{𝑟 ≠ (𝑣 + ℎ)mod 3}] . (18)
Both individual marginals are uniform; the relation carries information about 𝐻. The 3 reliabilities are (0.65, 0.8, 0.95)and costs
(0.02, 0.05, 0.1). Visual queries also use a 9-outcome alphabet, pairing their valence observation with an independent uniform
nuisance variable. Every query is one declared computational decision; this does not establish equal human perceptual effort,
duration or number of fixations. In the separate label-only regime, visual channels depend only on 𝑍 and all boundary-question
outcomes are uniform. Its labels have no distinguishing observation law.
The joint posterior updates only through the selected query and supplied observation. Zero prior support remains zero. The
integrated policy applies Equation (15) over 16 queries, with information evaluated once over the joint state:
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## Page 45

𝐼𝑡(𝑗) = ∑
𝑧,ℎ,𝑜
𝑞𝑡(𝑧, ℎ)𝐴(𝑗)
𝑜,𝑧,ℎ log
𝐴(𝑗)
𝑜,𝑧,ℎ
∑𝑧′,ℎ′ 𝑞𝑡(𝑧′, ℎ′)𝐴(𝑗)
𝑜,𝑧′,ℎ′
. (19)
Visual utility, action precision, information weight and spatial costs are imported from the actual gaze declaration. Boundary
questions have zero immediate visual utility and their separately declared costs. Their selection can therefore trade current-
scene sampling against encoding information. Visual-only sampling exactly reduces to the imported gaze policy over appearance;
boundary-only sampling admits only the 3 questions; uniform sampling admits all 16 equally. The restricted policy uses the
same choices while excluding H2. No gate requires the integrated policy to win.
The matched-query condition is a nonautonomous sham: it follows the paired integrated agent’s schedule and observes the same
outcomes, but discards the randomized-action component when updating from a boundary question. The remaining response
marginal supplies no encoding update. Its updater deliberately ignores information potentially conveyed by the demonstrator’s
adaptive schedule. It is therefore a precisely specified erasure comparator, not a proof that the entire schedule is information-free
or a simulation of a person’s unawareness.
In the label-only regime, all query histories preserve the prior odds of encodings:
𝑞𝑡(𝐻 = ℎ)
𝑞𝑡(𝐻 = ℎ′)= 𝐷𝐻(ℎ)
𝐷𝐻(ℎ′), 𝐷 𝐻(ℎ′) > 0. (20)
More independent replicates cannot resolve that equality. In the diagnostic regime, scene-only and boundary-only data each leave
𝑍 uniform for the open agent, whereas their joint use can resolve the reference scene. This provides an executable intersection
without equating identification of a stipulated encoding with realization of emptiness.
Reference-frame transfer and proper boundary scores
The common transfer target explicitly anchors the reference encoding at 𝐻 = 0 . It tests whether inferred appearance and
encoding jointly support prediction in that reference condition. It is an intervention on the reference frame, not ordinary future
prediction under the original unchanged scene process. With final scene marginal 𝑞𝑍 and true reference scene 𝑧∗, excess expected
log loss is
ℛ0(𝑞𝑍; 𝑧∗) = 1
13
13
∑
𝑎=1
∑
𝑜
𝐴𝑟(𝑎)(𝑜 ∣ 𝑧∗)log
𝐴𝑟(𝑎)(𝑜 ∣ 𝑧∗)
∑𝑧 𝐴𝑟(𝑎)(𝑜 ∣ 𝑧)𝑞𝑍(𝑧). (21)
This exact population KL score is zero for the true predictive channel. The second endpoint is multicategorical boundary Brier
loss, ∑ℎ(𝑞𝐻(ℎ) −1{ℎ = ℎ∗})2. It stays finite when the true encoding is excluded; no infinite log loss is silently clipped. Current-
scene prequential regret, boundary-question allocation, declared expenditure and posterior entropy remain separate diagnostics.
The anchored target assumes an available reference intervention and known channels; those assumptions need independent
justification in any empirical translation.
S3. Experimental design, estimands and uncertainty procedures
Paired exposure and matched recall dose
The main design uses 5 fixed luckiness strata and 1024 independent seeded replicates per stratum. The resulting design contains
5120 independently seeded agent-world units, each evaluated in 4 paired conditions. One baseline is trained for each unit and
copied into no recall, positive recall, dose-matched random recall, and absence appreciation. Every condition receives the same
intervention-phase environmental states and observations. Their shared exposure digest records that identity. Evaluation data
and optimism-task priors are independently generated from the training stream but reused across paired conditions and pre/post
assessment.
No recall continues ordinary learning. Positive and random recall differ in selected event content while sharing dose and replay
precision. Absence appreciation follows exactly the no-recall inference and learning path, then assigns a separate value to
designated uneventful observations. This condition supplies an intentionally exact belief null. Any belief difference between
it and no recall would indicate an implementation or contract failure; agreement is not evidence that human gratitude can be
increased without changing beliefs.
The design is paired within each seeded unit and stratified across a fixed grid. It does not randomly sample people or environments
from a population. Its units are independent simulation streams, not independent time steps within a trajectory. Daily trajectory
plots retain only replicate zero in each stratum and condition. They illustrate paths through the implementation and must not
be read as population means or uncertainty estimates.
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## Page 46

Independent predictive evaluation and the optimism readout
Assessment freezes the learned likelihood and evaluates independent observations using the declared prior. It does not continue
learning during scoring. For the true binary hidden state 𝑦𝑖 and inferred going-well probability 𝑞𝑖, the latent-state Brier error is
BS = 1
𝑁
𝑁
∑
𝑖=1
(𝑞𝑖 − 𝑦𝑖)2. (22)
Brier loss scores predictive probabilities; it does not isolate calibration from discrimination or resolution. We therefore describe
Brier contrasts as predictive-loss results. Statistical calibration of an interval procedure is a separate question. The Brier
definition follows the probability-scoring lineage ( BRIER 1950 ).
Observation predictive log loss instead evaluates the probability of what was observed:
NLL = − 1
𝑁
𝑁
∑
𝑖=1
log (∑
𝑠
𝐴𝑜𝑖 𝑠𝐷𝑠) . (23)
These quantities answer different questions. Brier error evaluates posterior discrimination and probability accuracy against the
simulated hidden state. Log loss evaluates the observation distribution under the frozen model and prior. Lower values are better
for both scores, and neither is a well-being scale. Posterior entropy is reported as uncertainty in natural-log units; lower entropy
alone is not a success criterion because an agent can be confidently wrong. Proper scoring provides the relevant methodological
context ( BRIER 1950 ; Gneiting and Raftery 2007 ), while the finite formulas state precisely what is computed here.
Strict propriety concerns expected performance: reporting the data-generating distribution uniquely optimizes the
expected score, with our losses using the opposite sign from the reward convention in Gneiting and Raftery
(Gneiting and Raftery 2007, secs. 1, 3 ). It does not guarantee that a fitted forecast wins on every finite assessment
sample. Forecast calibration concerns agreement between issued probabilities and outcome frequencies; sharpness concerns
concentration of the predictive distributions. An aggregate loss comparison does not separately identify either property, and an
entropy decrease cannot substitute for evaluating outcomes. These forecast properties also differ from the repeated-sampling
coverage of the interval procedures in Figure 40 .
Model evidence and predictive scoring are related but evaluate different uses of observations. Integrated evidence averages
a calibration sequence’s likelihood under a declared prior; it can also be factored into sequential predictive probabilities
(Gneiting and Raftery 2007, sec. 7.1 , equations 50–53). Here that evidence selects a working family, whose fitted forecast is
then frozen and evaluated on new observations. Consequently, an evidence preference on the calibration batch does not establish
lower future loss. The exhaustive practice calculation evaluates both the process probability of each selection and its expected
consequence for a new outcome; the enacted experiment additionally includes action, access and expenditure.
The optimism task uses 2 declared binary news likelihoods, one for each world-belief mode. For each shared initial good-outcome
probability 𝑝, inference is performed separately after good and bad news in each mode. The resulting posteriors are mixed using
the agent’s mean assessed going-well probability 𝑤. If these mixed probabilities are 𝑞𝑔 and 𝑞𝑏, the readout is
𝑂 = mean𝑝 [(𝑞𝑔 − 𝑝) + (𝑞𝑏 − 𝑝)]. (24)
When bad news decreases the good-outcome probability, the second term is negative; the sum contrasts upward good-news
updating with downward bad-news updating. Both news conditions use the same initial probability rather than independently
resampled priors. The readout is an explicitly constructed function of the world-belief summary and news matrices. It is not an
independently validated psychological outcome, and covariance with world belief is partly built into its definition.
Estimands, intervals and Monte Carlo decisions
Let 𝐷ℎ𝑟 be the difference between two conditions’ pre/post changes for paired unit 𝑟 in fixed world ℎ. The primary target is the
equally weighted mean of world-specific expectations,
𝜃 = 1
𝐻
𝐻
∑
ℎ=1
𝐸[𝐷ℎ], ̂𝜃 = 1
𝐻
𝐻
∑
ℎ=1
̄𝐷ℎ. (25)
The 8 primary hypotheses combine optimism change and Brier-loss change with positive versus no recall, random versus no recall,
absence value versus no recall, and positive versus random recall. This revision retains that family and its data. Additional
world-specific and observation-log-loss analyses are exploratory, undertaken after inspecting the original results; they are not
retroactively preregistered hypotheses.
Bootstrap resampling draws complete paired units with replacement separately within each fixed world, preserving its weight.
It does not resample world labels or count time steps as independent units. The original percentile interval uses the 0.025 and
0.975 quantiles of bootstrap means ( Efron 1979 ). A studentized comparison uses each resample’s own within-world variance, as
well as the original estimated standard error ( boot package documentation, n.d. ):
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## Page 47

̂SE
2
(̂𝜃) = 1
𝐻2 ∑
ℎ
𝑠2
ℎ
𝑅 , 𝑇 ∗ =
̂𝜃∗ − ̂𝜃
̂SE
∗ . (26)
If 𝑞∗
𝛼 denotes a quantile of that root, the bootstrap t interval is [ ̂𝜃 − 𝑞 ∗
0.975 ̂SE, ̂𝜃 − 𝑞 ∗
0.025 ̂SE]. Studentization is not a universal
repair for percentile undercoverage; distributional conditions still matter ( Hall 1988 ). If the original variance or any resampled
variance is zero, the studentized interval is unavailable. No problematic draw is dropped, no finite interval is silently substituted,
and the degenerate-draw count is retained. In particular, a deliberately constant software null is justified by its mechanism
rather than a fabricated nondegenerate interval.
The numerical implementation subtracts each stratum’s first observation before computing its variance and bootstrap roots, and
subtracts each resample’s own first observation before computing its variance. These translations preserve the mathematical
variances while preventing constant decimal-valued samples from acquiring a small positive variance through floating-point mean
rounding. Exact-range controls independently verify degenerate-resample counts; no numerical tolerance or artificial noise turns
an unavailable interval into an available one.
Exact availability for the discrete stressor The empirical bootstrap draws independently with replacement from the
observed sample (Efron 1979, sec. 2 ). For our single-stratum centered Bernoulli stressor, centering leaves the variance unchanged.
Let 𝐾 ∼ Binomial(𝑛, 𝑝)be the original number of successes. Conditional on 𝐾 = 𝑘 , a size- 𝑛 resample is constant with probability
𝑞𝑘 = (𝑘/𝑛)𝑛 + (1 − 𝑘/𝑛)𝑛. Independence of the 𝐵 resamples therefore gives the following project-derived availability probability
under the stated strict failure rule:
𝐴(𝑛, 𝑝, 𝐵) =
𝑛−1
∑
𝑘=1
(𝑛
𝑘)𝑝𝑘(1 − 𝑝)𝑛−𝑘(1 − 𝑞𝑘)𝐵. (27)
Original constant samples contribute zero. The calculation uses the admitted sample size and draw count, and the independent
fixture’s generating probability; it neither estimates parameters from the observed availability nor fits a coverage curve. Exhaus-
tive enumeration of original binary samples and all small-sample resampling sequences independently checks the implementation.
For fixed finite 𝑛 and interior 𝑝, every interior 𝑞𝑘 is positive: 𝐴 decreases as 𝐵 increases and tends to zero. This behavior
follows from our all-resamples-positive-variance policy, not from a general assertion that more bootstrap draws worsen inference.
Dropping undefined roots or substituting a different interval would define a different procedure.
Writing 𝑉 for interval availability and 𝐶 for coverage, Figure 40 separately reports 𝑃 (𝑉 ), 𝑃 (𝑉 ∩ 𝐶)and 𝑃 (𝐶 ∣ 𝑉 ). The cov-
erage plotted across all experiments is 𝑃 (𝑉 ∩ 𝐶)and cannot exceed availability. Conditional coverage describes the selected
subset that returned intervals; it is undefined if none did. The exact formula benchmarks 𝑃 (𝑉 )alone and supplies no cover-
age guarantee. Reporting failures and their data dependence follows the simulation-study guidance of Morris and colleagues
(Morris et al. 2019, secs. 3.4, 5.1 ).
An analytic robustness comparator uses the same mean and within-world variance. With 𝑣ℎ = 𝑠 2
ℎ/𝑅, its Welch-Satterthwaite
degrees of freedom are (∑ℎ 𝑣ℎ)2/ ∑ℎ[𝑣2
ℎ/(𝑅 − 1)](WELCH 1947 ; Satterthwaite 1946). The resulting Student interval is exact
for a single Gaussian stratum and approximate for general finite-model contrasts. Percentile, bootstrap t and analytic intervals
target the same quantity and remain reported regardless of which appears most favorable.
The two-sided sign-flip test retains the original absolute mean statistic. Its null requires symmetric or appropriately ex-
changeable paired differences; a zero mean alone is insufficient. Finite Monte Carlo p-values use the plus-one convention
(Phipson and Smyth 2010 ). Holm correction applies to all 8 primary tests ( Holm 1979 ). Exact Clopper-Pearson intervals quan-
tify tail-probability simulation error with a Bonferroni allocation across that family ( CLOPPER and PEARSON 1934 ). A Holm
decision is reject only when its adjusted upper Monte Carlo bound is below 0.05, retain only when its lower bound exceeds 0.05,
and unresolved otherwise. Retaining a null does not establish equivalence. An independently enumerated small-sample sign
oracle checks tail counting and ties.
Inconclusive contrasts and equivalence claims
An interval spanning zero can leave scientifically meaningful effects unresolved. Lakens distinguishes failure to reject a difference
from evidence that an effect lies within justified equivalence bounds ( Lakens 2017 ). A future human study would need to define
those bounds from its substantive target before using an appropriate equivalence analysis. We have not fitted bounds to these
results or applied a simple-test rule to the joint bootstrap rectangles. Algebraic mechanism identities have a different warrant:
they follow from the declared operations, rather than from statistical nonrejection. The complete tables therefore retain their
exact, stochastic and unavailable statuses.
Joint uncertainty for the exploratory gaze family
The gaze analyses were added after the recall results, and this joint analysis was designed after examining version 0.5.0. Mul-
tiplicity adjustment does not make them preregistered. The original 8-test Holm family is unchanged. A separate, explicitly
exploratory rectangle covers all 16 transfer and 42 active-policy contrasts in one joint resampling operation.
Transfer resampling draws whole paired-agent vectors independently within each of the 5 fixed worlds; the same selected indices
serve every bridge, condition and endpoint. Active resampling first averages all 3 windows within each replicate, shares its indices
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## Page 48

across that context’s contrasts, and draws independently between contexts. Matching replicate numbers across separately seeded
contexts does not make them paired units. The critical maximum therefore preserves dependence within a block and combines
all 3 independent blocks in each draw.
For contrast 𝑗, let ̂ 𝑠𝑗 be the original standard error and let ̂𝜃∗(𝑏)
𝑗 be its jointly resampled mean. The declared single-step procedure
is
𝑀 ∗(𝑏)= max
𝑗∶ ̂ 𝑠𝑗 >0
∣
̂𝜃∗(𝑏)
𝑗 − ̂𝜃𝑗
̂ 𝑠𝑗
∣ ,
̂ 𝑐 =̂𝑄0.95(𝑀∗), ℐ 𝑗 = [ ̂𝜃𝑗 − ̂ 𝑐 ̂ 𝑠𝑗, ̂𝜃𝑗 + ̂ 𝑐 ̂ 𝑠𝑗].
(28)
Each draw uses the original standard errors; this is a standardized empirical-bootstrap maximum, not resample-studentized
bootstrap t or a stepdown algorithm. The finite-draw quantile is the order statistic at rank ⌈0.95𝐵⌉, with 𝐵 = 16383 . A
separate 99% binomial order-statistic bracket describes Monte Carlo error in that conditional quantile, including tied roots and
unbounded finite-rank endpoints. It does not measure the rectangle’s sampling coverage.
The joint-bootstrap lineage requires a consistent joint approximation and appropriate nondegenerate limiting distributions
(Romano and Wolf 2005 ). Covariance-aware simultaneous inference and positive-variance requirements supply related context
(Hothorn et al. 2008 ); the inspected Hothorn source is its author technical report, with journal identity verified separately. Nei-
ther citation establishes finite-sample coverage here. We retain all original pointwise procedures and measure all-target coverage
on independent Gaussian, correlated Gaussian, unequal-variance fixed-stratum, centered-exponential and rare Bernoulli fixtures.
No seed or coverage threshold is chosen to force success.
Valuation and sham zeros receive exact bounds only after their named intervention identities are verified against the complete
records. An accidentally constant sample receives no stochastic interval. If any such column is unavailable, the full-family status
is partial or unavailable and the supported subfamily is listed; it cannot be advertised as a complete 58-dimensional region.
Duplicated or opposite columns retain their dependence without covariance inversion or numerical jitter.
Independent sample expansion and intersection uncertainty
The corrected learning cohort has 1024 independent paired agents in each of 5 fixed worlds (5120 units); active gaze has 512 paired
replicates per context; enacted practice has 512 per context. Sensitivity cells use 128 agents per world. Known-answer operating
checks use 4096 independent experiments with 64 units per fixed stratum. These independent units are distinct from repeated
observations, windows, conditions and bootstrap draws. Original source reconstructions retain 1000 agents and 5 seed-42 gaze
runs.
The intersection has 2 regimes, 3 fixed scene values and 3 fixed encodings, each with 512 independent paired replicates and 24
decisions. Thus 9216 independent units generate 55296 6-policy episodes. Counterfactual query outcomes and action-selection
uniforms are shared within each unit. Query and observation sequences remain dependent within an episode. Nested prefixes of
16, 32, 64, 128, 256, 512 replicates are fixed in the GNN declaration; increasing N appends independent identities while preserving
earlier potential outcomes. Prefix stability is a Monte Carlo diagnostic, not an adaptive stopping criterion or a human-power
calculation.
The 7 policy comparisons, 2 endpoints, 2 regimes and 3 encoding contexts define a separate 84-member exploratory family. Of
these, 5 comparisons use visual-only as reference; integrated sampling is also compared directly with uniform and boundary-only
sampling. Each regime/H block equally averages 3 fixed scene strata and resamples complete paired replicate vectors within
those strata. Blocks use independent bootstrap streams, with a shared maximum across all members. The joint bootstrap
method and its conditional quantile bracket follow the earlier joint contract ; the intersection is not added retrospectively to the
8-test recall family or the 58-member gaze family. Fixed stratum origins are removed before variance and bootstrap centering
to avoid floating-point cancellation; a representable-translation negative control reproduces and rejects the former failure. The
active-comparator closure was added during development after the first numerical diagnostic run; all intersection analyses are
exploratory, not preregistered confirmatory tests.
Mechanism-exact constants require the admitted channel/prior symmetries and complete paired-record checks. Label-only Brier
contrasts and the diagnostic sham Brier null are exact; diagnostic boundary-only and sham anchored contrasts are also exact
because their scene marginals remain uniform. Restricted label-only Brier offsets are nonzero and can be adverse. Proven
offsets are subtracted for exact-zero admission and restored afterward. Other observed constants remain unavailable, and nearly
deterministic stochastic endpoints do not inherit an exactness license or a coverage guarantee. All 84 bounds and every nested-
prefix estimate are retained in the supplement and data record.
Simulation precision and crossed-design scope
Replication budgets, random-stream offsets, confidence level and diagnostic prefixes are declared model inputs. The analysis
protocol is preserved alongside the generating models. Larger replication budgets improve precision conditional on those models;
they do not broaden the sampled population or establish human power. Following simulation-study reporting guidance, indepen-
dent experiments, observations within an experiment and bootstrap resamples retain separate denominators ( Morris et al. 2019 ;
Koehler et al. 2009 ).
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## Page 49

For each displayed contrast, complete paired units are averaged within a fixed stratum. The mean across equally weighted
strata has estimated Monte Carlo standard error √∑ℎ 𝑠2
ℎ/𝑅/𝐻, using the same within-stratum variance as the analytic interval.
Repeated practice windows are averaged within their replicate before this calculation. The Figure 14 uses nested prefixes of the
same generated units. Those prefixes are correlated, and their stabilization is neither an independent replication nor a stopping
rule. The inverse-square-root guide is a precision reference conditional on finite variance, not a fitted law or a criterion for
selecting a favorable result ( Koehler et al. 2009 ).
The recall sensitivity design crosses every declared prior concentration with every declared recall precision. Crossing factors
can reveal response changes that a single-factor perturbation misses, but this finite grid neither samples all plausible generating
mechanisms nor supplies a global variance decomposition ( Saltelli and Annoni 2010 ). The grid, world-weight scenarios and
operating-characteristic controls therefore answer distinct questions: sensitivity to selected model settings, sensitivity to the
estimand’s environmental mixture and performance under known mathematical distributions.
W orld weighting and distribution-sensitive checks
For each positive-recall comparison, exploratory diagnostics report paired means, pointwise intervals, medians, quartiles and
the positive-difference fraction within each world. Brier and observation log loss are losses, so a positive difference is adverse
predictive performance for the first condition. An optimism-readout difference has a different interpretation. Unit quartiles
describe heterogeneity; they are not uncertainty intervals for a mean. Unadjusted world-specific intervals do not license subgroup
significance claims.
For nonnegative world weights summing to one, the target changes to 𝜃(𝑤) = ∑ℎ 𝑤ℎ𝐸[𝐷ℎ](Morris et al. 2019 ). Holding the
estimated world means fixed, the range over all such weights is their minimum to maximum. We also omit one world at a time
and equally weight the remaining worlds. These are conditional sensitivity ranges, not confidence intervals, new observations or
evidence of transport to a human population. They expose assumptions that an equally weighted synthetic average can otherwise
hide.
Statistical operating checks follow the distinction between estimand, procedure and data-generating distribution
(Morris et al. 2019 ; White et al. 2024 ). 6 independent mathematical fixtures span a standard Gaussian null, a +1 SD Gaussian
shift, a variance-standardized Student-t null with 3 degrees of freedom, a centered exponential null, 5 zero-mean Gaussian
strata with standard deviations 0.25, 0.5, 1, 2, 4, and a centered Bernoulli(0.1) null. Distribution shapes are known-answer
controls, independent of gratitude-model parameters; the GNN design declares replication, sample-size and resampling budgets.
All interval methods evaluate the same generated samples. Skewed exponential and Bernoulli differences intentionally violate
sign symmetry. Coverage success is counted over every experiment, with unavailable intervals counted as noncoverage and
availability reported separately. Exact binomial intervals and Monte Carlo standard errors accompany rate estimates. Failures
and undercoverage remain visible; there is no automatic backup procedure or seed selection ( White et al. 2024 ). These checks
characterize tested mathematical conditions, not empirical power for gratitude or a guarantee of coverage on every project
contrast.
Source custody and replay scope
The archived preprint and two preserved notebooks are digest-bound reconstruction inputs, not a moving external dependency.
Their selected numerical behavior is reported separately from the corrected experiments. The supplementary reconstruction
and attention sections retain the adapter scope and source findings. Every numerical producer consumes the preserved GNN
declarations; deterministic replay tests software identity, while independent assessment tests a specified predictive consequence.
S4. Complete results, including adverse and unavailable estimates
Precision across independent sample sizes
The diagnostic retains the signed contrast and its estimated Monte Carlo error at every declared prefix. The recall, reversal-
practice, reversal-gaze and diagnostic-intersection comparisons use their own native loss units and fixed-stratum definitions. Their
magnitudes should not be compared as a common psychological scale. Quartiles and positive-difference fractions are retained in
the machine-readable diagnostic even when the plotted mean is close to zero.
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## Page 50

Figure 14: More independent units improve numerical precision within a fixed model. Rows compare positive-minus-random
recall Brier change, reversal inquiry-minus-rigid practice loss, reversal inquiry-minus-open-utility gaze loss, and integrated-minus-
visual anchored loss for the final declared encoding. Left panels give equal-stratum paired means with one-MCSE whiskers and
a dotted full-budget reference. Right panels show the Monte Carlo standard error and an inverse-square-root guide anchored
at the full budget. Each row retains its own native units. Prefixes retain whole independent paired units within fixed strata;
repeated practice and gaze windows are averaged first. Prefixes share earlier units and are correlated. One-MCSE whiskers do
not claim nominal confidence coverage, and the scaling guide is not a guaranteed error rate. Stabilization and larger samples
do not validate the generating model, repair observation equivalence or establish human efficacy. An empirical constant is not
automatically a mechanism identity.
Exact conditional decisions and rare selections
The exhaustive analysis covered all 25 counts in a window of 24 observations. The open family was selected for channel-0 counts
0, 1, 2, 3, 4, 5, 6, 7, 8; exact ties retain the restriction.
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## Page 51

Process probability P(select open) Expected loss difference
0.15 0.994126513 -0.341492404
0.85 1.43362441e-08 +4.59820882e-09
These are conditional on an effective inquiry with the stated calibration size. The loss difference is evidence-selected minus
restricted prediction in nats per future observation, averaged over every possible calibration count. Probability masses and
selections use exact rational arithmetic; logarithms and loss values are evaluated numerically. There is no Monte Carlo interval.
A vailability, policy history, action cost and human parameter uncertainty are outside this calculation.
The declared process channels (0.15, 0.85) assign different calibration mass to the open-family region: selection is common under
the contradicted process, while a useful restriction retains a small but nonzero adverse-selection tail. Selection on evidence can
therefore help one declared process and slightly worsen another even before inquiry costs are counted. This is a result of the
stated finite repertoire and batch size, not a universal property of openness.
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Figure 15: Exhaustive selection exposes both useful and rare adverse decisions. Every possible channel-zero calibration count is
evaluated under the same admitted restricted and open families. Panel A shows log Bayes factors: circles select open and squares
retain restricted, with zero marking equal evidence. Panels B and C show the same count probabilities on linear and logarithmic
scales. Dotted vertical boundaries mark a change in the selected family between adjacent counts. The log view exposes nonzero
tails that visually merge with zero in the linear view. Count masses are exact finite binomial probabilities evaluated numerically;
they are distributions, not confidence bands, posterior family probabilities or repeated-policy activity rates. Connecting segments
guide the eye between discrete counts. This conditional one-window oracle is independent of the seeded trajectory sample and
does not establish that unrestricted prediction is universally better.
Figure 15 follows Equation (6) ; Equation (7) and Equation (8) average over count outcomes rather than sampled replicates.
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V aluing, choosing and enacting inquiry
Figure 16: Conditional revision must face new observations. Policies choose and fit a working family from calibration evidence
before assessment. The forecast panel compares process probabilities with mean frozen forecasts in reversal windows. Sham and
no-access forecasts equal rigid forecasts exactly and are not overplotted. The comparison panel shows policy-minus-rigid held-out
log loss. Whiskers are pointwise analytic 95% intervals over independent paired replicate averages; curves are descriptive window
means. Negative differences favor the policy in nats per outcome. Inquiry costs are retained separately, and forecast overlap is
a mechanism identity rather than missing data.
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The separate practice extension used 512 independent paired replicates per context and 12 repeated windows per replicate. Each
window contained 24 calibration observations and 512 independently generated assessment observations. Intervals resample
replicate averages; repeated windows are not treated as independent units.
Context / policy Chosen activity Effective access Cost / window
Stationary / Inquiry 0.768 0.768 0.154
Stationary / No
preference
0.225 0.225 0.045
Stationary / Sham 0.768 0.000 0.154
Stationary / No access 0.768 0.000 0.154
Reversal / Inquiry 0.834 0.834 0.167
Reversal / No
preference
0.340 0.340 0.068
Reversal / Sham 0.760 0.000 0.152
Reversal / No access 0.760 0.000 0.152
Context / policy Loss difference Analytic t 95% interval
Stationary / Inquiry +0.0000 [+0.0000, +0.0000]
Stationary / No preference +0.0000 [+0.0000, +0.0000]
Stationary / Sham +0.0000 [+0.0000, +0.0000]
Stationary / No access +0.0000 [+0.0000, +0.0000]
Reversal / Inquiry -0.1047 [-0.1064, -0.1030]
Reversal / No preference -0.0505 [-0.0543, -0.0466]
Reversal / Sham +0.0000 [+0.0000, +0.0000]
Reversal / No access +0.0000 [+0.0000, +0.0000]
Loss differences are policy minus rigid, in nats per held-out observation; negative values favor the policy. All intervals are
pointwise and exploratory, outside the original primary Holm family. Cost is a declared utility charge, reported separately rather
than subtracted from predictive loss. The supplement reports percentile and studentized bootstrap intervals for all 8 contrasts.
All finite mathematical and semantic controls passed.
The policy results make the distinction between aspiration and enactment visible. Sham and no-access agents can value inquiry
and spend its cost while retaining the rigid forecasts exactly. The no-preference condition can still inquire stochastically and
reinforce an observed gain, so its comparison tests the added declared value of examinability rather than all inquiry versus none.
Activity rates, effective access, predictive loss and cost must therefore be read together.
The stationary and reversal contexts also distinguish useful retention from conditional revision. The restricted repertoire contains
good predictors for the stationary process. The reversal interval supplies evidence that its omitted candidate may matter, and
the final interval permits a return to a useful restricted family. These are deliberately diagnostic contexts. Forecast trajectories
are averages of simulated replicates; a trajectory returning toward a channel probability is not a trajectory of contemplative
attainment.
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Figure 17: Choosing an activity does not guarantee access to alternatives. Matched policy conditions separate declared moti-
vation, chosen activity, effective access and expenditure. Within each pair, the solid gray bar on the left shows the fraction of
windows with chosen activity; the hatched teal bar on the right shows effective access. Labels give means to two significant
digits; a visible zero marks no access. Each context uses 512 independent paired replicates and 12 repeated windows. Bars are
descriptive finite means without inferential whiskers; windows are not additional independent agents. Sham and blocked access
can incur activity costs while providing no access. These rates describe software choices, not human adherence or insight.
The upstream interoperability receipt admits 3 practice identifiers and passes the pinned ongoing-revision controls. This is
source-qualified software interoperability, not an independent held-out result for the upstream diagnostic. The new assessment
split, action policy, acquisition/activity charge and blocked-access controls belong to Thanks for Nothing. Full numerical receipts
retain the exact model bytes and all comparisons, including nulls and any unfavorable scores.
The exhaustive stationary probability makes the seeded exact null interpretable: no open-family selection in a particular station-
ary run does not imply that such selection is mathematically impossible. Its probability is small but positive for this batch size.
The conditional oracle and repeated-policy estimates have different denominators and should not be substituted for one another.
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Paired recall, optimism and predictive loss
Figure 18: Complete primary recall contrasts on the fixed world grid. Each target is an equally weighted mean of paired post-
minus-pre changes across the declared worlds. Circles show percentile intervals and diamonds studentized bootstrap intervals;
horizontal values are multiplied by 1000. Negative Brier contrasts favor the first condition, while the optimism readout has a
separate interpretation. Both interval types are pointwise 95% intervals over complete agents within fixed strata. The exact
absence-value null has no studentized interval because variance is zero. Interval overlap does not encode the primary Holm
decision; sign-flip assumptions and Monte Carlo qualification remain separate.
The paired comparisons distinguish three questions: what additional rehearsal does relative to continued learning, what positive
selection does beyond an equal replay dose, and whether a separate valuation changes inference. Changes in the declared
optimism readout are interpreted alongside latent-state Brier error and observation log loss. Agreement among these measures is
possible, but is not imposed as an acceptance criterion. Their disagreement would be informative because each scores a different
property of the model.
Optimism-task change. Estimates and interval bounds are multiplied by 1000.
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Contrast Mean Bootstrap t 95% interval Holm p; MC decision
Positive - None -2.270 [-2.278, -2.262] 0.00098; reject
Random - None -0.017 [-0.031, -0.004] 0.23535; retain
Absence - None 0.000 Unavailable 1.00000; retain
Positive - Random -2.253 [-2.267, -2.239] 0.00098; reject
Brier-loss change. Estimates and interval bounds are multiplied by 1000.
Contrast Mean Bootstrap t 95% interval Holm p; MC decision
Positive - None 0.171 [0.135, 0.207] 0.44312; retain
Random - None 2.177 [2.125, 2.229] 0.00098; reject
Absence - None 0.000 Unavailable 1.00000; retain
Positive - Random -2.005 [-2.066, -1.946] 0.00098; reject
Intervals in this primary table and its accompanying figures are pointwise and unadjusted; the 8-test Holm family retains
simultaneous Monte Carlo tail bounds. The separate gaze rectangle is defined in the joint method . Retain does not establish
equivalence. Bootstrap t is unavailable for the exactly constant valuation null; its zero difference follows from the mechanism.
The interval comparison appendix retains percentile and analytic t intervals. Lower Brier loss is better predictive performance,
not a calibration-only diagnosis.
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Figure 19: Ensemble means and paired changes answer different trajectory questions. The extreme admitted worlds retain all
1024 independent paired agents per world. Upper panels show mean daily beliefs; lower panels subtract each agent’s no-recall
trajectory before averaging and multiply differences by 1000. Markers identify conditions, and the vertical line starts rehearsal.
Shaded bands are between-agent interquartile ranges, including ranges of paired changes below; they are not confidence intervals.
Days and decisions repeat within agents. Shared baselines produce exact paired zeros before rehearsal. Independent predictive
assessments, rather than a smooth belief trajectory, evaluate predictive consequences.
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Figure 20: Predictive loss depends on the world being modeled. The display separates absolute post-learning Brier performance
from paired changes caused by replay. The absolute-loss panel shows means and between-unit interquartile ranges; the contrast
panel compares positive recall with its named references at each fixed world probability. Contrast whiskers are pointwise analytic
95% intervals over 1024 independent paired units per world; interquartile ranges describe spread and are not confidence intervals.
Brier is a loss, so negative contrast values favor positive recall. These exploratory world comparisons do not establish subgroup
significance or isolate calibration from other score components.
W orld heterogeneity and mixture sensitivity
For positive minus no recall, Brier-loss change had an equal-grid mean of 0.000171; 2 world strata had negative means and 3
had positive means. Holding stratum estimates fixed, arbitrary nonnegative world weights yielded [-0.012401, 0.010826]. The
leave-one-world-out range was [-0.002493, 0.003314].
For positive minus no recall, observation log-loss change had an equal-grid mean of 0.002885; 2 world strata had negative means
and 3 had positive means. Holding stratum estimates fixed, arbitrary nonnegative world weights yielded [-0.000541, 0.009078].
The leave-one-world-out range was [0.001336, 0.003741].
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These are exploratory descriptions. Pointwise intervals are not adjusted for subgroup selection, and weighting ranges are sensi-
tivity scenarios rather than confidence intervals. A different world mixture changes the target; opposite signs do not establish
individual human benefit or harm.
Figure 21: A mean effect can conceal variation between paired agents. The display examines the distribution of predictive-
loss differences within each fixed world. Circles and squares mark medians for the named positive-recall comparisons; horizontal
segments show the interquartile range of complete paired units. The vertical axis is quantitative world probability. The segments
are distribution summaries, not confidence intervals; repeated decisions do not enlarge the sample. Negative loss differences favor
positive recall. These exploratory spreads complement, rather than replace, the equally weighted primary target.
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Figure 22: Changing world weights changes the estimand. The analysis reweights the same estimated world means without
generating new agents. Gray segments span all convex world mixtures, orange segments span leave-one-world-out estimates, and
diamonds mark equal weighting. Horizontal values use the multiplier 1000. These are ranges conditional on fixed estimated
means, with no sampling-confidence interpretation. A different population mixture can change the aggregate conclusion. The
ranges quantify that dependence rather than adding independent evidence.
Observed absence and the valuation-only null
Missingness preserved the prior with KL divergence 0.0000 bits; an observed absence produced 0.2577 bits. The imported finite
Blackwell comparator returned Bayes risk 0.2000 for its original channel and 0.5000 under erasure. These are separate declared
finite comparators, not measured psychological or contemplative changes.
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Figure 23: A recorded absence can inform; an unavailable record need not. The fixture compares the same hazard prior under
a functioning detector’s no-event result and the declared missing-observation rule. Bars show state probabilities; annotations
report KL information in bits for A: Observed absence and B: Missing observation. These are exact admitted finite calculations
with no sampling intervals. The no-update missingness rule is stipulated. This control distinguishes informational semantics and
does not measure gratitude or contemplative insight.
Absence appreciation and no recall have the same belief-update path by construction. Their equality is an executable null, and
any assigned appreciation is a reference-dependent valuation. The separate absence audit distinguishes an informative absence
observation from an uninformative observation and from missing evidence. This distinction is a property of the admitted
likelihood and missingness convention, not a claim that every real absence is informative or that an undetected harm is safe.
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Figure 24: Counterfactual value can change without new belief evidence. C: Counterfactual value evaluates an outcome against
a specified alternative while preserving the no-recall inference path. The value panel shows valuation means and between-
unit interquartile ranges. The equality panel reports maximum paired differences in belief, Brier loss and observation log
loss. Interquartile ranges describe unit spread; the paired maxima are exact numerical control quantities rather than estimated
confidence bounds. Equality is imposed by the valuation mechanism. It is a semantic null, not empirical evidence that human
appreciation is independent of belief.
Reconstructing and extending the gaze experiment
The exact 5-pair source run reproduces the published before bars to one decimal place:
Source profile Positive (%) Negative (%) Neutral (%)
Positive template 82.14 10.98 6.88
Negative template 54.62 11.80 33.58
The paper’s after bars are visible as 90.1/6.1/3.8 and 90.6/2.3/7.1 percent in positive/negative/neutral order. They are tran-
scribed observations about its figure, not reproduced values. The preserved executable notebook supplies no corresponding
intervention. Figure 25 therefore shows only the admitted before comparison, with original numeric paths on a newly registered
licensed background.
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Figure 25: The preserved notebook reproduces source-before occupancy only. The same seed 42 and alternating run order drive
the source adapter for 5 runs. Paths show the first 20 locations of the first positive and negative runs; occupancy summaries use
every source run. Lines connect discrete registered model sites. Paths are illustrative and occupancy summaries descriptive; no
executable source-after intervention or uncertainty interval is supplied. This is a new full-frame registration, not recovered eye
tracking. Artwork: Edvard Munch, The Scream (1893), NG.M.00939; photograph Nasjonalmuseet/Børre Høstland; CC BY 4.0;
rescaled with model overlays.
Direct likelihood transfer gave a positive-recall-minus-no-recall change in positive-location probability of +0.038492 [+0.038312,
+0.038670]; multiplying by 100 gives 3.849 percentage points. The corresponding scene-risk change was +0.002362 [+0.002175,
+0.002557] nats per outcome, indicating worse prediction under this bridge. The readout bridge instead gave -0.004677 [-0.004693,
-0.004661] probability units. All brackets are pointwise bootstrap t intervals, not multiplicity-adjusted tests. Open inquiry minus
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restricted utility changed scene-wide prequential log loss by +0.009639 [+0.008892, +0.010535] in the stationary context and
-0.115884 [-0.116824, -0.114765] in the reversal context. Access to the omitted candidate explains the reversal advantage: open
utility and uniform open sampling also improve over the restricted reference. The full table retains the direct inquiry-versus-
open-utility and inquiry-versus-uniform comparisons; their risk intervals include zero.
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Figure 26: A learned channel is transferred through an explicit bridge. Frozen pre/post likelihoods from the same paired agent
drive a distinct scene-sampling task. The positive-recall examples at world settings 0.3, 0.7 show the first 20 of 128 states. The
process, preferences and action uniforms remain paired. These first-agent paths are illustrations without inferential intervals. The
display uses the likelihood embedding, not the alternative readout projection or unavailable source-after code. Artwork: Edvard
Munch, The Scream (1893), NG.M.00939; photograph Nasjonalmuseet/Børre Høstland; CC BY 4.0; rescaled with registered
model overlays.
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Figure 27: An attention shift can coexist with worse prediction. The likelihood bridge transports actual frozen learned channels
into a separate scene task. The upper panels show descriptive pre/post positive-site policy changes by world. The lower panels
show equally weighted paired differences from no recall, keeping attention and scene-loss units separate. Whiskers are pointwise
analytic 95% intervals over complete paired agents. Exact nulls have zero-width analytic intervals and unavailable bootstrap t
intervals. More positive-location policy mass is not necessarily better prediction. The full tables preserve both bridges and every
contrast.
The transfer design contains 5 fixed strata with 1024 paired agents each and 4 conditions, evaluated under 2 bridges. The
resulting 40960 records are repeated conditions and mechanisms for 5120 independent agent-world units, not 40960 independent
participants. We resample whole paired agents within strata and report 16 exploratory transfer contrasts: 4 comparisons, 2
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endpoints and 2 bridges.
The active experiment contains 512 paired replicates per context, 3 windows and 6 policies: 18432 episodes. The 48 observations
per episode are dependent measurements, not independent units. Windows are averaged within each replicate before resampling.
The 7 policy comparisons, 3 endpoints and 2 contexts yield 42 exploratory active-policy contrasts. Every gaze contrast uses 4095
bootstrap draws, with percentile, bootstrap t and analytic t intervals retained. These 58 pointwise intervals do not extend the
original 8-test Holm family and carry no confirmatory p-value claim.
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Figure 28: Access and policy are distinct in active scene sampling. Restricted utility and open inquiry see matched potential
observations in stationary and reversal contexts. Each panel shows 20 samples from the first paired replicate and declared
example window. The background image stays fixed while the supplied regional likelihood changes. These paths illustrate model
decisions without uncertainty bands; the prior resets for each episode. A different scanpath does not identify a contemplative
mechanism. Artwork: Edvard Munch, The Scream (1893), NG.M.00939; photograph Nasjonalmuseet/Børre Høstland; CC BY
4.0; the registration and overlays are authored displays.
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Figure 29: Predictive benefit and movement cost require separate comparisons. Open and restricted policies share a decision
budget and complete paired potential outcomes. Estimates compare each policy’s 3-window average with restricted utility.
Prediction and movement are separate endpoints; uniform open sampling is a same-budget comparator. Whiskers are pointwise
analytic 95% intervals over independent complete replicate averages; proved constant contrasts have zero width. Open access
can help reversal prediction while incurring stationary costs. An inquiry-specific claim additionally requires direct comparison
with already-open utility and uniform sampling, retained in the complete tables.
The strongest supported distinction is structural access under a contradicted restriction. These settings do not establish an
additional scene-risk advantage from the information bonus over open utility or uniform open sampling. In the stationary
setting, a correct restriction remains useful. More visits to a positive region, more uncertainty, a longer path and a lower scene-
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wide loss are different outcomes. Descriptive coverage, revisits, transition entropy and geometric step lengths are available in
the executable gaze companion; none is interpreted as human fixation duration or contemplative attainment.
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Joint gaze uncertainty and the cost of nominal confidence
Figure 30: Selected gaze differences retain their full-family uncertainty. The display compares likelihood transfer, readout
projection, and inquiry against already-open comparators without pooling those mechanisms. Gray circles show pointwise
analytic t bounds; teal diamonds use the single exploratory 58-contrast standardized bootstrap rectangle; purple squares retain
mechanism-exact valuation zeros. Each panel uses its native loss scale. The joint region resamples complete paired vectors
within fixed independent blocks; its nominal level is 95%. The selected display does not shrink the tested family. Bounds neither
establish an extra inquiry-specific benefit nor guarantee finite-sample coverage.
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The exploratory joint region has status complete across 58 contrasts: 48 estimated, 10 mechanism-exact zeros and 0 unavailable
sample constants. Its original-SE-standardized maximum uses 16,383 joint draws and critical value 3.2099. The separate 99%
Monte Carlo bracket for that conditional critical quantile is [3.182691, 3.247739]. This is nominal joint uncertainty under
bootstrap approximation, not measured coverage for the gaze experiment or a new confirmatory testing family. Mechanism
identities supply their own zero contrasts; an accidentally constant sample would remain unavailable.
The joint analysis leaves the point estimates and independent units unchanged. It makes the scope of simultaneous interpreta-
tion explicit, rather than reading a collection of pointwise exclusions as family-level evidence. The direct inquiry-versus-open-
comparator scene-risk contrasts remain compatible with zero under the larger joint rectangle. Access and information-seeking
policy remain different explanations.
Each fixture uses 4096 independent experiments, 64 units per stratum, 6 zero-mean contrasts and 1,023 joint bootstrap draws
per experiment. Coverage requires every target and interval; unavailable cases count as noncoverage. Both coverage columns
give percentages and exact binomial 95% intervals.
Fixture Joint region (%)
Pointwise t, complete
family (%) A vailable (%)
independent gaussian 93.5 [92.7, 94.2] 73.4 [72.0, 74.7] 100.0
correlated gaussian 93.6 [92.8, 94.3] 85.6 [84.5, 86.7] 100.0
heterogeneous gaussian 93.6 [92.8, 94.3] 73.2 [71.8, 74.5] 100.0
centered exponential 88.5 [87.5, 89.5] 69.0 [67.6, 70.5] 100.0
rare bernoulli 1.3 [0.9, 1.7] 1.3 [0.9, 1.7] 1.3
These are operating characteristics of the stated fixtures, not human power or universal coverage. Rare-event sample constants
are not licensed as exact population zeros.
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Figure 31: Nominal family confidence needs known-answer checks. Each independent repetition generates a family whose true
contrasts are all zero; successful coverage must include every target. Circles apply unadjusted analytic t intervals and diamonds
the joint bootstrap rectangle. A separate panel records complete-region availability. Whiskers are exact binomial 95% intervals
over independent experiments. Unavailable regions count as noncoverage; the nominal 95% line is a reference, not a tuned
acceptance rule. Skew-related undercoverage and unavailable rare-event families remain findings. This is statistical software
calibration, not empirical power for gratitude.
These controls distinguish family adjustment from distributional adequacy. Near-nominal performance in a Gaussian fixture
cannot repair the substantial undercoverage in the centered-exponential fixture. The rare-event fixture can produce sample
constants even though its population mean is known; reporting an unavailable region is more informative than inventing certainty
from the sample. No simulated coverage rate licenses a claim about human gratitude or realization.
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Gaze on a scene and inquiry into its encoding
Figure 32: Encoding recovery and reference transfer can diverge. Diagnostic-regime policies are compared with visual-only
sampling for each true encoding: H0, H1, H2. Columns separate anchored excess log loss from encoding Brier loss. Negative
values favor the named policy; squares mark proved constants and crosses unavailable intervals. Bounds use the global 84-member
exploratory bootstrap maximum, including label-only contrasts. Independent paired replicates are resampled within fixed scene
strata. The restricted prior excludes H2. Better encoding Brier loss alone does not establish useful reference prediction.
The joint experiment used 9216 independent paired units across 18 fixed regime/scene/encoding cells, with 512 replicates per
cell and 24 decisions per episode. The 55296 policy episodes are repeated conditions on those units, not additional independent
agents.
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Diagnostic-regime anchored excess-log-loss differences (first policy minus visual-only; nats per outcome) were:
Integrated: H0: -0.10122 [-0.10745, -0.09499]; H1: -0.05443 [-0.06459, -0.04426]; H2: -0.07931 [-0.08658, -0.07204].
Boundary only: H0: 0.00000 [0.00000, 0.00000]; H1: 0.00000 [0.00000, 0.00000]; H2: 0.00000 [0.00000, 0.00000].
Uniform: H0: -0.09643 [-0.10136, -0.09150]; H1: -0.04655 [-0.05581, -0.03729]; H2: -0.06559 [-0.07283, -0.05835].
Restricted: H0: -0.10588 [-0.11029, -0.10147]; H1: -0.05799 [-0.06805, -0.04792]; H2: 0.11568 [0.10111, 0.13025].
Yoked sham: H0: 0.00000 [0.00000, 0.00000]; H1: 0.00000 [0.00000, 0.00000]; H2: 0.00000 [0.00000, 0.00000].
Integrated minus Uniform, anchored regret: H0: -0.00479 [-0.01243, 0.00284]; H1: -0.00788 [-0.02119, 0.00544]; H2: -0.01372
[-0.02399, -0.00345].
Integrated minus Uniform, boundary brier: H0: -0.02105 [-0.05349, 0.01139]; H1: -0.02641 [-0.06071, 0.00788]; H2: -0.01757
[-0.04905, 0.01390].
Integrated minus Boundary only, anchored regret: H0: -0.10122 [-0.10745, -0.09499]; H1: -0.05443 [-0.06459, -0.04426]; H2:
-0.07931 [-0.08658, -0.07204].
Integrated minus Boundary only, boundary brier: H0: 0.05410 [0.02825, 0.07994]; H1: 0.05537 [0.02922, 0.08151]; H2: 0.04817
[0.02399, 0.07235].
The separate 84-contrast exploratory family retained 54 stochastic estimates, 30 mechanism-exact constants and 0 unavailable
sample constants. Bounds use one 95% original-standard-error-standardized empirical-bootstrap maximum across all 6 indepen-
dent regime/H blocks, with 16383 resamples. They do not establish finite-sample coverage or human construct validity.
The conditional critical value was 3.3196; its 99% order-statistic Monte Carlo bracket was [3.2749, 3.3612]. This bracket concerns
bootstrap simulation error, not an additional effect interval.
In the label-only regime, every boundary posterior retained its admitted prior. The restricted-prior Brier differences were
H0: -0.166667; H1: -0.166667; H2: +0.833333, with mechanism-exact bounds; other label-only Brier differences were zero.
Boundary-only inquiry retained the uniform scene posterior. These identities distinguish information, support and joint use of
scene/encoding evidence; posterior entropy is not metacognitive sensitivity.
All 12 independent mathematical/admission controls passed. The sham is a nonautonomous matched-query updater that discards
action identity and ignores adaptive-schedule information. The anchored H=0 score is a declared reference-frame intervention,
not ordinary future prediction under the original scene process.
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Figure 33: The action-response relation can identify what its marginals cannot. The matrices display declared response probabil-
ities conditional on the randomized action, using the middle probe at reliability 0.8. The diagnostic columns differ by encoding;
the label-only channel has no encoding dependence. Shared probability scales and numeric cell labels permit direct comparison.
These are exact channel declarations with no sampling intervals; both separate marginals remain uniform. The information lies
in the paired relation. These finite matrices are not observed eye movements or measured biological boundary channels.
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Figure 34: Spatial gaze and nonspatial questions share one budget. The preselected example uses the first scene, H2, and the
first paired replicate. Upper panels show the first 20 visual samples; lower panels retain all 24 decisions, including contingency
questions. Straight lines connect displayed sites across intervening questions. This is an illustrative trajectory, selected by its
input indices rather than its result; it carries no inferential interval. A question is not a spatial fixation. Artwork: Edvard
Munch, The Scream (1893), NG.M.00939; photograph Nasjonalmuseet/Børre Høstland; CC BY 4.0; registration and overlays
are authored displays.
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Figure 35: Information, prediction and expenditure are separate outcomes. Policies allocate a common decision budget between
scene samples and encoding questions. Points are equal-fixed-stratum means of question allocation, current-scene excess pre-
dictive loss and declared cost; vertical segments show pooled whole-episode interquartile ranges. Each panel retains its own
units. Segments describe whole-unit spread across the fixed scene/encoding mixture, including between-cell variation; they are
not confidence intervals. Repeated decisions are not independent samples. An informative question can reduce scene sampling
even when reference transfer improves. Expenditure and encoding knowledge are not interchangeable with predictive success or
realization.
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Figure 36: More independent agents reduce Monte Carlo error, not structural ambiguity. The preselected H2 case is evaluated
at the declared nested replicate prefixes. Points show paired anchored-risk contrasts averaged over 3 fixed scene strata, alongside
their Monte Carlo standard errors. Horizontal axes are logarithmic. Prefixes share earlier units and are correlated; repeated
decisions do not enlarge the independent N. Point estimates need not change monotonically. The full convergence record retains
both endpoints and all declared contexts. Enlarging N cannot identify observation-equivalent encodings.
What the imported boundary analyses establish
The pinned QRF audit assigned the same complete 64-outcome distribution to 3 label profiles; this equality is constructed,
not fitted from observations. A normalized altered distribution was detected independently. In a separate six-variable Gaussian
fixture, precision-support F1 was 1.00, partial-correlation best F1 1.00, and the best F1 across every possible marginal-correlation
threshold interval was 0.80. Inverting the known full covariance recovered precision to maximum error 4.44e-16. Thus the
threshold limitation does not imply general non-identifiability from joint observations. The upstream perturbation audit retained
200/200 positive-definite draws; its recovery fractions are conditional on that admission. These fixtures and the new sampled
structural-inquiry experiment test different mathematical claims. All 8 upstream integration and independent mathematical
controls passed; actual module, declaration and serialized-API digests are retained.
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Figure 37: Marginal association and conditional independence answer different questions. This separate pinned Realizing Empti-
ness Gaussian fixture compares the known precision matrix with full marginal correlations. The matrices describe the same
Gaussian law. Exhaustive marginal-threshold intervals fail exact blanket recovery, while inversion of the full covariance recov-
ers precision. Entries are deterministic finite mathematical values, not estimated biological correlations or confidence intervals.
Gaussian variables and QRF bit labels name different objects. This comparator is not another participant or observation in the
scene/encoding experiment.
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S5. Mechanistic interpretation and competing explanations
Gratitude as an orientation toward continued inquiry
The stronger proposal is that appreciation can support the practice of examining what seems compulsory in one’s way of
construing experience. Gratitude for an opportunity to inquire need not demand a favorable conclusion. A practice can reveal
that a distinction is contingent while preserving its everyday usefulness; it can also reveal that a particular alternative does not
help. This orientation differs from collecting agreeable evidence. It values the possibility of revising the terms in which evidence
is understood, while continuing to answer to consequences.
The finite extension makes this proposal more demanding than a verbal endorsement. Preference must affect action; action must
actually provide access; accessible comparison must consume evidence; and a selected working representation must face indepen-
dent observations. The sham and no-access nulls show where the chain can break. Their role is not to devalue aspiration, but
to prevent its presence from being counted as an enacted mechanism. The no-preference condition also shows why instrumental
inquiry and appreciation for its possibility need separate identification. Here the latter is declared, not inferred from simulated
behavior or validated as human gratitude.
Useful self/world models can persist after their assumed necessity is questioned ( Sandved-Smith et al. 2026 ). Our model reflects
that point by allowing a restricted working family to be retained or reused when its evidence is better. Returning to useful
distinctions need not reinstate the rule that alternatives are inadmissible: future inquiry remains available. This is the substantive
difference between a representation that is employed and a restriction that cannot be examined. The finite family switch supplies
a constrained analogy; it does not exhaust the source’s physical or contemplative claims.
Practice also has a temporal structure. A moment of insight would not remove changing conditions or the need to examine
future constructions. The repeated reversal design therefore asks about continued revisability rather than a one-way progression
through named attainments. Its costs matter as well. More inquiry can be predictively useful while consuming resources; if an
adequate model already works, the charge can remain without a predictive gain. Our separate cost column makes that possibility
visible instead of declaring every relaxation beneficial.
Examinability , instrumental information and welcome answers
The stipulated opportunity value is not the only reason to seek information. In Kobayashi and Hsu’s actionable-lottery task,
models separated instrumental value, fixed or entropy bonuses and anticipation of future outcomes; the combined anticipatory
account improved behavioral prediction within that task ( Kobayashi and Hsu 2019 ). The authors leave room for different motives
elsewhere. Their comparison does not identify our information coefficient, and the article’s neural results do not supply a neural
interpretation of this model.
Information can also be sought without changing a payoff. In van Lieshout and colleagues’ second experiment, participants could
incur an additional delay to learn an outcome whose payout was already fixed ( Lieshout et al. 2018 ). Their uncertainty predictor
multiplied entropy by the difference in possible payoffs; it was not the pure candidate information gain used here. Willingness
to incur that delay is a useful behavioral measure, but does not itself establish revisability or appreciation.
Together with the patience result ( DeSteno et al. 2014 ), these studies sharpen the proposed mechanism. Inquiry could increase
because information is useful, because good news is anticipated, because delay has become less costly, or because any requested
activity is followed more readily. Appreciation of examinability would require discriminating effects beyond these alternatives. In
particular, valuing examination should remain compatible with learning an unwelcome result and retaining a useful representation.
The current finite models stipulate an orientation and test its enabling consequences; they do not estimate which motive a person
has.
Process evaluation adds a complementary distinction between what is delivered, how it produces change and the context in
which it operates. Moore and colleagues distinguish fidelity to intended delivery, the amount delivered and the audience reached,
while noting disagreement over the boundaries of these implementation components ( Moore et al. 2015 , MRC process evaluation
framework). A human study should therefore record the activity performed, whether the intended opportunity to examine
alternatives was available, how participants used it, and the subsequent independent outcome. Context can change effects even
when implementation is similar. Our separate activity and access rates illustrate the need for distinct records; they are not
validated measures of human fidelity, dose or reach. The guidance motivates a measurement strategy, rather than establishing
that this proposed practice works or that an informative alternative constitutes contemplative realization.
Revisability , useful precision and philosophical sufficiency
Maintaining the distinction between a model and its referent is useful even without a philosophical identification. The same
prediction can survive consistent relabeling of hidden states; a semantic label is not an additional measurement. Our permutation
control checks that prerequisite. The practice extension goes further by making an alternative predictor accessible, but a finite
KL divergence still does not measure emptiness. Lower precision need not mean greater wisdom: it can simply mean poorer
discrimination. This is why the implementation compares explicit predictive models, refits their posteriors, retains useful structure
and scores independent observations rather than rewarding entropy or a label named nondual.
The inspected historical texts encourage care about both existence/non-existence and the residual presence acknowledged when
something is absent ( Thanissaro Bhikkhu 1997b , 1997a). The catalog distinguishes these textual readings from the more limited
access to the philosophical books ( Garfield 1995 , 2001). They do not provide a shortcut from numerical uncertainty to con-
templative realization. Likewise, a computational affect model can offer a formal account while leaving empirical identification
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open ( Hesp et al. 2021 ). The present extension is most useful when these gaps remain visible: philosophical reasoning, human
experience, and algorithmic invariants answer different questions.
Laukkonen and Slagter offer a different predictive-processing account, proposing reduced temporal and conceptual depth and dis-
cussing a radical nondual endpoint while acknowledging differences among traditions ( Laukkonen and Slagter 2021 ). Predictive
switching in our finite menu is neither that proposed endpoint nor an agreed definition of emptiness. A system could improve
reversal prediction yet reify whichever description currently wins. Revisability therefore supplies a candidate enabling condition,
not a sufficient criterion of realizing emptiness. Our positive target is the examinability and conditional use of representations;
the stronger philosophical claim still needs argument beyond a score.
Rehearsal and the choice of a benefit criterion
The central methodological issue is not whether positive-event rehearsal can move a probability. Such movement depends on
the specified selection rule, likelihood, concentration, and update. The harder question is what that movement accomplishes
under an independently defined objective. In this study, the objective is deliberately plural: the optimism readout, latent-state
error, observation prediction, and uncertainty are retained together. A model that feels conceptually more hopeful in its labels
may become less accurate, while a calibrated model may continue to represent an unfavorable world. Neither result should be
concealed by renaming the preferred endpoint well-being.
The source preprint itself supplies an important boundary. It excludes trauma and unstable environments from its initial
simulations and warns that optimism can be maladaptive when favorable opportunities are unavailable ( Fisher et al. 2025 ). The
corrected stationary worlds do not remove that limitation. They improve causal comparison within a finite experiment by
holding exposures fixed, but do not simulate the practical consequences of engagement, withdrawal, protection, grief, or social
support. There is no action-outcome welfare measure demonstrating that optimistic engagement benefits an agent in a dangerous
environment.
Metacognitive gaze without reifying its target
Task-directed human gaze can change which scene regions are sampled ( Castelhano et al. 2009 ). In the inspected counterbalanced
search/memorization experiment, critical search scenes omitted the target; task effects on region selection did not imply the same
effects for every aggregate or early-viewing measure. Those observations motivate treating a gaze task as part of a sampling
process. They do not license reading gratitude, self-understanding or meta-awareness from an altered scanpath.
The new model extends the question from where to look to which relation would make an encoding examinable . Its contribution
is the joint use of visual evidence and contingent questions, together with exact cases where either operation alone is insufficient.
A question can concern the conditions under which a distinction works without discovering a metaphysically privileged boundary.
Label-only equality constrains the claim in the opposite direction: no amount of sampling reveals a difference that the observation
model does not contain. These are complementary limits, not competing descriptions of one dataset.
The proposal about appreciation remains a further link. A person might value the conditions that permit careful inspection,
notice a framing assumption, and choose an informative question. Our integrated agent supplies an explicit finite mechanism
for the last operation. It does not infer that motive from scene behavior or simulate a learned appreciation-to-inquiry transition.
Nelson and Narens’ monitoring/control distinction and Fleming and Lau’s measurement distinctions therefore constrain the
empirical program ( Nelson and Narens 1990 ; Fleming and Lau 2014 ). Posterior certainty can concern an incomplete candidate
menu, and lower entropy can accompany a wrong model. Neither maximum doubt nor maximum certainty is our criterion for
practicing realization of emptiness.
Appreciation without invented evidence
The absence-appreciation condition makes a limited possibility explicit: a value can be assigned relative to a reference without
changing the likelihood or posterior used for state inference. This separation prevents a particular computational error, namely
treating a preferred interpretation as a newly observed favorable event. It also reveals the dependence of appreciation on the
reference. Changing the assumed hazard or cost changes the assigned value even when the experienced observations remain
identical. That dependence is a feature to expose, not an inconvenience to hide.
Human counterfactual reflection may have effects absent from this implementation. Imagining alternatives could change memory,
attention, affect, beliefs about future hazards, or social judgments. Gratitude toward a benefactor may additionally involve
intentions and perceived sacrifice ( Yu et al. 2018 ). It may evoke indebtedness ( He et al. 2022 ). Consequently, the exact belief
null here should be understood as a clean software separation and a candidate empirical contrast, not a prediction that real
appreciation is psychologically isolated from inference.
Interpreting observed absence also requires a detection model. An interval without an alarm can favor safety when alarms
reliably detect harm, convey little when the detector is unreliable, or be misleading when reporting is selectively suppressed.
Our missingness sentinel assumes no update; real missingness may instead be informative. Seaman and colleagues distin-
guish realized and everywhere missing-at-random conditions and explain that ignorability depends on the inference being made
(Seaman et al. 2013, sec. 2 and 5). Their sufficient Bayesian conditions also concern the relation between priors for data and miss-
ingness parameters. A missing symbol alone establishes none of these conditions, and missing at random is not synonymous with
zero information. The finite audit clarifies our choice but does not solve inference under arbitrary observation failure. A model
of gratitude for an absence should therefore state what could have been detected, what was recorded, and how counterfactual
value was assigned.
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S6. What these models do and do not identify
The source reconstruction covers selected numerical cells under a documented adapter. It does not reproduce every interface
action, excluded plotting helper, software environment of the original session, or later version of the notebooks. Detailed paper
analysis is limited to preprint version one; the journal abstract establishes publication identity and broad scope only. The
scholarship catalog records whether each supporting source was inspected in full, at abstract level, or only through bibliographic
metadata. Bibliographic presence alone is not evidence of an effect.
The corrected learning model is intentionally small. It uses discrete valence categories, a fixed world grid, a stationary process
within each stratum, and a restricted observation model. It does not represent interpersonal intentions, memory decay inde-
pendent of the chosen update schedule, self-report demand, embodied behavior, or an agent’s ability to change its environment.
Replay and precision are imposed computational operations. The optimism readout is partly determined by its construction.
Learned gaze transfer now has an explicit embedding, but its sign depends on that mapping and its predictive consequences
can be adverse. The active scene model assumes known candidate channels and a hand-authored region partition; it neither
infers painting semantics from pixels nor fits human eye movements. A richer model is not automatically better; its additional
parameters would require identifiability and predictive tests.
The intersection additionally assumes known query channels, independent uniform scene/encoding priors, an authored cyclic map
and an available reference anchor. It learns within a supplied menu; it does not learn how to construct a new representation or a
metacognitive architecture. Query costs are declared utilities, not measured effort. The matched-query sham ignores the demon-
strator’s adaptive-schedule likelihood. Its numerical identities therefore concern that updater, not complete absence of available
information. Near-deterministic stochastic scores can remain poorly characterized by finite-sample bootstrap approximations
even after numerical centering is corrected.
The practice model has additional, different limits. Its candidate repertoire, structural restriction, neutral channel schedules,
opportunity value, access probability and cost are authored design choices. Restricted and open priors are compared by exact
refitting within an episodic window, not by a fitted model of human metacognition. The reversal context gives the omitted
predictor a known advantage and cannot establish a general advantage of relaxation. Evidence gain is scaled into utility by a
declared coefficient. There is no learned gratitude state, no measurement of first-person realization and no validated translation
from the sector labels to experience. The full appreciation–practice–realization proposal is therefore a conceptual research
program with one executable enabling mechanism, not a completed reduction.
S7. Human research: manipulations, measurements and recovery checks
Distinguishing absence, missingness and valuation
A first study would separate positive-event recall, dose-matched random-event recall, appreciation of an observed uneventful
interval, and counterfactual reflection about avoided harm. It would measure gratitude, relief, indebtedness, perceived safety,
and well-being separately while matching expectancy and task engagement as closely as feasible. The absence and missingness
manipulation would include explicit information about detector reliability. If participants treat missing reports as favorable
evidence despite knowing the detector failed, the resulting behavior would challenge the simplest missingness convention rather
than validate it.
Mechanism testing would require repeated behavioral observations, parameter recovery, alternative models, and held-out predic-
tion. A precision-based explanation should outperform simpler changes in response bias or outcome coding and predict transfer
where transfer is claimed. An attention study could compare pre/post scene behavior while controlling preferences and exposure;
failure of transfer would directly constrain the proposed bridge. An optimism shift accompanied by worse calibration or adverse
outcomes would count against a general benefit claim. Statistical planning would use empirical variability and clinically or
theoretically meaningful outcomes, not the number of synthetic agents reported here.
T esting appreciation, access and appropriate revision
A prospective inquiry study could randomize appreciation of enabling conditions, pleasant-event reflection and neutral factual
reflection, crossed with actual availability of an alternative explanation. Stable and changed contexts would test useful retention
and warranted revision. Recognition probes would measure whether an available alternative was noticed; later independent trials
would evaluate predictions. These are proposed studies, not experiments or preregistrations completed here.
For example, let 𝜇𝑧𝑥 be expected later predictive loss under orientation 𝑧 and assigned access 𝑥. A candidate primary estimand
compares enabling-condition appreciation 𝐸 with pleasant-event reflection 𝑃:
𝜃emp = (𝜇𝐸1 − 𝜇𝑃 1) − (𝜇𝐸0 − 𝜇𝑃 0). (29)
A negative interaction would favor an access-dependent predictive consequence, provided the randomized design, missing-data
plan and intended population justify that interpretation. It would not establish gratitude as the mediator or realization as the
outcome. This estimand would need prospective selection, empirically grounded sample-size planning, a meaningful effect scale
and separate process measures before data collection.
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Rival explanation Discriminating manipulation or measure Observation that constrains the proposal
Pleasant affect or expectancy Pleasant-event comparator and
measured expectations
Only favorable-language ratings change
Instrumental information value Useful and noninstrumental information
at comparable uncertainty
Choices follow expected task benefit
alone
Anticipated good news Welcome and unwelcome information
with usefulness controlled
Inquiry increases only for desired
answers
Patience rather than inquiry value Independently varied delay, effort and
monetary costs
Waiting changes without generalizing to
other inquiry costs
A vailability without awareness Alternative-recognition and
comprehension probes
Alternatives are exposed but neither
noticed nor used
Compliance or indiscriminate doubt Stable accurate and contradicted
representations
Accurate beliefs weaken regardless of
evidence
Temporary task switching Later independent prediction and
renewed access checks
Immediate switching does not sustain
appropriate revisability
An appreciation increase without access or appropriate revision would interrupt the proposed chain. Indiscriminate weakening
of accurate beliefs would fail its retention requirement. Separate social-attribution, curiosity, patience and demand measures
would help compare mechanisms, but adding questionnaires alone would not solve identification. Philosophical interpretation
and first-person reports require their own methods and could disagree with predictive scores.
Before interpreting fitted human parameters, parameter recovery must cover the relevant parameter range, competing models
must be tested through model-recovery confusion matrices, and simulated behavior must reproduce patterns not used for fitting
(Wilson and Collins 2019 ). The initial policy’s value–cost confounding illustrates why exact software replay cannot substitute for
identification. The exhaustive count oracle characterizes this finite menu; a winning menu member may still be an inadequate
explanation. Social attribution and matched positive affect also belong in the inquiry comparison, given the boundaries of costly
interpersonal gratitude ( Bartlett and DeSteno 2006 ). Access and control need separate process measures rather than being
inferred from the final choice ( Sandved-Smith et al. 2021 ).
Finally, adverse and unstable environments should be central boundary conditions in later work rather than extrapolations from
benign worlds. Any human study would need independent ethical review, informed consent, appropriate support, and a design
that does not encourage false reassurance or avoidance of necessary care. These requirements define what new evidence would
be needed. They are not recommendations to deploy the simulated operations as an intervention.
Coupled gaze and boundary inquiry in a human study
Experiential reports would require a specified collection and analysis method. The inspected visual-task study used training
and participant-derived experiential categories before grouping trials for behavioral and EEG analyses ( Lutz et al. 2002 ). We
take this as a methodological example: reports can add constraints to a study, while their interpretation remains distinct from
first-order performance, gratitude and philosophical sufficiency.
A direct empirical extension would combine a scene-search task with an explicit action-contingency task. Participants could
choose scene observations or costly questions about a learned reference mapping; a separate label-only condition would lack
any distinguishing observation law. Randomized action assignments, event-pair identities and access to both components would
be retained. First-order scene/reference predictions, trialwise confidence, encoding judgments, dwell times and spatial sam-
pling would be measured separately. Confidence bias, sensitivity and efficiency would require their own estimands and models
(Fleming and Lau 2014 ).
Equal decision counts would not establish equal effort: query duration, motor demands and the number of observable components
require measurement and appropriate comparators. A replayed-query comparator would need to account for information conveyed
by the demonstrator’s adaptive schedule or explicitly restrict the available record. A reference-frame transfer assessment would
need to instantiate its anchor experimentally, rather than reinterpret an ordinary future trial after the fact. Proper recovery
studies would test omitted encodings, misspecified channels and curiosity-only alternatives before assigning a fitted parameter a
metacognitive meaning.
Crossing that task with enabling-condition appreciation, pleasant reflection and neutral reflection could test the proposed orien-
tation toward examinability. The focal evidence would be appropriate allocation and later prediction, including useful retention,
rather than a generalized rise in doubt or positive reports. An informative action–response relation would identify a task encod-
ing, not the source preprint’s physical or contemplative thesis. Human sample-size planning would require empirical variability,
participant-level dependence and prespecified effect targets; the larger synthetic cohorts cannot supply those quantities.
S8. Source custody, operating diagnostics and complete interval tables
Digest-bound source reconstruction
The primary source is the archived version-one preprint and two separately preserved notebooks: the gratitude/belief-updating
notebook linked by the user and the modified Yarbus notebook identified in the preprint’s code-availability section. Whole-file
digests bind execution to those artifacts. The reconstruction executes selected numerical definitions and cells with isolated
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seeded sampling. It excludes package installation, plotting, downloads, interactive exports, and stored notebook outputs. It is
a bounded headless reconstruction, not a complete replay of the original Colab interface.
The gratitude adapter permits reduced dimensions only through a manifest of integer-literal substitutions in the pinned source.
The original dimensions remain available. Baseline arrays are copied before subsequent mutation so that the reconstruction
can expose aliasing rather than silently correcting it. The Yarbus adapter extracts the original agent class and preserves its
action-first transition convention. Numerical findings are reported separately from static observations about excluded plotting
helpers. This approach makes the source executable while retaining the behavior that the corrected study later changes.
An independent unequal-column-mass example returned posterior well probability 0.9000 from raw counts versus 0.5000 after
column normalization. The seeded source adapter measured a maximum aliased snapshot mutation of 75.6530. The original
plot binning excluded 1 endpoint-grid agent(s). In the attention reconstruction (seed 42, 100 steps), 33 sampled observations
had zero likelihood under the separately declared process. The independent preference-plus-ambiguity oracle matched the source
energy to maximum absolute error 0.
The source audit distinguishes executable facts from judgments about how a model should be interpreted. In the gratitude
notebook, accumulated likelihood entries are used as weights without column normalization. This makes accumulated mass
relevant in addition to relative observation probabilities. Baseline and intervention snapshots are saved at different points relative
to daily learning, and a view of a saved baseline can be mutated during intervention. The phases also change environmental
observation and transition processes, so their before/after difference does not isolate the rehearsal operation. Updating-task
priors are redrawn rather than paired. The implementation’s clamp includes selected positive or neutral observations, whereas
the preprint’s description emphasizes positive-event rehearsal.
These findings motivate the corrected design; they do not demonstrate that every possible count-weight interpretation is invalid.
Nor should a difference in tensor convention be called a defect without checking its use. The Yarbus source indexes its transition
tensor action-first, and that convention is internally valid. Its observation sampling uses the agent likelihood despite a separately
declared environmental likelihood. Its implemented policy score contains a conditional-entropy term, which must not be relabeled
as an independently calculated information-gain quantity. The source’s plotted paths remain illustrative discrete visits with
plotting transformations, not eye-tracking measurements.
Exogenous attention: implementation and interpretation
The attention extension uses a 13-location scene with positive, negative, and neutral categories. The agent consumes declared
likelihood, transition, preference, and initial-state tensors, with the canonical transition axes ordered next state, previous state,
action. Native GNN execution qualifies a matched agent/process model. A separate counterpart invokes the active-inference
agent while holding the environmental observation likelihood fixed across exogenous precision profiles. Preferences and initial
beliefs are perturbed as discriminating controls. Numerical receipts retain observations, actions, beliefs, and policy probabilities.
Category summaries aggregate mean policy probability over the designated locations. They describe model policy mass, not
measured gaze, subjective preference, or a learned effect of gratitude practice. The selective-attention literature motivates this
precision manipulation ( Mirza et al. 2019 ). In an adjacent affect-congruent attention experiment, modeled attention and gaze
were not identical measures, and gaze findings depended on probe type and normalization ( Bennett et al. 2023 ). That study
did not manipulate gratitude. This exogenous comparator has no learning bridge; the separate primary extension in the transfer
model consumes actual frozen learned channels. The distinction between native matched-model qualification and a fixed-process
comparison is essential to interpreting the result.
The positive precision model assigned mean policy probability 0.9870 to positive, 0.0049 to neutral, and 0.0081 to negative
locations over 8 steps.
The negative precision model assigned mean policy probability 0.6218 to positive, 0.3731 to neutral, and 0.0051 to negative
locations over 8 steps.
The attention comparison asks whether changing declared precision profiles changes policy probabilities under the specified agent
and process. It does not estimate a gratitude-to-gaze effect. Native execution and the fixed-process counterpart answer different
qualification questions, so numerical validity of the former cannot substitute for the latter. Preference and initial-prior controls
help establish that the implementation consumes its declared inputs rather than merely returning a plausible-looking path.
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Figure 38: Precision profiles alter policy mass in a fixed-process comparator. Positive and negative attention profiles are
exogenously assigned rather than learned from gratitude rehearsal. Circles and squares identify profiles. Values aggregate policy
probability over the declared positive, negative and neutral sites; all masses, including small negative-site values, are labeled.
Gray connectors compare profiles and are not uncertainty intervals. Native matched-model qualification is separate. These policy
probabilities are neither measured gaze nor evidence of learned transfer.
Statistical operating checks and model sensitivity
Each fixture used 4096 independent experiments, with 64 paired units per stratum, 1023 bootstrap draws and 1023 sign-flip
draws. Methods share each generated sample.
Fixture Percentile cover Analytic t cover Bootstrap t cover t available
Gaussian null 3864/4096 3898/4096 3887/4096 4096/4096
Gaussian shift
(+1 SD)
3860/4096 3893/4096 3881/4096 4096/4096
Heavy-tail null (t,
df=3)
3804/4096 3885/4096 3786/4096 4096/4096
Skewed null
(exponential)
3835/4096 3864/4096 3896/4096 4096/4096
5 Gaussian
variance strata
3869/4096 3895/4096 3891/4096 4096/4096
Discrete null
(Bernoulli 0.1)
3837/4096 3895/4096 1495/4096 1576/4096
Coverage counts use the total denominator: unavailable bootstrap t intervals count as noncoverage. A vailability is shown
separately, without dropping degenerate samples. Exact binomial intervals and Monte Carlo standard errors accompany rates
in the data.
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Mean-zero fixture Rejections
Exact binomial 95%
interval Sign symmetry
Gaussian null 190/4096 [0.040, 0.053] Satisfied
Heavy-tail null (t, df=3) 224/4096 [0.048, 0.062] Satisfied
Skewed null (exponential) 231/4096 [0.050, 0.064] Violated
5 Gaussian variance strata 191/4096 [0.040, 0.054] Satisfied
Discrete null (Bernoulli
0.1)
232/4096 [0.050, 0.064] Violated
For the rare Bernoulli fixture, exact bootstrap t availability under the declared failure rule is 38.82%; observed availability is
38.48%. Unconditional coverage is 36.50%, whereas coverage conditional on an available interval is 94.86%. The exact calculation
benchmarks availability alone; it does not establish a coverage guarantee.
The +1 SD Gaussian control rejected in 4096/4096 experiments (95% binomial interval [0.999, 1.000]). Skewed mean-zero
fixtures deliberately violate the sign-flip assumption; any rejection distortion remains a reported boundary. No seed, benchmark
or method is selected to achieve a desired coverage rate.
Across 25 separately admitted grid cells, the positive-minus-random optimism change contrast ranged from -0.00329 to -0.00128;
the corresponding Brier contrast ranged from -0.00276 to -0.00106. Each cell used 128 independent agents per fixed stratum,
sharing seeds across cells.
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## Page 89

Figure 39: A finite parameter grid tests dependence on declared choices. Each prior-concentration and recall-precision cell is
independently admitted from a modified GNN declaration. Colors show positive-minus-random contrasts in endpoint changes;
the panels retain their own units and zero-centered scales. Cells share seeds and are conditional fixed-grid comparisons, not
independent replications or confidence regions. The grid makes model dependence visible. It does not estimate uncertainty over
unexamined parameters or establish human robustness.
The operating-characteristic output separates successful interval coverage, availability and null rejection. Its exact binomial
intervals describe uncertainty across independent synthetic experiments. Skew and discrete-boundary stressors show where a
mean-zero target does not supply sign symmetry or a usable studentized variance. The controls characterize each tested procedure
and distribution; they do not turn software qualification into empirical validation.
85

## Page 90

Figure 40: Distribution shape limits the interpretation of nominal confidence. Known-answer fixtures test coverage, interval
availability and mean-zero rejection using the same generated samples for every method. The coverage panel spans 6 fixtures
and uses a data-derived detail axis; the rejection panel separates null distributions from the positive-shift control. Bootstrap
t availability is displayed for every fixture. The Bernoulli annotation distinguishes exact availability, observed availability
and coverage conditional on an available interval. Whiskers are exact binomial 95% intervals over independent experiments;
unavailable intervals count as noncoverage. Reference lines are 0.95 coverage and 0.05 rejection. Centered exponential and
Bernoulli differences violate sign symmetry despite zero means. The exact Bernoulli calculation benchmarks availability under
the strict zero-variance failure rule, not coverage. The benchmarks are not retuned to make a method pass.
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## Page 91

Complete primary interval comparisons
The following tables retain all retained pointwise 95% procedures on the same primary contrasts. Display scaling matches the
primary figures. The analytic interval is a robustness approximation outside the single-Gaussian control; unavailable bootstrap
t intervals remain unavailable rather than borrowing another method.
Optimism-task change; all values x1000.
Contrast Percentile 95% Bootstrap t 95% Analytic t 95%
Positive - None [-2.278, -2.263] [-2.278, -2.262] [-2.278, -2.263]
Random - None [-0.031, -0.004] [-0.031, -0.004] [-0.031, -0.004]
Absence - None [0.000, 0.000] Unavailable [0.000, 0.000]
Positive - Random [-2.267, -2.239] [-2.267, -2.239] [-2.267, -2.239]
Brier-loss change; all values x1000.
Contrast Percentile 95% Bootstrap t 95% Analytic t 95%
Positive - None [0.135, 0.207] [0.135, 0.207] [0.135, 0.208]
Random - None [2.124, 2.228] [2.125, 2.229] [2.124, 2.229]
Absence - None [0.000, 0.000] Unavailable [0.000, 0.000]
Positive - Random [-2.064, -1.945] [-2.066, -1.946] [-2.065, -1.946]
Complete practice interval comparisons
All 8 exploratory policy-minus-rigid contrasts retain percentile, studentized bootstrap and analytic t intervals at the paired-
replicate level. Units are nats per held-out observation. Unavailable studentized intervals remain labeled; their degenerate
resample counts are retained in the numerical receipt.
Context / policy Percentile 95% Bootstrap t 95% Analytic t 95%
Stationary / Inquiry [+0.0000, +0.0000] Unavailable (degenerate
sample)
[+0.0000, +0.0000]
Stationary / No preference [+0.0000, +0.0000] Unavailable (degenerate
sample)
[+0.0000, +0.0000]
Stationary / Sham [+0.0000, +0.0000] Unavailable (degenerate
sample)
[+0.0000, +0.0000]
Stationary / No access [+0.0000, +0.0000] Unavailable (degenerate
sample)
[+0.0000, +0.0000]
Reversal / Inquiry [-0.1064, -0.1030] [-0.1064, -0.1029] [-0.1064, -0.1030]
Reversal / No preference [-0.0543, -0.0467] [-0.0543, -0.0466] [-0.0543, -0.0466]
Reversal / Sham [+0.0000, +0.0000] Unavailable (degenerate
sample)
[+0.0000, +0.0000]
Reversal / No access [+0.0000, +0.0000] Unavailable (degenerate
sample)
[+0.0000, +0.0000]
Complete gaze interval comparisons
These tables include all 58 declared contrasts, including direct comparisons between open sampling policies. Estimates retain their
native units. Complete episodes and agents, rather than locations or observations, determine interval precision. Studentization
failures are explicit; the underlying exact null is retained.
T ransfer: likelihood.
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Contrast; endpoint Mean Percentile 95% Bootstrap t 95% Analytic t 95%
Positive - None;
Positive probability
change
+0.038492 [+0.038314,
+0.038673]
[+0.038312,
+0.038670]
[+0.038309,
+0.038674]
Positive - None;
Scene-risk change
+0.002362 [+0.002166,
+0.002548]
[+0.002175,
+0.002557]
[+0.002175,
+0.002549]
Random - None;
Positive probability
change
+0.026996 [+0.026838,
+0.027152]
[+0.026840,
+0.027153]
[+0.026841,
+0.027151]
Random - None;
Scene-risk change
-0.007860 [-0.008103, -0.007621] [-0.008099, -0.007619] [-0.008112, -0.007608]
Absence - None;
Positive probability
change
+0.000000 [+0.000000,
+0.000000]
Unavailable [+0.000000,
+0.000000]
Absence - None;
Scene-risk change
+0.000000 [+0.000000,
+0.000000]
Unavailable [+0.000000,
+0.000000]
Positive - Random;
Positive probability
change
+0.011496 [+0.011280,
+0.011711]
[+0.011282,
+0.011712]
[+0.011281,
+0.011710]
Positive - Random;
Scene-risk change
+0.010222 [+0.009907,
+0.010537]
[+0.009908,
+0.010538]
[+0.009908,
+0.010536]
T ransfer: posterior readout.
Contrast; endpoint Mean Percentile 95% Bootstrap t 95% Analytic t 95%
Positive - None;
Positive probability
change
-0.004677 [-0.004693, -0.004661] [-0.004693, -0.004661] [-0.004694, -0.004661]
Positive - None;
Scene-risk change
+0.000096 [+0.000092,
+0.000100]
[+0.000091,
+0.000100]
[+0.000092,
+0.000100]
Random - None;
Positive probability
change
-0.000051 [-0.000079, -0.000023] [-0.000078, -0.000022] [-0.000078, -0.000023]
Random - None;
Scene-risk change
+0.000026 [+0.000024,
+0.000027]
[+0.000024,
+0.000027]
[+0.000024,
+0.000027]
Absence - None;
Positive probability
change
+0.000000 [+0.000000,
+0.000000]
Unavailable [+0.000000,
+0.000000]
Absence - None;
Scene-risk change
+0.000000 [+0.000000,
+0.000000]
Unavailable [+0.000000,
+0.000000]
Positive - Random;
Positive probability
change
-0.004627 [-0.004657, -0.004599] [-0.004654, -0.004597] [-0.004655, -0.004598]
Positive - Random;
Scene-risk change
+0.000070 [+0.000066,
+0.000074]
[+0.000066,
+0.000074]
[+0.000066,
+0.000074]
Active: stationary .
Contrast; endpoint Mean Percentile 95% Bootstrap t 95% Analytic t 95%
Open utility -
Restricted utility;
Scene risk
+0.009202 [+0.008492,
+0.009968]
[+0.008517,
+0.010023]
[+0.008459,
+0.009945]
Open utility -
Restricted utility;
Positive occupancy
-0.034261 [-0.036431, -0.032132] [-0.036556, -0.032209] [-0.036362, -0.032160]
Open utility -
Restricted utility;
Movement penalty
+0.000964 [+0.000847,
+0.001082]
[+0.000850,
+0.001086]
[+0.000846,
+0.001083]
Open inquiry -
Restricted utility;
Scene risk
+0.009639 [+0.008862,
+0.010479]
[+0.008892,
+0.010535]
[+0.008832,
+0.010447]
88

## Page 93

Contrast; endpoint Mean Percentile 95% Bootstrap t 95% Analytic t 95%
Open inquiry -
Restricted utility;
Positive occupancy
-0.039551 [-0.041865, -0.037277] [-0.041970, -0.037382] [-0.041877, -0.037225]
Open inquiry -
Restricted utility;
Movement penalty
+0.000553 [+0.000437,
+0.000669]
[+0.000440,
+0.000671]
[+0.000441,
+0.000666]
Restricted inquiry -
Restricted utility;
Scene risk
+0.000003 [-0.000034,
+0.000044]
[-0.000032,
+0.000047]
[-0.000036,
+0.000043]
Restricted inquiry -
Restricted utility;
Positive occupancy
+0.001424 [+0.001166,
+0.001709]
[+0.001164,
+0.001716]
[+0.001148,
+0.001701]
Restricted inquiry -
Restricted utility;
Movement penalty
-0.000179 [-0.000238, -0.000124] [-0.000238, -0.000123] [-0.000237, -0.000121]
Sham - Restricted
utility; Scene risk
+0.000000 [+0.000000,
+0.000000]
Unavailable [+0.000000,
+0.000000]
Sham - Restricted
utility; Positive
occupancy
+0.000000 [+0.000000,
+0.000000]
Unavailable [+0.000000,
+0.000000]
Sham - Restricted
utility; Movement
penalty
+0.000000 [+0.000000,
+0.000000]
Unavailable [+0.000000,
+0.000000]
Uniform open -
Restricted utility;
Scene risk
+0.008750 [+0.007942,
+0.009592]
[+0.007950,
+0.009602]
[+0.007923,
+0.009578]
Uniform open -
Restricted utility;
Positive occupancy
-0.606906 [-0.610460, -0.603317] [-0.610493, -0.603334] [-0.610542, -0.603271]
Uniform open -
Restricted utility;
Movement penalty
+0.069156 [+0.068742,
+0.069572]
[+0.068737,
+0.069573]
[+0.068742,
+0.069569]
Open inquiry - Open
utility; Scene risk
+0.000437 [-0.000043,
+0.000918]
[-0.000017,
+0.000957]
[-0.000037,
+0.000911]
Open inquiry - Open
utility; Positive
occupancy
-0.005290 [-0.006700, -0.003893] [-0.006806, -0.003973] [-0.006693, -0.003887]
Open inquiry - Open
utility; Movement
penalty
-0.000411 [-0.000514, -0.000308] [-0.000517, -0.000308] [-0.000515, -0.000307]
Open inquiry -
Uniform open; Scene
risk
+0.000889 [-0.000135,
+0.001964]
[-0.000137,
+0.001956]
[-0.000155,
+0.001933]
Open inquiry -
Uniform open;
Positive occupancy
+0.567356 [+0.563151,
+0.571642]
[+0.562984,
+0.571531]
[+0.563093,
+0.571618]
Open inquiry -
Uniform open;
Movement penalty
-0.068603 [-0.069032, -0.068183] [-0.069017, -0.068175] [-0.069029, -0.068176]
Active: reversal.
Contrast; endpoint Mean Percentile 95% Bootstrap t 95% Analytic t 95%
Open utility -
Restricted utility;
Scene risk
-0.115899 [-0.116915, -0.114866] [-0.116828, -0.114730] [-0.116933, -0.114865]
Open utility -
Restricted utility;
Positive occupancy
-0.328586 [-0.331394, -0.325675] [-0.331356, -0.325587] [-0.331494, -0.325678]
Open utility -
Restricted utility;
Movement penalty
-0.000588 [-0.000799, -0.000368] [-0.000809, -0.000377] [-0.000804, -0.000373]
89

## Page 94

Contrast; endpoint Mean Percentile 95% Bootstrap t 95% Analytic t 95%
Open inquiry -
Restricted utility;
Scene risk
-0.115884 [-0.116868, -0.114839] [-0.116824, -0.114765] [-0.116929, -0.114839]
Open inquiry -
Restricted utility;
Positive occupancy
-0.335232 [-0.338230, -0.332334] [-0.338052, -0.332119] [-0.338137, -0.332327]
Open inquiry -
Restricted utility;
Movement penalty
-0.001136 [-0.001338, -0.000930] [-0.001343, -0.000935] [-0.001340, -0.000933]
Restricted inquiry -
Restricted utility;
Scene risk
-0.000033 [-0.000071,
+0.000005]
[-0.000072,
+0.000004]
[-0.000072,
+0.000006]
Restricted inquiry -
Restricted utility;
Positive occupancy
+0.001289 [+0.001044,
+0.001560]
[+0.001041,
+0.001566]
[+0.001025,
+0.001552]
Restricted inquiry -
Restricted utility;
Movement penalty
-0.000150 [-0.000209, -0.000093] [-0.000212, -0.000095] [-0.000208, -0.000092]
Sham - Restricted
utility; Scene risk
+0.000000 [+0.000000,
+0.000000]
Unavailable [+0.000000,
+0.000000]
Sham - Restricted
utility; Positive
occupancy
+0.000000 [+0.000000,
+0.000000]
Unavailable [+0.000000,
+0.000000]
Sham - Restricted
utility; Movement
penalty
+0.000000 [+0.000000,
+0.000000]
Unavailable [+0.000000,
+0.000000]
Uniform open -
Restricted utility;
Scene risk
-0.114215 [-0.115239, -0.113110] [-0.115212, -0.113041] [-0.115285, -0.113145]
Uniform open -
Restricted utility;
Positive occupancy
-0.593872 [-0.597421, -0.590350] [-0.597410, -0.590268] [-0.597454, -0.590290]
Uniform open -
Restricted utility;
Movement penalty
+0.067621 [+0.067178,
+0.068087]
[+0.067152,
+0.068071]
[+0.067168,
+0.068073]
Open inquiry - Open
utility; Scene risk
+0.000015 [-0.000565,
+0.000595]
[-0.000553,
+0.000615]
[-0.000570,
+0.000601]
Open inquiry - Open
utility; Positive
occupancy
-0.006646 [-0.008296, -0.005018] [-0.008400, -0.005119] [-0.008286, -0.005006]
Open inquiry - Open
utility; Movement
penalty
-0.000548 [-0.000656, -0.000442] [-0.000658, -0.000443] [-0.000656, -0.000441]
Open inquiry -
Uniform open; Scene
risk
-0.001669 [-0.003012, -0.000253] [-0.003080, -0.000332] [-0.003064, -0.000274]
Open inquiry -
Uniform open;
Positive occupancy
+0.258640 [+0.254304,
+0.263075]
[+0.254268,
+0.263073]
[+0.254221,
+0.263059]
Open inquiry -
Uniform open;
Movement penalty
-0.068757 [-0.069169, -0.068339] [-0.069177, -0.068343] [-0.069182, -0.068331]
Exact constant contrasts have zero-width percentile and analytic intervals; the bootstrap t method reports degenerate_sample
rather than manufacturing an interval. Probability endpoints are in probability units; loss uses natural-log nats per outcome;
movement is the GNN-weighted unit-square distance per sampled step.
Complete joint gaze bounds
These bounds belong to the single exploratory family in the joint method . Each is expressed in the same native units as its
pointwise estimate. The family status and conditional critical-quantile bracket appear in the joint results . Exact identities are
distinct from unavailable sample constants; no stochastic bound is borrowed from another method.
T ransfer: likelihood.
90

## Page 95

Contrast; endpoint Joint 95% bounds Status
Positive - None; Positive probability
change
[+0.038193, +0.038790] estimated
Positive - None; Scene-risk change [+0.002055, +0.002668] estimated
Random - None; Positive probability
change
[+0.026742, +0.027250] estimated
Random - None; Scene-risk change [-0.008273, -0.007448] estimated
Absence - None; Positive probability
change
[+0.000000, +0.000000] mechanism exact
Absence - None; Scene-risk change [+0.000000, +0.000000] mechanism exact
Positive - Random; Positive probability
change
[+0.011145, +0.011847] estimated
Positive - Random; Scene-risk change [+0.009708, +0.010736] estimated
T ransfer: posterior readout.
Contrast; endpoint Joint 95% bounds Status
Positive - None; Positive probability
change
[-0.004704, -0.004650] estimated
Positive - None; Scene-risk change [+0.000089, +0.000102] estimated
Random - None; Positive probability
change
[-0.000095, -0.000006] estimated
Random - None; Scene-risk change [+0.000023, +0.000028] estimated
Absence - None; Positive probability
change
[+0.000000, +0.000000] mechanism exact
Absence - None; Scene-risk change [+0.000000, +0.000000] mechanism exact
Positive - Random; Positive probability
change
[-0.004674, -0.004580] estimated
Positive - Random; Scene-risk change [+0.000064, +0.000076] estimated
Active: stationary .
Contrast; endpoint Joint 95% bounds Status
Open utility - Restricted utility; Scene
risk
[+0.007988, +0.010416] estimated
Open utility - Restricted utility; Positive
occupancy
[-0.037694, -0.030828] estimated
Open utility - Restricted utility;
Movement penalty
[+0.000770, +0.001158] estimated
Open inquiry - Restricted utility; Scene
risk
[+0.008320, +0.010959] estimated
Open inquiry - Restricted utility;
Positive occupancy
[-0.043351, -0.035751] estimated
Open inquiry - Restricted utility;
Movement penalty
[+0.000369, +0.000737] estimated
Restricted inquiry - Restricted utility;
Scene risk
[-0.000062, +0.000068] estimated
Restricted inquiry - Restricted utility;
Positive occupancy
[+0.000972, +0.001876] estimated
Restricted inquiry - Restricted utility;
Movement penalty
[-0.000273, -0.000084] estimated
Sham - Restricted utility; Scene risk [+0.000000, +0.000000] mechanism exact
Sham - Restricted utility; Positive
occupancy
[+0.000000, +0.000000] mechanism exact
Sham - Restricted utility; Movement
penalty
[+0.000000, +0.000000] mechanism exact
Uniform open - Restricted utility; Scene
risk
[+0.007398, +0.010103] estimated
Uniform open - Restricted utility;
Positive occupancy
[-0.612847, -0.600966] estimated
Uniform open - Restricted utility;
Movement penalty
[+0.068480, +0.069831] estimated
91

## Page 96

Contrast; endpoint Joint 95% bounds Status
Open inquiry - Open utility; Scene risk [-0.000338, +0.001212] estimated
Open inquiry - Open utility; Positive
occupancy
[-0.007582, -0.002997] estimated
Open inquiry - Open utility; Movement
penalty
[-0.000582, -0.000240] estimated
Open inquiry - Uniform open; Scene risk [-0.000816, +0.002595] estimated
Open inquiry - Uniform open; Positive
occupancy
[+0.560391, +0.574320] estimated
Open inquiry - Uniform open;
Movement penalty
[-0.069299, -0.067906] estimated
Active: reversal.
Contrast; endpoint Joint 95% bounds Status
Open utility - Restricted utility; Scene
risk
[-0.117588, -0.114210] estimated
Open utility - Restricted utility; Positive
occupancy
[-0.333338, -0.323834] estimated
Open utility - Restricted utility;
Movement penalty
[-0.000940, -0.000236] estimated
Open inquiry - Restricted utility; Scene
risk
[-0.117591, -0.114177] estimated
Open inquiry - Restricted utility;
Positive occupancy
[-0.339979, -0.330486] estimated
Open inquiry - Restricted utility;
Movement penalty
[-0.001469, -0.000804] estimated
Restricted inquiry - Restricted utility;
Scene risk
[-0.000096, +0.000030] estimated
Restricted inquiry - Restricted utility;
Positive occupancy
[+0.000858, +0.001719] estimated
Restricted inquiry - Restricted utility;
Movement penalty
[-0.000245, -0.000055] estimated
Sham - Restricted utility; Scene risk [+0.000000, +0.000000] mechanism exact
Sham - Restricted utility; Positive
occupancy
[+0.000000, +0.000000] mechanism exact
Sham - Restricted utility; Movement
penalty
[+0.000000, +0.000000] mechanism exact
Uniform open - Restricted utility; Scene
risk
[-0.115964, -0.112467] estimated
Uniform open - Restricted utility;
Positive occupancy
[-0.599724, -0.588020] estimated
Uniform open - Restricted utility;
Movement penalty
[+0.066882, +0.068359] estimated
Open inquiry - Open utility; Scene risk [-0.000941, +0.000972] estimated
Open inquiry - Open utility; Positive
occupancy
[-0.009326, -0.003966] estimated
Open inquiry - Open utility; Movement
penalty
[-0.000724, -0.000372] estimated
Open inquiry - Uniform open; Scene risk [-0.003948, +0.000611] estimated
Open inquiry - Uniform open; Positive
occupancy
[+0.251420, +0.265860] estimated
Open inquiry - Uniform open;
Movement penalty
[-0.069452, -0.068061] estimated
Complete scene/boundary intersection bounds
The following is a separate 84-member exploratory family. Z scene strata are fixed and equally weighted; paired independent
replicates are the resampling units. Anchored loss refers to the stipulated H=0 reference intervention. Exact nonzero offsets
retain their adverse or favorable signs. Unavailable constants, if any, do not receive artificial zero-width intervals.
92

## Page 97

Regime / H Contrast Endpoint Mean Joint interval Status
diagnostic / H0 Integrated -
Visual only
Anchor loss -0.101220 [-0.107449,
-0.094991]
estimated
diagnostic / H0 Integrated -
Visual only
Boundary Brier -0.612571 [-0.638418,
-0.586724]
estimated
diagnostic / H0 Boundary only -
Visual only
Anchor loss 0.000000 [0.000000,
0.000000]
mechanism exact
diagnostic / H0 Boundary only -
Visual only
Boundary Brier -0.666667 [-0.666667,
-0.666667]
estimated
diagnostic / H0 Uniform - Visual
only
Anchor loss -0.096426 [-0.101357,
-0.091495]
estimated
diagnostic / H0 Uniform - Visual
only
Boundary Brier -0.591520 [-0.614552,
-0.568488]
estimated
diagnostic / H0 Restricted -
Visual only
Anchor loss -0.105880 [-0.110288,
-0.101473]
estimated
diagnostic / H0 Restricted -
Visual only
Boundary Brier -0.616534 [-0.641923,
-0.591145]
estimated
diagnostic / H0 Yoked sham -
Visual only
Anchor loss 0.000000 [0.000000,
0.000000]
mechanism exact
diagnostic / H0 Yoked sham -
Visual only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
diagnostic / H0 Integrated -
Uniform
Anchor loss -0.004794 [-0.012426,
0.002838]
estimated
diagnostic / H0 Integrated -
Uniform
Boundary Brier -0.021051 [-0.053491,
0.011389]
estimated
diagnostic / H0 Integrated -
Boundary only
Anchor loss -0.101220 [-0.107449,
-0.094991]
estimated
diagnostic / H0 Integrated -
Boundary only
Boundary Brier 0.054096 [0.028249,
0.079943]
estimated
diagnostic / H1 Integrated -
Visual only
Anchor loss -0.054426 [-0.064589,
-0.044263]
estimated
diagnostic / H1 Integrated -
Visual only
Boundary Brier -0.611300 [-0.637446,
-0.585153]
estimated
diagnostic / H1 Boundary only -
Visual only
Anchor loss 0.000000 [0.000000,
0.000000]
mechanism exact
diagnostic / H1 Boundary only -
Visual only
Boundary Brier -0.666667 [-0.666667,
-0.666667]
estimated
diagnostic / H1 Uniform - Visual
only
Anchor loss -0.046550 [-0.055812,
-0.037287]
estimated
diagnostic / H1 Uniform - Visual
only
Boundary Brier -0.584887 [-0.608699,
-0.561076]
estimated
diagnostic / H1 Restricted -
Visual only
Anchor loss -0.057989 [-0.068054,
-0.047924]
estimated
diagnostic / H1 Restricted -
Visual only
Boundary Brier -0.625979 [-0.648755,
-0.603203]
estimated
diagnostic / H1 Yoked sham -
Visual only
Anchor loss 0.000000 [0.000000,
0.000000]
mechanism exact
diagnostic / H1 Yoked sham -
Visual only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
diagnostic / H1 Integrated -
Uniform
Anchor loss -0.007876 [-0.021187,
0.005435]
estimated
diagnostic / H1 Integrated -
Uniform
Boundary Brier -0.026412 [-0.060705,
0.007881]
estimated
diagnostic / H1 Integrated -
Boundary only
Anchor loss -0.054426 [-0.064589,
-0.044263]
estimated
diagnostic / H1 Integrated -
Boundary only
Boundary Brier 0.055367 [0.029220,
0.081514]
estimated
diagnostic / H2 Integrated -
Visual only
Anchor loss -0.079314 [-0.086584,
-0.072044]
estimated
diagnostic / H2 Integrated -
Visual only
Boundary Brier -0.618498 [-0.642679,
-0.594317]
estimated
diagnostic / H2 Boundary only -
Visual only
Anchor loss 0.000000 [0.000000,
0.000000]
mechanism exact
diagnostic / H2 Boundary only -
Visual only
Boundary Brier -0.666667 [-0.666667,
-0.666667]
estimated
93

## Page 98

Regime / H Contrast Endpoint Mean Joint interval Status
diagnostic / H2 Uniform - Visual
only
Anchor loss -0.065590 [-0.072833,
-0.058347]
estimated
diagnostic / H2 Uniform - Visual
only
Boundary Brier -0.600923 [-0.621706,
-0.580141]
estimated
diagnostic / H2 Restricted -
Visual only
Anchor loss 0.115680 [0.101109,
0.130252]
estimated
diagnostic / H2 Restricted -
Visual only
Boundary Brier 1.127626 [1.110108,
1.145144]
estimated
diagnostic / H2 Yoked sham -
Visual only
Anchor loss 0.000000 [0.000000,
0.000000]
mechanism exact
diagnostic / H2 Yoked sham -
Visual only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
diagnostic / H2 Integrated -
Uniform
Anchor loss -0.013723 [-0.023993,
-0.003454]
estimated
diagnostic / H2 Integrated -
Uniform
Boundary Brier -0.017575 [-0.049050,
0.013901]
estimated
diagnostic / H2 Integrated -
Boundary only
Anchor loss -0.079314 [-0.086584,
-0.072044]
estimated
diagnostic / H2 Integrated -
Boundary only
Boundary Brier 0.048169 [0.023988,
0.072349]
estimated
label only / H0 Integrated -
Visual only
Anchor loss -0.000195 [-0.001288,
0.000898]
estimated
label only / H0 Integrated -
Visual only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H0 Boundary only -
Visual only
Anchor loss 0.113064 [0.111446,
0.114681]
estimated
label only / H0 Boundary only -
Visual only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H0 Uniform - Visual
only
Anchor loss 0.005338 [0.001974,
0.008701]
estimated
label only / H0 Uniform - Visual
only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H0 Restricted -
Visual only
Anchor loss -0.000195 [-0.001288,
0.000898]
estimated
label only / H0 Restricted -
Visual only
Boundary Brier -0.166667 [-0.166667,
-0.166667]
mechanism exact
label only / H0 Yoked sham -
Visual only
Anchor loss -0.000195 [-0.001288,
0.000898]
estimated
label only / H0 Yoked sham -
Visual only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H0 Integrated -
Uniform
Anchor loss -0.005533 [-0.008889,
-0.002177]
estimated
label only / H0 Integrated -
Uniform
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H0 Integrated -
Boundary only
Anchor loss -0.113259 [-0.114819,
-0.111698]
estimated
label only / H0 Integrated -
Boundary only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H1 Integrated -
Visual only
Anchor loss 0.000142 [-0.001480,
0.001763]
estimated
label only / H1 Integrated -
Visual only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H1 Boundary only -
Visual only
Anchor loss 0.112967 [0.111599,
0.114334]
estimated
label only / H1 Boundary only -
Visual only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H1 Uniform - Visual
only
Anchor loss 0.004775 [0.001831,
0.007719]
estimated
label only / H1 Uniform - Visual
only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H1 Restricted -
Visual only
Anchor loss 0.000142 [-0.001480,
0.001763]
estimated
label only / H1 Restricted -
Visual only
Boundary Brier -0.166667 [-0.166667,
-0.166667]
mechanism exact
94

## Page 99

Regime / H Contrast Endpoint Mean Joint interval Status
label only / H1 Yoked sham -
Visual only
Anchor loss 0.000142 [-0.001480,
0.001763]
estimated
label only / H1 Yoked sham -
Visual only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H1 Integrated -
Uniform
Anchor loss -0.004634 [-0.007733,
-0.001534]
estimated
label only / H1 Integrated -
Uniform
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H1 Integrated -
Boundary only
Anchor loss -0.112825 [-0.114504,
-0.111147]
estimated
label only / H1 Integrated -
Boundary only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H2 Integrated -
Visual only
Anchor loss -0.000270 [-0.001567,
0.001027]
estimated
label only / H2 Integrated -
Visual only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H2 Boundary only -
Visual only
Anchor loss 0.112203 [0.110722,
0.113684]
estimated
label only / H2 Boundary only -
Visual only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H2 Uniform - Visual
only
Anchor loss 0.003161 [0.000451,
0.005871]
estimated
label only / H2 Uniform - Visual
only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H2 Restricted -
Visual only
Anchor loss -0.000270 [-0.001567,
0.001027]
estimated
label only / H2 Restricted -
Visual only
Boundary Brier 0.833333 [0.833333,
0.833333]
mechanism exact
label only / H2 Yoked sham -
Visual only
Anchor loss -0.000270 [-0.001567,
0.001027]
estimated
label only / H2 Yoked sham -
Visual only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H2 Integrated -
Uniform
Anchor loss -0.003431 [-0.006028,
-0.000834]
estimated
label only / H2 Integrated -
Uniform
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
label only / H2 Integrated -
Boundary only
Anchor loss -0.112473 [-0.113747,
-0.111198]
estimated
label only / H2 Integrated -
Boundary only
Boundary Brier 0.000000 [0.000000,
0.000000]
mechanism exact
S9. Model settings injected from admitted declarations
Model / setting Admitted value
study seed 20261015
study replicates 1024
study luckiness 0.1, 0.3, 0.5, 0.7, 0.9
study baseline days 7
study intervention days 7
study steps per day 12
study recall count 3
study recall precision 4
study learning rate 2
study forgetting 1
study prior concentration 8
study bootstrap draws 8191
study permutation draws 8191
study assessment trials 70
study task prior min 0.05
study task prior max 0.95
study sensitivity replicates 128
study sensitivity prior concentrations 1, 2, 8, 32, 128
95

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Model / setting Admitted value
study sensitivity recall precisions 0.25, 1, 4, 16, 64
study calibration replicates 4096
study calibration sample size 64
study calibration bootstrap draws 1023
study calibration permutation draws 1023
study evaluation trials 1024
study reference hazard 0.3
study harm cost 1
practice seed 1729
practice replicates 512
practice calibration samples 24
practice assessment samples 512
practice bootstrap draws 4095
practice action precision 6
practice practice cost 0.2
practice examinability preference 0.4
practice previous gain weight 1
practice metacognitive access 1
practice prior precision 2
gaze seed 91073
gaze source seed 42
gaze source steps 1000
gaze source runs 5
gaze transfer steps 128
gaze transfer ambiguity weight 0.5
gaze transfer precision 1.5
gaze trajectory steps 20
gaze example strata 0.3, 0.7
gaze example window 1
gaze replicates 512
gaze steps 48
gaze bootstrap draws 4095
gaze action precision 4
gaze information weight 4
gaze saccade cost 0.2
gaze structural model emptiness_practice
gaze initial location 10
gaze regions 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2
boundary seed 620715
boundary replicates 512
boundary steps 24
boundary prefixes 16, 32, 64, 128, 256, 512
boundary probe reliabilities 0.65, 0.8, 0.95
boundary probe costs 0.02, 0.05, 0.1
boundary endpoints anchored_regret, boundary_brier
boundary gaze model gaze
boundary anchor mapping 0
boundary joint seed 620716
joint seed 91074
joint draws 16383
joint confidence 0.95
joint monte carlo confidence 0.99
joint calibration experiments 4096
joint calibration units 64
joint calibration draws 1023
replicates 1024
practice reversal schedule 0.85 for 4 windows; 0.15 for 4 windows; 0.85 for 4 windows
practice stationary probability 0.85
boundary middle reliability 0.8
S10. Textual editions, translation choices and comparison limits
The Figure 2 adds further edition-specific distinctions. Guru Nanak’s Japji is read in Sant Singh Khalsa’s undated translation,
with the conclusion and immediate context separately identified ( Guru Nanak, n.d. , ang 1, pauris 1–2). The Analects reciprocity
96

## Page 101

exchange is located under different numbering in the two inspected editions: Legge’s edition and Eno’s teaching translation
(Confucius 2002, XV.23 ; 2015, 15.24 ). Kulp’s Avot wording is lot, with its psalm and labor context retained ( Kulp, n.d.-b, 4:1 ).
The Qur’an addition separates translation from tafsir, as before ( Khattab, n.d.-b, 31:12 ), and the Gītā addition distinguishes
sacrificial participants in the verses from modern commentary’s broader analogies ( Swami Mukundananda, n.d.-b, 3.10–13 ). Our
MMK summary is an attributed paraphrase of the inspected Sanskrit e-text, whose print-source field is blank; the digital con-
version date does not date Nāgārjuna or establish a critical edition ( Nagarjuna 2020, 24.8–10 and 24.18). The source companion
attaches these qualifications to the authored comparison rows. The selective atlas gives no common scale and makes no claim
about traditions or witnesses omitted from it.
The expanded main-text comparison uses named primary-text editions. Thich Nhat Hanh’s Heart Sutra rendering is explic-
itly a contemporary revision; its explanation is attributed to the translator rather than silently treated as ancient scripture
(Thich Nhat Hanh 2014 ). The Bhagavadgītā quotation follows Mukundananda’s Translation field, distinguished from his com-
mentary ( Swami Mukundananda, n.d.-a ). Christian thanksgiving follows the NRSVUE text, whose date identifies translation
copyright (New Revised Standard Version Updated Edition 2021). The Qur’an passage follows the credited Khattab translation
rather than the site’s tafsir ( Khattab, n.d.-a ). Mishnah wording follows Joshua Kulp’s named version; the Talmudic blessing
and discussion follow the separately identified William Davidson annotated English edition ( Kulp, n.d.-a ; Berakhot, n.d. ). The
ellipsis within the short blessing excerpt belongs to that displayed edition. Rolt’s Pseudo-Dionysius translation is Christian
theological writing rather than a biblical passage; interleaved translator notes remain distinct from the translated argument
(Pseudo-Dionysius the Areopagite, n.d. ). Where an edition’s publication year was not established, the bibliography leaves it
undated. These targeted readings do not constitute a systematic or philological survey, establish historical influence, or support
a shared psychological mechanism.
The main text quotes Ṭhānissaro Bhikkhu’s catalogued translations of the Kaccayanagotta discourse and the Cula-suññata
discourse ( Thanissaro Bhikkhu 1997b , 1997a). The Access to Insight edition identifies translation copyright separately from its
later site revision. Current dhammatalks editions revise introductions, notes and some wording; those later translator notes
are interpretations and are not silently substituted for the cited discourse. A separately inspected Bhikkhu Sujato comparison
preserves the absent/present distinction and the conditioned character of refined concentration. It is a translation comparison,
not an assertion of doctrinal consensus. The source dossier records exact pages, segments, acquisition failures and quotation
checks. The added readings distinguish a translated discourse from its translator’s introduction, and ancient composition from an
inspected translation or digital edition’s publication. Siderits’ account explains the reliance on transmitted texts and subsequent
interpretation ( Siderits 2026, sec. 1 ). These witnesses do not supply unmediated access to a single original doctrine. The
Epictetus citation follows the visually inspected scanned title and pages; the conflicting TEI date remains disclosed in the source
dossier. These texts constrain the philosophical interpretation of nothingness; they do not validate a gratitude intervention or
identify Bayesian model revision with the realization they describe.
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*Extraction method: pypdf*