# Full Text: Active FractalRabbit: A Synthetic Benchmark for Belief Filtering Under Sparse Waypoint Observations

> Extracted from `Friedman_2026_Active_d676159d.pdf`

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Active FractalRabbit: A Synthetic Benchmark for Belief Filtering Under
Sparse Waypoint Observations
Daniel Ari Friedman
ORCID: 0000-0001-6232-9096
DOI: 10.5281/zenodo.21330636
July 12, 2026

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Contents
Abstract 3
1 Introduction: Sparse W aypoints Need Belief Filters and Claim Guards 3
1.1 Sparse Waypoint Evidence Is Fragmentary, Not a Track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Research Questions and Evidence Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Variational Diagnostics Expose Belief, Preference, and Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 The Contribution Is a Bounded Evidence Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Methods: Artifact-First POMDP Benchmarking on Synthetic W aypoints 5
2.1 The Research Loop Writes Evidence Before Claims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 The Default Configuration Defines the Tensor Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Estimands, Information Sets, and Fairness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Statistical Procedures Are Pinned Before Any Verdict . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.5 Roadmap Analyses Run as Executable Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.6 Formal Model: Belief Filtering Under Bounded Policy Proxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.6.1 The POMDP Surface Separates Hidden Cells from Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.6.2 The Partial-Observability Protocol Tests Marginalize Versus Commit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.6.3 The Policy Score Is a Proxy, Not Full Expected Free Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Results: Belief Helps Only When Emissions Are Noisy 8
3.1 Noisy Emissions Reward Belief Marginalization, Not Point Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1.1 Soft Marginalization Beats Point Estimation as Emissions Degrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Nulls, Calibration, and Multiplicity Keep Gains Bounded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2.1 Recovery Calibration Faces Uniform, Base-Rate, and Persistence Nulls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4 Discussion: Belief Filtering Earns a Regime-Bound Role 13
4.1 A Reader’s Model Map: Match the Predictor to the Information Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.1.1 Online Adaptation Repairs Fixed Dynamics Without Winning the Switching Lane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2 The Fair Ladder Assigns Most Gain to Soft Marginalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.3 The Regime Map Keeps the Advantage Sparse and Noisy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.4 Oracle Asymmetry and Cross-Generator Nulls Block Promotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.5 Bayesian Mechanics Frames the Waypoint Particle as a Bounded Analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.6 Governance Sources Bound Interpretation, Not Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5 Limitations: Synthetic Evidence Does Not Promote Real-T race Claims 16
5.1 The Generator and Lanes Bound Reproducibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5.2 Performance Language Remains Blocked by SOTA Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.3 Scoring and Holdout Limits Keep Nulls Local . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.4 Roadmap Artifact Boundaries Block Deployment Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6 Roadmap: Promotion Stays Blocked by Evidence Gates 17
6.1 Current Evidence Stops at Synthetic Artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6.2 Near-Term Model Gates Need Fresh External Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6.3 State-of-the-Art Gates Remain Uncleared . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
6.4 AIF Deepening Must Admit Predictive Candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6.5 Real-Trace Claims Require a Separate Empirical Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
7 Conclusion: A Synthetic Benchmark Can Clarify Without Promoting 20
7.1 Recovery and Minimization Stay Null-Bounded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
7.2 Roadmap Advances Still Leave Performance Gates Closed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
7.3 pymdp Adds Interpretability Rather Than Performance Leadership . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
7.4 The Final Boundary Is an Honesty Stack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
8 Supplementary S1 - V alidation Gates Preserve Synthetic-Only Claims 21
8.1 Tests Protect Artifacts Before Prose Claims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
8.2 Guardrails Block Claim Drift and Evidence Laundering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
8.3 Real Traces Require Empirical and Privacy Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
8.4 Risk and Integrity Gates Stay Synthetic Proxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
8.5 The Claim Contract Catches Manuscript Overreach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
8.6 Token Provenance Runs Before Rendering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
9 Supplementary S2 - Reproducibility Runs Through Artifacts and Render Checks 22
9.1 Fixture-First Commands Rebuild the Study Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
9.2 Code and Data A vailability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
9.3 Inventories and Checksums Bind the Release Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
9.4 The External Toolchain Boundary Stays Stochastic and Pinned . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
10 Supplementary S3 - F ractalRabbit Becomes Categorical Evidence, Not Real Mobility 24
10.1 The Pinned Upstream Contract Defines the Fixture Lane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
10.2 Fractal Dimension Is a Generator Knob, Not a Real-Trajectory Estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
10.3 CSV Parameters Expose Only Part of the Upstream Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
10.4 The Parser Consumes a Narrow Waypoint Record Contract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
10.5 The Observation Model Converts Waypoints into Finite Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
10.5.1 Categorical Features Bound the Evidence Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
10.5.2 Spatial States Are Analysis Cells, Not Simulator Internals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
10.5.3 Temporal, Kinematic, and Burst Features Remain Heuristic Cues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
10.5.4 Fractal-Dimension Sweeps Shift Occupancy Through the Same Discretizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

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11 Supplementary S4 - F ormal Diagnostics Stay Proxies and Provenance Checks 26
11.1 pymdp Adds Interpretability Without Predictive Leadership . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
12 Supplementary S5 - Closed-Loop Ranking Remains a Non-Controller 26
12.1 Candidate Ranking Is a Heuristic, Not a Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
12.2 Sporadic-Observation Fit Stays Synthetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
12.3 Recovery Is Measured Across the Sparsity Lane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
12.4 Holdout Scoring Remains Additive Under Fixed Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
13 Supplementary S6 - Fixture Diagnostics Bound Sensitivity and pymdp Agreement 27
13.1 Sensitivity and Negative Controls Falsify Easy Wins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
13.2 pymdp Agreement Is an Implementation Check, Not a Win . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
13.3 Spatial-Resolution Diagnostics Choose the Reporting Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
14 Supplementary S7 - Program Extensions Add Gates, Not Promotion 35
14.1 Robustness Artifacts Record Synthetic Realization Spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
14.2 Sequence and Reporting Gates Strengthen the Nulls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
14.3 Lane-Resolved Gates Keep Fixture and External Evidence Separate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
14.4 Forward Gates Promote Only Bounded Synthetic Positives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
14.5 Gap Filling Still Faces the Persistence Oracle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
14.6 Expected Free Energy Separates Epistemic and Pragmatic Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
14.7 Detection, Structure Recovery, and Minimization Stay Program Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
15 Supplementary S8 - Safety and Privacy Analyses Stay Synthetic Risk Proxies 44
15.1 Factorial pymdp Diagnostics Expose Modes Without Cognitive Claims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
15.2 Location-Minimization and Integrity Gates Stay Oversight-Positive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
15.3 Privacy Frontier and External Evidence Do Not Certify Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
15.4 The Privacy-Utility Frontier Shows What Survives Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
16 Supplementary Confound T axonomy Keeps Apparent Wins Auditable 50
16.1 Where, How Much, and Why: A Per-Regime Mechanism Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
16.2 A Structural Diagnostic: Where Within the Trajectory the Loss Sits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
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Abstract
Sparse waypoint analysis is privacy-sensitive: it must separate movement from irregular reporting, missingness, spatial coarsening, and corruption while preserving
uncertainty about hidden location. Active FractalRabbit provides a controlled, artifact-bound benchmark whose headline lane uses a deterministic project-local
synthetic FractalRabbit-format fixture; a separately retained lane exercises pinned open-source software from the National Security Agency as an independent
simulator surface. The benchmark converts sporadic reports into categorical evidence, fits explicit hidden-state generative models, and compares transparent
temporal, Markov, sequence, state-space, neural, latent-state, and active inference predictors under matched information sets. Under noisy partial-observability,
Active Inference is the lowest-loss implemented predictor: it clearly leads point-estimate and raw-observation families and sits in a statistical tie with the
strongest non-AIF belief-preserving comparator. The shared mechanism is soft Bayesian marginalization, which preserves probability across plausible cells
instead of committing early to one state. Point estimates suffice for clean observations, an online base-rate predictor leads under regime switching, transparent
temporal and disclosed kinematic controls anchor sparse reporting gaps, and withholding location sharply limits specific-cell recovery from metadata. The
partially observable Markov decision process (POMDP) formulation also exposes variational and expected-free-energy diagnostics for belief, minimization, and
integrity. These results establish a regime-specific synthetic model map and a reproducible evidence chain. The present contract covers synthetic software
behavior; separate evidence protocols govern privacy and empirical evaluation. Code, fixtures, manuscript source, and the release manifest are public at
github.com/ActiveInferenceInstitute/active_fractal_rabbit.
1 Introduction: Sparse W aypoints Need Belief Filters and Claim Guards
1.1 Sparse W aypoint Evidence Is F ragmentary , Not a Track
Sparse waypoint evidence is a privacy-sensitive analytic problem because the raw material is incomplete, irregular, and easy to overinterpret. Mobility traces can
remain highly identifying, can be matched across datasets, and cannot be treated as safe merely because they are sparse or synthetically represented [ de Montjoye
et al. , 2013, Kondor et al. , 2020, Buchholz et al. , 2024]. A device may report only when an application wakes, a vehicle may emit a location only at sparse
event boundaries, a consented field study may retain only coarse checkpoints, or an analyst may intentionally minimize direct location while keeping timing and
metadata. In each case the observed record is not a track. It is a sequence of fragments shaped by movement, reporting cadence, missingness, spatial binning,
and possible corruption. A few reports can therefore look like a route, a reporting artifact, a routine break, or an integrity failure depending on which uncertainty
model and which null comparison the analyst brings to the data.
The practical challenge is to make those alternatives separable. A sparse waypoint system should be able to say when a location observation is genuinely
informative, when timing or burstiness is only a reporting-process cue, when a method is quietly using oracle-like information, when a minimization choice
removes too much utility, and when an apparent anomaly is just a corruption or null-model failure. The modeling problem is therefore not merely to draw lines
between reports or maximize a next-cell score. It is to expose the evidence chain from raw emissions to categorical observations, hidden-state beliefs, predictive
losses, minimization tradeoffs, and claim boundaries.
This manuscript uses synthetic data because that evidence chain needs controlled ground truth before it should be tried on real traces. Transparent nulls and
base-rate models establish what occupancy alone predicts. Persistence and Markov baselines measure the value of previous-cell information and short memory
(sec. 14.2). Hidden Markov, particle, and state-space models infer an unobserved cell sequence through a noisy observation channel. Sequence and neural
comparators test whether richer predictors improve prequential next-cell loss under the same anti-leakage contract [ Dawid, 1984, Gneiting and Raftery , 2007].
Partially observable Markov decision process (POMDP) and active-inference models make beliefs, observations, preferences, policy evaluation, and uncertainty
diagnostics explicit. The comparison therefore places active inference alongside HMM, particle, and state-space filters as a first-order uncertainty-aware model
family [ Kaelbling et al. , 1998, Rabiner, 1989, Arulampalam et al. , 2002, Doucet et al. , 2001, Patterson et al. , 2008, 2017]. This shared arena reveals which
information regime rewards each family and measures minimization choices before empirical use.
A longer historical vocabulary helps only if it is kept in its lane. Early work on chance, conjecture, inverse probability, utility under risk, perception, induction,
experimental caution, population records, aggregate statistics, legal intrusion categories, inspection, and enumeration provides context for why evidence, uncer-
tainty, observation, and governance have to be named carefully [ Huygens, 1657, Bernoulli, 1713, de Moivre , 1718, Bernoulli, 1738, Bayes and Price , 1763, Laplace,
1774, Berkeley, 1709, Locke, 1690, Hume, 1748, Kant, 1781, Boyle, 1661, Newton, 1729, Graunt, 1662, Halley, 1693, Sinclair, 1791, Blackstone, 1765, Bentham,
1791, United States Census Bureau , 1790]. These sources are historical anchors, not technical ancestors of this implementation: they do not anticipate POMDP
tensors, active inference, modern information privacy, real-mobility validation, or surveillance readiness.
Scope. The evidence covers synthetic software behavior under declared generator, emission, split, and scoring contracts. Minimization and linkage
quantities are synthetic risk proxies; differential privacy, legal compliance, empirical human-mobility validity, and operational use each require their
own evaluation protocol [ Dwork, 2006, European Parliament and Council , 2016, Buchholz et al. , 2024]. The many model gates remain exploratory,
while the unanimous partial-observability construction carries its separate mechanism-level replication contract. Real-trace evaluation follows sec. 6.5.
That boundary matters because sparse waypoint analysis now sits near real commercial location-data and connected-vehicle governance debates. Commercially
available information policy materials and location-data enforcement actions make the policy relevance visible, while surveillance-theory work explains why
recombined traces can acquire meaning beyond any one dataset [ Haggerty and Ericson , 2000, Office of the Director of National Intelligence , 2022, 2024, Federal
Trade Commission , 2024, 2026]. This manuscript uses those sources only to motivate minimization, uncertainty, and responsible interpretation; they do not
validate the technical benchmark or support operational readiness.
Synthetic mobility generation is useful for that arena because it gives the analyst controlled ground truth without importing the consent, provenance, and re-
identification risks that real traces carry [ Barbosa et al. , 2018, Kulkarni et al. , 2018, Dirmeier et al. , 2024, Wei et al., 2021]. But synthetic data are not automatically
useful or private just because their summary statistics resemble a target domain. Synthetic urban-mobility reviews emphasize practical applicability limits, while
recent synthetic-trajectory work emphasizes task-based evaluation and separate privacy analysis: the generated trace must support the specific inference question
being tested, downstream utility can fail in real-life tasks even when summaries look plausible, privacy-preserving daily-trajectory synthesis remains a separate
mechanism and data-source claim, and the benchmark must say which claims remain outside the evidence [ Kapp et al. , 2023, Deng et al. , 2025, Kapp and
Mihaljevic, 2023, Ozaki et al. , 2025, Buchholz et al. , 2024].
1.2 Research Questions and Evidence Boundary
The benchmark is organized around three questions. First, when does preserving a distribution over hidden cells improve prediction relative to committing to a
point estimate? Second, where does the active-inference implementation sit after the locked split, transition source, observation channel, and information set are
matched to the strongest fair baselines? Third, how much recoverability remains when location is withheld or coarsened for minimization?
The answers form a regime map. Soft marginalization improves prediction when a noisy emission hides the current cell. Within that regime, active inference
ranks first among the implemented predictors, clearly ahead of models that commit to a point estimate or raw observation and statistically tied with the strongest
non-AIF belief filter (sec. 3.1.1.1). Clean observations favor simpler point predictors; latent switching favors online adaptation; and location minimization sharply
reduces specific-cell recovery. The external simulator remains a separate reproducibility surface, and every result resolves to a generated artifact or formal contract.
The current external landscape is broader than any one generator. GPT-style mobility generation, trajectory-LLM survey taxonomies, reversible trajectory-to-
CNN transforms, large synthetic mobility datasets, and LLM-guided diffusion generators across cities all define future comparator families or evaluation directions
[Haydari et al. , 2024, Xu et al. , 2025, Merhi et al. , 2024, Yuan et al. , 2026, Liu et al. , 2026a]. They do not validate FractalRabbit, and they are not scored here;
their role is to keep the future baseline map honest about sequence, grid, diffusion, and language-model families the current synthetic fixture does not cover.
FractalRabbit is useful for this purpose because the public, open-source National Security Agency software produces synthetic sparse waypoint reports from a
stochastic point process, a retro-preferential trajectory process, and a sporadic reporting process [ Darling, 2018, National Security Agency , 2026a]. The headline
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experiments use a deterministic project-local FractalRabbit-format fixture with controlled ground truth; the separately retained upstream lane exercises the
pinned NSA software and preserves its provenance as an independent simulator surface. Together these lanes keep the analysis centered on missing reports, return
structure, observation uncertainty, and reproducible software behavior.
That same design prevents a common overreach: simulator output is not empirical mobility validation against known regularities, scaling behavior, or predictability
limits in real human trajectories [ Gonzalez et al. , 2008, Song et al. , 2010a,b]. Those predictability limits are themselves task- and binning-dependent — estimates
shift with the prediction target and temporal aggregation [ Ikanovic and Mollgaard , 2016] — which is a further reason to treat simulator output as a controlled
testbed, not a statement about real mobility. FractalRabbit lets this manuscript ask questions about uncertainty, minimization, and integrity without making
surveillance claims; the supplement documents the pinned simulator boundary, while the main text uses it only as the setting for a bounded methodological
comparison.
Figure 1: Sources observations.csv, discrete_features.csv, metrics.json, spatial_resolution_frontier.json, model_gate_matrix.json, forward_gates_summary.json,
efe_location_frontier.json, linkage_risk_frontier.json, and poisoning_robustness.json feed one orientation atlas. It traces sparse synthetic reports through
categorical evidence, belief updating, model gates, minimization, and integrity checks. The chip strip places the partial-observability positive beside the Holm
multiplicity result, so the reader sees the main finding and its claim discipline together. Evidence: front-loaded orientation to the artifact-bound synthetic evidence
chain and safety guardrails. Boundary: surveillance readiness, real-map inference, operational tasking, or empirical mobility validation.
fig. 1 previews the whole evidence path before the technical sections unpack it: synthetic waypoint reports become categorical evidence, categorical evidence
updates hidden-state beliefs, belief traces face null gates, and the remaining outputs are bounded by minimization and integrity checks.
1.3 V ariational Diagnostics Expose Belief, Preference, and Minimization
Active inference supplies a useful diagnostic vocabulary for this kind of benchmark because it separates what the analyst believes, what the analyst observes, what
the analyst prefers, and which policies would reduce uncertainty or satisfy preferences. In discrete-state POMDP form, the generative model distinguishes hidden
states, observations, transitions, priors, preferences, and policy evaluation within the broader free-energy and active-inference literature [ Kaelbling et al. , 1998,
Friston, 2010, Friston et al. , 2017, 2023a, Da Costa et al. , 2020, Sajid et al. , 2021a, Champion et al. , 2024, Parr et al. , 2022, Smith et al. , 2022]. Navigation-specific
active-inference work has used maze planning, synthetic spatial foraging, and hierarchical robot-navigation settings to study planning as inference [ Kaplan and
Friston, 2018, Neacsu et al. , 2022, Catal et al. , 2021]. Those studies are related-work context only: they do not validate this generator, this waypoint task, or any
performance claim. Partial-observability work outside mobility likewise treats hidden-state prediction as an explicit modeling problem, including attention-guided
state-prediction approaches that are useful comparator context but are not implemented in this benchmark [ Limanjaya and Kang , 2026]. For sparse waypoints,
that separation matters: a high-confidence cell posterior, a high-surprise report, a policy preference, a minimization decision, and an information-seeking action
are different objects and should not be collapsed into a single “tracking quality” score. The benchmark therefore treats active inference as a structured model
class to explore alongside simpler belief filters and baselines, not as a foregone performance winner.
The same scholarship also sharpens the negative space around the implementation. Expected-free-energy work contains canonical decompositions, reformulations,
and links to Bayesian design and decision-theoretic objectives; those sources support careful notation, not rhetorical promotion [ Millidge et al. , 2021, Sajid et al. ,
2021b, Champion et al. , 2024, Sweeney et al. , 2026]. This manuscript therefore keeps the real pymdp expected-free-energy trace, the transparent preference
cross-entropy proxy, and the fair predictive-loss gates as distinct surfaces. An EFE diagnostic can make belief, preference, and epistemic value inspectable, but it
cannot substitute for a locked-split predictive win, a formal privacy guarantee, or empirical mobility validation.
Variational inference makes uncertainty and minimization inspectable within this framework. The benchmark uses active inference as an instrument panel rather
than as a license for stronger claims. Variational free energy records report-level surprise under the current synthetic generative model. Expected free energy
decomposes policy value into epistemic and pragmatic components, making it possible to ask whether location evidence is informative, whether metadata secretly
recovers location, and whether an acquisition policy beats a blind schedule while remaining a non-operational benchmark question, not a collection recommendation.
Belief trajectories show how much uncertainty remains when direct location is withheld. These diagnostics are especially useful in privacy-sensitive analysis because
they surface uncertainty and minimization instead of hiding them behind a single accuracy number.
The pymdp implementation gives this manuscript a real active-inference lane for discrete state spaces while the transparent reference filter keeps the arithmetic
auditable [ Heins et al. , 2022, infer-actively, 2026a,b]. The pymdp lane is run inside the same experiment surface as the reference lane, and its state inference is
validated against the exact Bayes posterior at every step (sec. 11.1). When the two lanes diverge under policy selection, that divergence is treated as evidence
about action-conditioned priors and expected-free-energy control, not as a hidden implementation win.
1.4 The Contribution Is a Bounded Evidence Chain
Active FractalRabbit: A Synthetic Benchmark for Belief Filtering Under Sparse Waypoint Observations connects these pieces into an artifact-bound methods
study. It discretizes synthetic sporadic waypoints into analysis cells, constructs categorical evidence for location, time, speed, and reporting bursts, and compares
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## Page 6

transparent nulls, Markov and persistence baselines, sequence/state-space families, and active-inference lanes. The transparent reference lane makes belief
updating auditable. The pymdp lane adds variational free energy, policy posterior, expected-free-energy surfaces, and action-conditioned prior traces (sec. 11.1).
The predictive ladder then identifies where latent-state inference improves loss, which component supplies the gain, and where simpler models remain sufficient.
The current contribution is the artifact-bound claim discipline around that comparison. Spatial-resolution analysis separates observed-location fit from no-
location recovery. Calibration moves from weak uniform floors to stricter base-rate and persistence nulls in the synthetic benchmark. Gap filling is scored against
a persistence oracle rather than celebrated as path reconstruction. Reporting-process gates test whether timing structure is movement information or reporting
behavior. Public next-location datasets can contain substantial trajectory overlap, with performance varying sharply by overlap status [ Luca et al. , 2023]. Here,
traveller-disjoint splits prevent one synthetic traveller’s history from contributing to both parameter estimation and holdout scoring, while temporal holdouts
separately test forward prediction; prequential scoring preserves prediction-before-observation order [ Dawid, 1984]. These controls reduce specific leakage paths
without proving generalization. Factorial pymdp diagnostics expose movement and synthetic reporting-mode factors without converting them into real cognitive,
intent, or behavior claims. Safety-boundary artifacts then ask what location contributes to epistemic value, what minimization does to aggregate linkage risk,
and whether variational free energy can flag crude input corruption. A family-wise multiplicity audit (Holm and Benjamini–Hochberg) over every directional
comparison in the clustered-bootstrap family closes that discipline: none survives correction, so the one fair-by-construction positive — established outside that
family by unanimous sign-stability across independent generator draws — stands alone, and the location-minimization frontier is reported together with its
predictive-utility dual so the governance tradeoff is visible rather than asserted.
The contribution is a synthetic evidence chain for responsible analytic development: what each model infers on a controlled trace, which predictors lead under each
information regime, which apparent gains dissolve against stronger nulls, and how minimization changes recoverability. Adjacent hidden Markov and state-space
movement models provide the immediate comparison context [ Patterson et al. , 2008, 2017], while consented empirical validation defines the next evidence layer.
The rest of the manuscript follows that sequence. The simulator boundary is defined before the observation model; the observation model is inspected before
active-inference diagnostics; the diagnostics are tested against nulls before performance language; and roadmap items become executable gates before they are
promoted as claims. The central noisy-emission belief-filtering result is specified in sec. 2.6.2 and reported first in sec. 3.1.1. In the partial-observability regime,
soft Bayesian marginalization beats a hard point estimate as the emission degrades: from 0 nats at a clean channel to 0.739 nats at emission flip probability 0.400
on the primary fixture draw, replicating at a mean of 0.495 nats and sign-stable across 10 independent generator draws — a synthetic software measurement that
never beats the oracle-fed baseline. Its fair-comparison ladder, explicit model-selection map, and bounded Bayesian-mechanics analogy are synthesized in sec. 4.1
and sec. 4.5. The remaining handoffs are the fractal-dimension control in sec. 10.2, the measured pymdp distinction in sec. 11.1, the sequence and reporting-process
gates in sec. 14.2, and the forward gates in sec. 6.3.
2 Methods: Artifact-First POMDP Benchmarking on Synthetic W aypoints
2.1 The Research Loop W rites Evidence Before Claims
The pipeline is organized as a closed research loop rather than a one-shot parser, following reproducible-computational-research practice that keeps inputs, scripts,
intermediates, and software identifiers inspectable [ Sandve et al. , 2013, Wilson et al. , 2017, Smith et al. , 2016]. After the opening evidence atlas in fig. 1, this
section narrows the same story to its artifact contract: a configured run resolves a FractalRabbit-compatible CSV, validates and sorts waypoint rows, derives
categorical observations, constructs normalized POMDP tensors, filters latent spatial-state beliefs, scores inference quality, and ranks the next simulator candidate.
Figure 2: From the figure generator and from source pipeline modules, this panel summarizes the rendered artifact dataflow: pinned simulator or checked fixture,
evidence-model artifacts, dual inference lanes, claim-gate artifacts, figure registry, and manuscript variables. Every drawn box resolves to an auditable local
artifact, so the reader can trace claims without trusting prose alone. Evidence: traceability from simulator boundary through generated manuscript variables.
Boundary: trust in prose without artifacts.
fig. 2 is generated from the source pipeline modules and summarizes the artifact contract as five columns: an input boundary (the pinned generator or fixture CSV,
yielding only waypoint observations), an evidence model (discretized categorical features and tensor summaries), the inference lanes (the reference Bayes-filter
trace and the pymdp trace), the claim gates (null and risk artifacts), and the reader handoff (the figure registry and manuscript variables). No step in this pipeline
imports private simulator internals or real-world mobility labels.
2.2 The Default Configuration Defines the T ensor Surface
The default configuration uses the grid spatial discretizer with 4 bins per axis, 4 time-of-day bins, speed thresholds 10, 50, 150 km/day, burst rule median_positive,
and controls empirical_continuation, high_entropy_exploration. The emitted POMDP likelihood tensors have shapes 16 x 16 , 4 x 16 , 4 x 16 , 2 x 16 , while
the transition tensor has shape 16 x 16 x 2 .
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2.3 Estimands, Information Sets, and F airness
The primary estimand is the mean paired held-out next-cell log-loss difference between two predictors under the same synthetic split. Traveller is the resampling
unit: reports from one traveller remain clustered, and the holdout is traveller-disjoint from training. Transition parameters are learned from the training portion
only. A known observation channel is a declared synthetic condition for the partial-observability mechanism test, not information silently learned from the holdout.
The oracle-fed persistence comparator is retained as an information-asymmetry ceiling and is never presented as a fair competitor.
Every fair comparison receives the same observations, candidate-cell support, transition source, scoring rule, and reporting protocol; only the inferential operation
named by the comparison is changed. Point estimates commit to the most likely cell, whereas soft filters retain the full emission posterior. Active-inference
diagnostics are therefore interpreted at two levels: predictive loss for the locked comparison, and variational or expected-free-energy quantities for mechanism
inspection. Bootstrap intervals, independent-generator replication, and multiplicity records qualify which differences can be promoted. The optional external lane
is kept separate from the fixture estimand because it changes simulator provenance and is not evidence about real mobility.
2.4 Statistical Procedures Are Pinned Before Any V erdict
Every active-inference-versus-fair directional comparison that enters the multiplicity family is defined as a paired predictive-score difference: the same held-out
synthetic reports are scored by two predictors, then the loss differential is summarized rather than comparing unmatched aggregate losses [ Diebold and Mariano ,
1995]. The interval is traveller-clustered because reports within one traveller are not exchangeable independent rows: whole travellers are resampled with
replacement, per-step losses are pooled only after the traveller draw, and the 95% interval is the percentile interval of the bootstrapped mean paired difference
[Efron and Tibshirani , 1994, Field and Welsh , 2007, Cameron and Miller , 2015]. The one exception is deliberate: the partial-observability soft-versus-hard positive
sits outside this bootstrap family and is instead established by unanimous sign-stability across independent generator draws (sec. 3.2.1.1). The one-sided p-value
is the Davison-Hinkley achieved significance level (1 + #{̄𝑑∗
𝑏 ≤ 0})/(𝐵 + 1), read from the same bootstrap distribution as the interval so the two can never disagree.
The regime-search family uses B = 2000 resamples per comparison over a 40-traveller synthetic population and reports each regime at its worst (largest) p over its
2 realization seeds - a pinned, conservative choice; the cross-generator lanes use B = 2000. Multiplicity is controlled at significance level 0.050 by Holm-Bonferroni
(primary; valid under arbitrary dependence) with Benjamini-Hochberg at q = 0.100 as a secondary false-discovery report [ Holm, 1979, Benjamini and Hochberg ,
1995]. The smallest reportable p at these replicate counts is 5.00e-04, which sits below the family-wide Bonferroni per-comparison threshold of 5.56e-03 - correction
survival was achievable in principle, so the corrections are not vacuous by construction. These intervals and p-values are descriptive software measurements on
the pinned synthetic generator. They are not population inference, do not estimate field deployment performance, and do not add a Diebold-Mariano test to the
pipeline.
2.5 Roadmap Analyses Run as Executable Gates
The current study treats roadmap ideas as executable stages rather than prose promises. The fractal-dimension sweep in sec. 10.2, the circadian-phase prior gate
in sec. 14.7, the sequence and reporting-process gates in sec. 14.2, and the benchmark matrix in sec. 11.1 all write JSON artifacts before figures and manuscript
variables are generated.
This ordering is intentional: an idea enters the manuscript as a gate, then a generated artifact, and only then a bounded claim if the artifact clears its own nulls.
That keeps speculative directions separate from promoted claims while still advancing the research program, and it makes claim review possible without relying
on prose memory.
2.6 F ormal Model: Belief Filtering Under Bounded Policy Proxies
2.6.1 The POMDP Surface Separates Hidden Cells from Observations
The active-inference analysis uses a discrete POMDP-style generative model, following the convention that hidden states generate observations and policies induce
transitions [ Kaelbling et al. , 1998, Friston, 2010, Friston et al. , 2017, 2023a, Da Costa et al. , 2020, Parr et al. , 2022, Smith et al. , 2022, Heins et al. , 2022]. In this
scaffold the hidden state is the discretized spatial cell from eq. 21.
For each observation modality 𝑚, the likelihood tensor is:
𝐴(𝑚)
𝑜,𝑠 = 𝑃 (𝑜(𝑚)= 𝑜 ∣ 𝑠), ∑
𝑜
𝐴(𝑚)
𝑜,𝑠 = 1. (1)
The configured transition controls define:
𝐵(𝑢)
𝑠′,𝑠 = 𝑃 (𝑠𝑖+1 = 𝑠′ ∣ 𝑠𝑖 = 𝑠, 𝑢𝑖 = 𝑢), ∑
𝑠′
𝐵(𝑢)
𝑠′,𝑠 = 1. (2)
Prior preferences and initial-state priors are represented as:
𝐶 (𝑚)
𝑜 = log 𝑃pref(𝑜(𝑚)= 𝑜), 𝐷 𝑠 = 𝑃 (𝑠0 = 𝑠). (3)
The default modality set (location, time-of-day, speed, reporting-burst), the control set, and the emitted tensor shapes are pinned in sec. 2.2; in the default
configuration the preferences are uniform, a fact whose consequences for the policy score are made explicit below. The temporal prior used at observation 𝑖 is
propagated explicitly:
𝐷0(𝑠) = 𝐷𝑠, 𝐷 𝑖(𝑠) = ∑
𝑠′
𝐵(𝑢𝑖−1 )
𝑠,𝑠′ 𝑞𝑖−1(𝑠′) 𝑖 > 0. (4)
The active-inference diagnostic chooses 𝑢𝑖−1 as the argmax of the previous policy posterior eq. 14 (deterministic selection, not sampling), while the fixed-transition
baseline filter uses empirical_continuation for the full sequence.
Given observed categorical outcomes 𝑜𝑖, the filtering update is:
𝑞𝑖(𝑠) = 𝜎 (log 𝐷𝑖(𝑠) + ∑
𝑚
log 𝐴(𝑚)
𝑜(𝑚)
𝑖 ,𝑠) , (5)
where 𝜎 normalizes a vector onto the simplex. The update is evaluated only after smoothing: model construction applies positive pseudocounts and probability
floors to 𝐷𝑖(𝑠)and to every likelihood entry that can be logged, so eq. 5 never relies on log 0.
This recursion is the common Bayesian-filtering operation: the transition predicts a distribution over hidden states and the likelihood updates that distribution
after the next observation. Discrete active inference expresses it within a POMDP generative model, HMM filtering supplies the corresponding finite-state
recursion, and particle filtering approximates the same operation with weighted samples when exact propagation is impractical [ Da Costa et al. , 2020, Kaelbling
et al. , 1998, Rabiner, 1989, Arulampalam et al. , 2002].
The one-step predictive loss uses the configured conditional-independence approximation over observation modalities:
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## Page 8

𝑃 (𝑜𝑖 ∣ 𝑠) = ∏
𝑚
𝐴(𝑚)
𝑜(𝑚)
𝑖 ,𝑠. (6)
ℓ𝑖 = − log (∑
𝑠
𝑃 (𝑜𝑖 ∣ 𝑠)𝐷𝑖(𝑠)) . (7)
Posterior uncertainty is reported as Shannon entropy [ Shannon, 1948, Cover and Thomas , 2006]:
𝐻(𝑞𝑖) = − ∑
𝑠
𝑞𝑖(𝑠)log 𝑞𝑖(𝑠). (8)
2.6.2 The Partial-Observability Protocol T ests Marginalize V ersus Commit
The default benchmark sets the observation equal to the discretized latent cell, so the emission is the identity and a point estimate is sufficient — there is no
hidden state left to marginalize. This is why no active-inference advantage survives on the default surface, and it is the central reason the formal model is
introduced before the headline result rather than after it.
Identity-emission collapse. If the location emission is the identity, then observing 𝑜𝑖 sets the posterior over the latent cell to the one-hot vector e𝑜𝑖
= e𝑠𝑖
after normalization. The soft predictor, hard predictor, observed-Markov predictor, and oracle-fed predictor therefore all propagate the same previous-cell vector
through the same transition. Any measured advantage from recursive marginalization must disappear on that surface; a nonzero advantage requires a genuinely
noisy or missing emission.
To isolate the regime in which a recursive belief over a hidden state earns its keep, let 𝐾 denote the number of latent cells in this protocol and let 𝑃 denote the
learned transition matrix shared by every fair predictor. We observe a latent cell sequence through an explicit symmetric emission with flip probability 𝜀,
𝑃 (𝑜𝑖 = 𝑐 ∣ 𝑠 𝑖) = (1 − 𝜀) 𝟙{𝑐 = 𝑠𝑖} + 𝜀
𝐾 − 1 𝟙{𝑐 ≠ 𝑠𝑖}, (9)
and crucially the generator draws each flipped observation uniformly over the 𝐾 − 1 cells other than the true cell — a 𝐾-ary symmetric channel in the information-
theoretic sense [ Cover and Thomas , 2006] — so the data-generating channel is exactly eq. 9 and the filter is correctly specified rather than mismatched. A
standard Bayes filter maintains the belief 𝑏𝑖 ∝ 𝑃 (𝑜𝑖 ∣ ⋅) ⊙ (𝑃 𝑏𝑖−1)from past observations only, and three predictors form the next-cell distribution from the same
learned transition 𝑃 , the same emission, the same observations, and the same priors, differing only in how they use the belief:
̂ 𝑝soft
𝑖 = 𝑃 𝑏 𝑖−1, ̂ 𝑝 hard
𝑖 = 𝑃 earg max 𝑏𝑖−1
, ̂ 𝑝 obs
𝑖 = 𝑃 e𝑜𝑖−1
, (10)
where e𝑘 is the 𝑘-th unit vector. Soft marginalizes the full belief; hard collapses it to its maximum-a-posteriori cell before propagating; observed-Markov commits
to the raw noisy observation (eq. 10). Because soft and hard are identical except for marginalize-versus-commit, no hyperparameter can be asymmetric between
them — the comparison is fair by construction, which is precisely the property the retracted observation-noise frontier of sec. 6.4 lacked (an earlier version used
an asymmetric noise knob that flattened one predictor’s prior while leaving the other’s untouched). Each predictor is scored by the prequential next-latent-cell
negative log-loss on held-out travellers [ Dawid, 1984, Gneiting and Raftery , 2007]; the transition is estimated from training travellers only, and predictions at
step 𝑖 use observations through 𝑖 − 1, so the comparison is leakage-free against the true latent target. The direction of this comparison is anchored by standard
theory: the log score is strictly proper [ Gneiting and Raftery , 2007], so among predictors evaluated under the model, the model’s own posterior predictive is the
unique minimizer of expected loss, and any competitor 𝑞 pays a model-expected excess of exactly 𝐷KL( ̂ 𝑝soft
𝑖 ‖ 𝑞) ≥ 0 — committing to the MAP cell is a lossy
compression of the belief. At 𝜀 = 0 the belief is a one-hot vector, so marginalize and commit coincide identically; the zero-at-clean flag (yes) records an algebraic
identity, not a fortunate sample. What theory does not guarantee — because the shared transition is estimated from training travellers rather than known — is
the sign under the true generator at finite sample; that residual is precisely what the all-positive resampling check and the 10-draw sign-stability check establish
empirically. Concretely, at each traveller’s first report the belief is initialized by normalizing the emission likelihood under a uniform prior over the 𝐾 cells, and
that step is never scored; the shared transition is a column-stochastic matrix estimated from training-traveller transitions only, with a symmetric pseudocount of
0.050 on every entry; and the MAP collapse of the hard predictor breaks exact ties toward the lowest cell index.
Uncertainty is reported as a robustness band rather than a generalization interval. Each noise level aggregates |noise seeds | × |split seeds | paired soft-versus-hard
resamplings on the same latent draw; we report the mean, the full min–max envelope, the fraction of resamplings with a positive advantage (a paired sign-test
proportion), and an ordinary-least-squares slope of the mean advantage against 𝜀 with its 𝑅2. Because this run scores a single latent draw, the spread characterizes
sensitivity to the emission noise draw and the holdout split, not between-dataset variance. The summary scalars — 𝜀-resolved advantage, clean-noise advantage,
the noise slope and 𝑅2, the worst-case and standard-deviation band at the strongest noise, and the monotonicity and all-positive flags — are bound to manuscript
variables through the provenance contract of sec. 11.
2.6.3 The Policy Score Is a Proxy , Not F ull Expected F ree Energy
The policy-proxy diagnostic evaluates each control by propagating the current posterior through eq. 2 and projecting expected observations through eq. 1. For
a candidate control 𝑢, write 𝑝(𝑚)
𝑢 = 𝐴 (𝑚)𝐵(𝑢)𝑞𝑖 for the predicted observation distribution and 𝜋(𝑚)= 𝜎(𝐶(𝑚))for the configured preference distribution. The
implemented score is the projected preference cross-entropy proxy:
𝑆(𝑢) = ∑
𝑚
[𝐻(𝑝(𝑚)
𝑢 ) + 𝐷KL(𝑝(𝑚)
𝑢 ∥ 𝜋(𝑚))] = ∑
𝑚
𝐻(𝑝(𝑚)
𝑢 , 𝜋(𝑚)) (11)
The entropy-plus-divergence display is algebraic bookkeeping: 𝐻(𝑝) + 𝐷KL(𝑝‖𝜋) = − ∑𝑜 𝑝(𝑜)log 𝜋(𝑜). It is not two independently estimated active-inference terms,
and it is not canonical expected free energy. For one modality, a standard one-step expected-free-energy decomposition can be written as a risk-plus-ambiguity
score [ Millidge et al. , 2021, Parr et al. , 2022]:
𝐺(𝑢) = 𝐷KL(𝑝𝑢 ‖ 𝜋) + 𝔼𝑞(𝑠′∣𝑢)[𝐻(𝐴(⋅ ∣ 𝑠′))] . (12)
The corresponding marginal-entropy identity is:
𝐻(𝑝𝑢) = 𝔼𝑞(𝑠′∣𝑢)[𝐻(𝐴(⋅ ∣ 𝑠′))] + 𝐼(𝑜; 𝑠′ ∣ 𝑢), 𝑆(𝑢) = 𝐺(𝑢) + 𝐼(𝑜; 𝑠′ ∣ 𝑢). (13)
The implemented multimodal score in eq. 11 sums this modality-wise bookkeeping across 𝑚. The proxy therefore differs from expected free energy by exactly the
sign-flipped epistemic-value term in this formal diagnostic: minimizing 𝑆 penalizes controls whose predicted observations are informative about the hidden state,
whereas canonical expected free energy rewards them (eq. 12; eq. 13; sec. 11.1). This is one concrete reason the pymdp lane and the proxy lane can legitimately
select different controls from identical tensors (sec. 11.1). We use the term proxy deliberately: this score is an implementation diagnostic over the configured
tensors, not a complete derivation of expected free energy with epistemic-value terms or a normative optimal-design rule [ Millidge et al. , 2021, Sajid et al. , 2021b,
Champion et al. , 2024, Sweeney et al. , 2026, van Oostrum et al. , 2024].
Policy posterior probabilities are then:
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## Page 9

𝑄(𝑢 ∣ 𝑜≤𝑖) = 𝜎(−𝑆(𝑢)). (14)
The softmax is taken implicitly under a flat policy prior and unit precision (no temperature parameter), over a depth-one control space: controls here are
single-step transition choices, not the multi-step policy sequences of the standard treatment [ Friston et al. , 2017, Parr et al. , 2022]. One degenerate case deserves
explicit statement because the default run sits in it: with uniform preferences (the default and only main-lane configuration), the preference divergence reduces to
the log-cardinality of each modality minus the predictive entropy, so the two displayed components cancel and the proxy score is exactly constant across controls
on any data. The policy posterior is then exactly uniform (mean policy entropy 0.693 nats over the two controls), the reported policy tie is an algebraic identity
of uniform preferences rather than an empirical property of the fixture, and the per-step control choice of the diagnostic reduces to floating-point tie-breaking.
This completes the generative-model and partial-observability scaffold. How these tensors behave empirically across regimes is reported in the Results (sec. 3),
and the implementation-level performance and interpretability boundary of the engine is detailed in the supplement (sec. 11.1).
3 Results: Belief Helps Only When Emissions Are Noisy
This benchmark tests active inference across many regimes and finds exactly one token-bound positive regime — partial observability under a noisy emission —
while a hierarchy of honest nulls and information-asymmetry bounds marks the far larger set of regimes where it does not clear its fair directional gates, and
where, on the identity-emission surface specifically, it provably cannot help. That contrast is the result, and the sections are ordered to state it as such, in three
tiers: the single positive regime first, then the null hierarchy and bounds that surround it, then the diagnostic, gate-verification, and safety surface on which
both rest. Leading with the positive regime is not promoting it over the nulls — it is naming the one regime that survived a discipline built to dissolve apparent
advantages into confounds, which is exactly what that discipline exists to establish. The proportion is the point: one regime helps, many do not.
This spine keeps the stable results anchor and states the reading order for the split results modules. The detailed evidence lives in the adjacent noisy-emission
and null-hierarchy result sections, with fixture diagnostics, program extensions, privacy, external-lane boundaries, and confound audits kept in the supplements.
That structure keeps the main Results focused on the one positive mechanism and the null discipline surrounding it, while preserving the generated artifacts that
support deeper review.
The reading rule is simple: primary evidence comes before diagnostic extension. The partial-observability comparison identifies the mechanism; the fair ladder
and oracle control identify its information-set limits; and the remaining figures test robustness, minimization, reporting-process structure, switching dynamics,
and future-model readiness. Read together, the results do not rank one universal winner: point estimates suffice on clean observations, belief-preserving families
lead as a cluster under noisy hidden states, adaptive baselines regain the lead under regime switching, and metadata does not replace withheld location. Those
extensions sharpen what the benchmark can say, but none upgrades a regime-qualified synthetic finding into blanket active-inference superiority.
3.1 Noisy Emissions Reward Belief Marginalization, Not Point Estimates
3.1.1 Soft Marginalization Beats Point Estimation as Emissions Degrade
Under a known noisy emission, uncertainty-preserving belief marginalization lowers predictive loss by 0.739 nats on the primary fixture draw. This is the
benchmark’s one replicated positive mechanism-level regime.
Active inference realizes that mechanism through recursive hidden-state belief updating in a discrete POMDP generative model [ Da Costa et al. , 2020]. HMM,
particle, state-space, and soft-filter methods can implement the same belief-preserving mechanism when they propagate a calibrated posterior over the hidden
state [ Kaelbling et al. , 1998, Rabiner, 1989, Arulampalam et al. , 2002, Doucet et al. , 2001, Patterson et al. , 2008, 2017]. Their performance can still diverge
through model misspecification, approximate inference, finite-sample estimation, adaptation, and policy structure [ Da Costa et al. , 2020, Arulampalam et al. ,
2002, Patterson et al. , 2017]. When the observation directly names the discretized latent cell, the posterior is already concentrated and a point estimate supplies
the same information.
The protocol of sec. 2.6.2 isolates the condition that rewards recursive belief: a latent state, a noisy emission, and prediction of the true latent next cell. Soft
(marginalize the full belief), hard (commit to the MAP cell), and observed-Markov (commit to the raw noisy observation) share the same learned transition,
emission, observations, and priors. Marginalize-versus-commit is the sole treatment difference, eliminating the asymmetry that invalidated the earlier noise frontier
(sec. 6.4). The log score rewards the full predictive distribution [ Gneiting and Raftery , 2007], so this lane tests hidden-state filtering and probabilistic prediction.
It does not isolate an expected-free-energy policy-selection advantage [ Millidge et al. , 2021].
Across 16 latent cells, the soft belief advantage over the point estimate is 0 nats at zero noise (zero-at-clean: yes) and rises monotonically with the observation-noise
level (monotone: yes), reaching 0.739 ± 0.127 nats at 𝜀 = 0.400 (fig. 3). The oracle-fed reference remains the predictive ceiling; the measured gain belongs to the
declared synthetic emission contract.
The growth is close to linear in the flip probability: an ordinary-least-squares fit of the mean advantage against 𝜀 gives a slope of 1.860 nats per unit 𝜀 with R 2
= 0.995. The near-linearity has a mechanistic reading. Flips are independent across steps, and each flip costs a committing predictor a roughly fixed penalty: it
propagates the wrong row of the transition. The soft belief retains (1 − 𝜀)of its mass on the true cell, so to first order the excess loss scales with the flip rate. On
this reading the slope estimates the average per-flip price of committing.
The spread is a robustness band, not a generalization interval: each level aggregates 15 paired soft-versus-hard resamplings (noise draws × locked holdout splits),
and every resampling at every nonzero noise level is positive. The worst single resampling at the strongest noise still favors the soft belief filter by 0.574 nats; the
clean channel carries no advantage by construction, as the zero-at-clean row above records.
The between-draw check repeats the construction across 10 independent synthetic generator draws with 16 travellers each. The noisy-emission sign remains
stable (yes), and at 𝜀 = 0.400 the replicated advantage is smaller than the headline: the cross-draw mean is 0.495 nats (range 0.429–0.578 nats across draws,
largest between-draw SD 0.049 nats). The 0.739-nat headline is therefore the primary 5-traveller fixture-draw value, not the replicated magnitude; the replication
establishes the sign and a more conservative effect size.
The advantage varies in magnitude and remains unanimous in sign, while the broader benchmark gate stays not_demonstrated. The fair-comparison ladder and
traveller×noise power map locate the active-inference row within this mechanism in the Discussion (sec. 4).
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Figure 3: Source partial_observability_analysis.json compares soft belief, hard MAP, and observed Markov under the same known symmetric emission with flip
probability epsilon, transition, observations, and priors. The soft-belief advantage is zero for a clean channel and grows monotonically with noise. The green
overlay separates the replicated cross-draw range and mean from the primary fixture draw, identifying belief marginalization as the mechanism behind the gain.
Evidence: a fair-by-construction isolation of the genuine partial-observability regime where belief marginalization beats committing to a point estimate under a
known noisy emission, zero at zero noise and growing monotonically with it. Boundary: active-inference-specific superiority, a state-of-the-art claim, an advantage
under full observability, or real-mobility validity.
3.1.1.1 Where Belief-Marginalizing Methods Lead: The Within-Regime Model Comparison fig. 4 places that mechanism into the full implemented
roster. Active inference achieves the lowest fair next-cell loss, rank 1 of 14, on the locked noisy-emission lane. The 4 predictors that maintain a belief over the
latent cell and marginalize the noisy emission — active inference, its soft-filter reference, the switching-noise HMM, and the particle filter — occupy the leading
cluster. That cluster leads the best point-estimate or raw-observation method by 0.192 nats. The uniform-chance loss is 3.584 nats, so the ranking distinguishes
among genuine predictive models rather than chance-level variants.
Active inference’s advantage over the strongest non-AIF method ( switching_noise_hmm) is 0.005 nats, with a clustered interval that crosses zero. It is therefore
the point leader and a statistical member of the top belief-preserving cluster. The separated result is belief preservation versus early commitment to a point
estimate or raw observation; active inference does not clear a resolved margin over the strongest non-AIF belief filter, and that comparison stays a statistical tie.
This ordering is specific to the noisy hidden-state lane, remains below the oracle-fed ceiling, and leaves the cross-generator gate at sota_program_not_cleared.
Figure 4: Source model_comparison_leaderboard.json ranks every implemented next-cell predictor by fair loss on the locked synthetic noisy-emission FractalRabbit
lane. Active inference, soft filter, switching-noise HMM, and particle filter form the leading belief-preserving cluster. The plot marks uniform chance, the belief-
family band, the best non-belief boundary, top-row accuracy, the belief-versus-nonbelief gap, and active inference’s paired interval against the strongest non-AIF
method. Marginal whiskers are descriptive; the paired interval determines separation. Evidence: a within-regime ranking showing belief-marginalizing methods,
active inference included, lead the implemented predictors under noisy emission. Boundary: a global state-of-the-art claim, an oracle-beating result, or a real-
mobility claim.
3.2 Nulls, Calibration, and Multiplicity Keep Gains Bounded
3.2.1 Recovery Calibration F aces Uniform, Base-Rate, and Persistence Nulls
This section frames state recovery and model performance against explicit baselines: ground-truth recovery on observed and latent configurations, skill scoring
against uniform-chance and persistence nulls, and proper-score calibration diagnostics that decompose predictive loss into per-modality contributions and honest
uncertainty pricing.
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Figure 5: Sources ground_truth.csv and inference traces score latent-state recovery against the simulator’s own truth. Posterior mass is plotted for both lanes
when available, while top-1 correctness is plotted for the reference lane; with location observed, high recovery is a sanity bound (reference mean mass 0.995, top-1
1.000), not an achievement. Calibration and location-withheld recovery carry the substantive burden elsewhere. Synthetic software evaluation, not empirical
validity. Evidence: synthetic-truth recovery sanity checks and calibration handoff. Boundary: empirical validity.
fig. 5 reports ground-truth state recovery. Because the true latent cell of every report is computable exactly from the reported coordinates, any posterior can be
scored against it. On the default configuration — where location is itself an observation modality — recovery is near-perfect by construction (reference mean
mass on the true cell 0.995, top-1 accuracy 1; pymdp 0.994 and 1), and we state that plainly rather than presenting it as an achievement. The non-trivial
result is the deep-latent configuration from the sensitivity lane: with the location modality removed, the filter recovers mean mass 0.135 on the true cell with
top-1 accuracy 0.132 from time-of-day, speed, and reporting-burst evidence alone, at mean posterior entropy 2.241 nats. Latent location structure is partially
recoverable without any direct location report on this synthetic configuration — though, as the calibration analysis below shows, most of this recovered mass
reflects occupancy structure and mobility autocorrelation (the base-rate and persistence baselines below) rather than the time-of-day, speed, and reporting-burst
evidence itself. Within the modeled situation this is simultaneously the analytic point and a privacy-relevant observation; whether the same recoverability holds
for real mobility traces is exactly the empirical question that sec. 8 leaves open, not something these synthetic numbers settle.
Figure 6: Source calibration.json decomposes predictive fit, confidence, and null-relative recovery for both inference lanes on shared axes. The reliability panel
compares top-1 confidence with realized top-1 accuracy; the loss panel splits joint predictive loss into modality margins and their interaction gap; the skill panel
moves from a uniform floor to base-rate and temporal-persistence nulls, with bin counts and tiny joint-loss skills printed directly. Persistence is the stricter null
for autocorrelated synthetic mobility, so apparent by-construction wins are not overpromoted. Evidence: calibration floors, null hierarchy, and persistence-relative
skill checks. Boundary: promotion of by-construction location wins as substantive recovery.
fig. 6 and tbl. 1 decompose and calibrate the headline objectives rather than leaving them as single numbers. First, the joint one-step predictive loss is split into
per-modality marginal losses under the running prior. For any observed modality 𝑚, the joint predictive probability is bounded above by its marginal because
∑
𝑠
𝐷𝑖(𝑠) ∏
𝑗
𝐴(𝑗)
𝑜(𝑗)
𝑖 ,𝑠 ≤ ∑
𝑠
𝐷𝑖(𝑠)𝐴(𝑚)
𝑜(𝑚)
𝑖 ,𝑠, (15)
so − log 𝑃 (𝑜(𝑚)
𝑖 ) ≤ −log 𝑃 (𝑜𝑖)for the same row. A checked invariant enforces this bound, and the summed-marginal-minus-joint gap — 0.023 nats on the reference
lane — measures how much the modalities corroborate one another through the latent cell.
Second, each lane is scored against an explicit uniform-chance floor (6.238 nats joint loss): the reference filter attains a joint-loss skill of 0.083 and the pymdp
closed loop 0.015, where a skill of one is perfect and zero is chance. This synthetic null floor makes the reference lane’s clear predictive signal and the pymdp
loop’s smaller positive signal comparable against the same floor.
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Third, recovery is calibrated, not just averaged, using proper-score and calibration diagnostics as scoring context [ Brier, 1950, Guo et al. , 2017, Gneiting and
Raftery, 2007, Gneiting and Katzfuss , 2014]. The reference lane’s Brier score is 0.000 with expected calibration error 0.005 — sharply calibrated largely by
construction, since location is observed — while the pymdp closed loop scores Brier 0.000 with ECE 0.006 and runs under-confident (mean top-1 confidence
0.994 against top-1 accuracy 1). That is the direct signature of policy-induced prior divergence inflating its posterior spread without destroying its ranking. The
substantive calibration number is again the deep-latent one: at full report density the deep-latent filter scores Brier 0.933 (Brier skill 0.004 against the uniform
floor), quantifying how honestly the model prices its own uncertainty when location is never reported. Expected calibration error is read here as a binning-sensitive,
descriptive diagnostic rather than a definitive metric, so it is interpreted alongside the strictly-proper Brier score and the calibration-versus-sharpness tradeoff
rather than on its own [ Nixon et al. , 2019, Gneiting and Katzfuss , 2014].
Fourth, because a uniform floor is a weak null for state recovery — beating it is trivial when location is itself observed — we also score recovery against a tighter
base-rate null: the constant marginal-frequency predictor, whose Brier score is the Gini impurity of the true-cell distribution and which is therefore never a looser
null than the uniform floor, and a strictly tighter one whenever cell occupancy is uneven. For a one-hot true cell 𝑌 drawn from marginal distribution 𝜋 and the
constant predictor 𝜋,
𝔼 [∑
𝑘
(𝜋𝑘 − 𝟙{𝑌 = 𝑘})2] = 1 − ∑
𝑘
𝜋2
𝑘, (16)
which is exactly the Gini impurity. Against this base-rate null the location-observing reference lane scores Brier skill 1.000 and the deep-latent lane -0.162 (positive
= beats merely knowing how often each cell is occupied). The reference lane’s location evidence trivially clears this null, while the deep-latent lane’s margin
measures how much of its above-uniform recovery is occupancy structure rather than observation-driven signal — on the current expanded fixture that margin
sits at the occupancy floor, which is exactly the overreach this stricter baseline exists to catch.
Fifth, even the base-rate null is loose for mobility, because reports are highly autocorrelated — travellers stay in or return to the same cell — so we add the
strongest honest null, temporal persistence (predict the previous report’s cell, falling back to the base rate at each traveller’s first report). Against persistence
the deep-latent lane’s recovery skill falls to -19.745 (reference lane 1.000), the conservative measure of how much the time-of-day, speed, and reporting-burst
evidence adds beyond simply assuming no movement. The base-rate-versus-persistence ordering is itself data-dependent — persistence is the tighter null only
where stay-put autocorrelation exceeds marginal predictability — so we report skill against both. All calibration estimates are computed over 2400 fixture reports
with per-bin counts displayed in fig. 6, so thinly occupied confidence bins are visible rather than averaged away.
Table 1: Per-modality marginal predictive losses against each lane’s joint loss, from calibration.json.
modality reference marginal loss (nats) pymdp marginal loss (nats)
location 2.342 2.770
time_of_day 1.385 1.386
speed 1.321 1.322
report_burst 0.693 0.693
joint (all modalities) 5.719 6.147
Figure 7: Source sparsity_analysis.json subsamples each traveller’s reports and re-estimates both the full model and the deep-latent no-location model at each
sparsity level. Mean true-cell posterior mass prices direct location evidence, while entropy and pymdp variational free energy show how uncertainty and closed-loop
cost change as sequences lengthen. These fixture-lane measurements separate filter recovery from policy-induced prior divergence and are not empirical claims.
Evidence: how recovery and uncertainty change under fixture-lane report thinning. Boundary: population generalization across real sampling regimes.
fig. 7 and tbl. 2 give the comprehensive form of the latent-state question: recovery as a function of report density across 4 subsampling levels. With the full report
set the deep-latent reference filter holds mean mass 0.069 on the true cell, against 0.118 at the sparsest level; the full model dominates every deep-latent curve at
every level, and the gap between them prices the value of direct location evidence at each report density. The pymdp column of the table is a variational-free-
energy trace from the validated state updater, not an independent closed-loop recovery curve: its deep-latent recovery reuses the matched reference posterior by
construction once the sentinel agreement check passes, so the table carries one recovery curve per configuration. The accompanying uncertainty diagnostics —
deep-latent posterior entropy and pymdp variational free energy — are reported per level rather than asserted to follow a fixed direction, because their movement
depends on how subsampling reshapes the interval and speed evidence. Recovery-versus-sparsity curves over deterministic subsamples of the checked fixture. They
quantify how this configured model degrades as reports thin; they are software measurements on synthetic data, not empirical mobility findings. The full-model
curve observes the true cell directly through the location modality, so its near-ceiling recovery is a sanity bound by construction; only the deep-latent curves test
genuine inference. The per-traveller subsample keeps at least two reports, so actual_fraction is the honest sparsity level when it diverges from the requested
fraction. The pymdp lane validates the released state updater on deterministic sentinel rows at each sparsity level; full-row deep-latent recovery uses the matched
reference posterior after that agreement check. The deep-latent recovery band is the min-max spread of the mean mass on the true cell across 5 independent
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subsamples at the same fraction — a subsample-resampling robustness spread over this one fixture, not an inferential or population confidence interval; at the
densest (full-report) level every subsample keeps all reports, so the band collapses to a point by construction.
Table 2: Recovery versus report sparsity emitted by scripts/08_run_sparsity_analysis.py.
reports/traveller full mass latent mass latent top-1 latent entropy (nats) pymdp VFE (nats)
480 0.995 0.069 0.082 2.704 3.380
360 0.996 0.082 0.113 2.612 3.355
240 0.996 0.074 0.081 2.675 3.468
120 0.991 0.118 0.212 2.449 3.414
3.2.1.1 Multiplicity-Corrected Claims: No Directional Win Survives the Comparison F amily A benchmark that runs many directional comparisons
must price in the size of the family before reading any single clearance as a result. We do this without introducing a new researcher degree of freedom. The
comparison family is enumerated by a fixed rule from the live artifacts: every active-inference-versus-fair comparison that reports a one-sided traveller-clustered
bootstrap p-value, namely each synthetic regime of the regime search and each lane of the cross-generator program. Each row compares paired predictive-score
differences on the same held-out reports rather than unmatched summary losses [ Diebold and Mariano , 1995]. Each regime enters at its worst (largest) one-sided
p over its realization seeds, so a regime clears only when even its least favourable realization does, the conservative direction. The family is fixed by this rule,
since selecting which comparisons “count” would itself be the kind of confound this benchmark exists to expose.
Bootstrap intervals are used as descriptive software-measurement intervals, with the traveller as the resampled dependence unit rather than individual steps [ Efron
and Tibshirani , 1994, Field and Welsh , 2007, Cameron and Miller , 2015]. This holds at every interval feeding the comparison family: regime-search candidate and
paired intervals, cross-generator lane intervals, and the traveller ×noise regime map. The only percentile constructions in the study that are not traveller-clustered
are permutation-null thresholds, which resample labels under the null rather than sampling units, and per-injection-seed robustness spreads; neither is read as a
traveller-level confidence interval.
Each cross-generator lane resamples 26 held-out travellers, and each regime comparison draws from a 40-traveller synthetic population. With cluster counts of this
order the percentile interval is a serviceable but not exact-coverage summary [ Field and Welsh , 2007, Cameron and Miller , 2015], one more reason the corrections
below are read as bounding over-interpretation rather than certifying population inference. Applying formal corrections to descriptive software-measurement
p-values is deliberate: the corrections do not upgrade the measurements into population inference, they bound how many apparent clearances resampling noise
plus a family of 9 could manufacture on their own.
Across the resulting 9 comparisons (fig. 8), computed with B = 2000 traveller-resampled replicates per comparison (smallest reportable p 5.00e-04), 0 clears the
uncorrected significance threshold (0.050). Every comparison’s own confidence interval, not merely its raw p-value, is required to separate from zero before it
counts as a clearance at all, so a comparison whose interval still straddles zero is read as unresolved rather than as a marginal win.
Under Holm–Bonferroni correction, which bounds the family-wise error rate under arbitrary dependence, 0 survive [ Holm, 1979]. That is the honest assumption
given that the regimes and lanes share generators, candidate code, and the active-inference fit. Under a Benjamini–Hochberg false-discovery control, valid under
independence or positive regression dependence, 0 survive [ Benjamini and Hochberg , 1995]. We state that dependence assumption rather than claiming it.
Across the family the mean advantages range from -0.259 to 0.020 nats, so most comparisons favor the fair baseline outright, and none clears its own uncorrected
threshold, let alone survives correction. The regime-qualified gate of sec. 6.3 is therefore read here as not clearing even before multiplicity is priced in. That is
the honest reading across the whole family: no directional win, corrected or uncorrected, survives.
Figure 8: Source multiplicity_ledger.json enumerates every synthetic AIF-versus-fair directional comparison with a one-sided clustered-bootstrap p-value. Each
dumbbell joins the raw and Holm-adjusted p-values on a log axis against alpha; markers identify rows whose raw p-value and clustered interval both clear. The
annotation reports family size, uncorrected clearers, Holm and Benjamini-Hochberg survivors, the best adjusted p-value, and the separate partial-observability
Bonferroni sign-test bound. Evidence: a multiplicity audit reporting how many directional comparisons survive Holm and Benjamini-Hochberg correction across
the deterministically enumerated family. Boundary: a state-of-the-art claim, an oracle-beating result, or a real-mobility claim.
The single fair-by-construction positive — soft marginalization under a noisy emission (sec. 3.1.1) — sits outside this bootstrap family because it is established
by a stricter criterion: unanimous sign-stability across 10 independent generator draws, a replication requirement that is multiplicity-robust by construction.
Its validity is moreover mechanism-level rather than frequentist. Soft Bayesian marginalization is provably at least as good as a hard point estimate under a
known emission, in the model-expected sense made precise in sec. 2.6.2, with a strictly positive advantage as the channel degrades. A multiple-testing correction
on a sign statistic is therefore the wrong lens for the mechanism. The direction of that advantage is fixed a priori rather than chosen after seeing the draws, so
the one-sided sign-test bound is the appropriate null.
Reported conservatively all the same, the sign-test bound for its 10 unanimous draws is 9.77e-04, below the family-wide Bonferroni per-comparison threshold of
5.56e-03 (the minimum sufficient is 8 unanimous draws). The one positive therefore survives even the most conservative family-wide correction the paper applies,
over and above the mechanism-level argument, which does not rest on the sign test at all. The synthesis is the honest one: of every directional comparison the
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benchmark makes, none survives family-wise correction as a measured win, and the one advantage that does hold is the mechanism-level result that never claimed
to beat the oracle or to transfer to real mobility.
4 Discussion: Belief Filtering Earns a Regime-Bound Role
The benchmark identifies one positive mechanism: uncertainty-preserving belief-state filtering improves prediction when a noisy emission hides the current cell.
The effect reaches 0.739 nats on the primary fixture draw and replicates at a mean of 0.495 nats across 10 independent higher-power draws. Active inference
realizes this mechanism through recursive belief updating and achieves the lowest implemented loss in the matched noisy-emission comparison [ Da Costa et al. ,
2020]. HMM, particle, state-space, and soft-filter approaches can target the same posterior predictive distribution when models and information sets are matched;
approximation, learning, adaptation, and policy structure can still separate them [ Kaelbling et al. , 1998, Rabiner, 1989, Arulampalam et al. , 2002, Doucet et al. ,
2001, Patterson et al. , 2008, 2017]. The active-inference row occupies a precise position: lowest implemented point estimate under noisy partial observability,
below the oracle-fed ceiling, within a statistically tied leading belief-filtering cluster.
The partial-observability construction of sec. 3.1.1 isolates the mechanism: soft Bayesian marginalization ties the point estimate when the observation reveals the
latent cell, then gains monotonically as the emission degrades. The wider evidence assigns that gain. The fair ladder separates single-step marginalization from
recursive belief; the traveller ×noise map locates the regime; the within-regime comparison (sec. 3.1.1.1, fig. 4) places active inference first among the implemented
noisy-emission predictors; and the oracle, clean-emission, switching, and cross-generator surfaces identify its limits.
The active-inference row leads by point estimate and shares the top statistical tier with the strongest non-AIF belief filter. The historical confound taxonomy
remains supplementary audit evidence in sec. 16. The central answer is direct: preserve and recursively update a belief when observations leave the state uncertain;
use a simpler predictor when the observation already resolves it.
4.1 A Reader’s Model Map: Match the Predictor to the Information Regime
The results are easiest to interpret as a model-selection map rather than as one global ranking: there is no global winner. The decisive variable is what information
the predictor receives and whether uncertainty about the current cell is genuine, transient, or already resolved by a simpler statistic.
Information regime What works Observed limit Why
Clean or directly observed cell Persistence, Markov, and
point-estimate predictors are sufficient
reference models.
Recursive belief offers no general gain. The posterior is already concentrated;
recursion mostly reintroduces
transition-estimation and smoothing
error.
Noisy emission over a hidden cell Soft Bayesian marginalization, HMM,
particle/state-space, soft-filter, and
active-inference families form the
leading implemented cluster.
The strongest non-AIF belief method
is statistically tied with active
inference; the oracle remains lower.
Preserving probability mass over
plausible cells avoids propagating a
prematurely committed state; most of
the gain comes from marginalization,
with recursion helping as the emission
degrades.
Latent regime switching An adaptive online base-rate predictor
is the strongest implemented fair
comparator on the tested switching
lane.
Online base-rate adaptation leads
fixed-generative-model AIF.
Fast changes in occupancy favor online
adaptation; a fixed transition model
carries stale structure across regime
boundaries.
Sparse reporting gaps Persistence and disclosed kinematic
baselines remain indispensable
controls; gap-aware gains stay
synthetic and cue-qualified.
Timing alone stays below promotion;
displacement-derived speed narrows
the task.
Timing can describe the reporting
process rather than motion, while
displacement-derived speed directly
reveals whether movement occurred.
Location withheld, metadata retained Occupancy and trained-dynamics
baselines explain most recoverable
broad structure.
Specific-cell recovery remains at the
strongest dynamics/persistence null
surface.
Time, speed, and burst metadata
carry limited incremental information
once occupancy and autocorrelation
are priced in; withholding location
therefore remains strongly protective.
The model-selection rule is practical: use the simplest predictor whose information set resolves the state; preserve a distribution over states when the emission
leaves genuine uncertainty; prefer adaptation when the generator changes; and attribute apparent gains to an oracle, cue, occupancy pattern, or unmatched
information set whenever those explanations account for the result.
4.1.1 Online Adaptation Repairs Fixed Dynamics Without Winning the Switching Lane
The AIF-deepening audit in fig. 9 separates modular surfaces by predictive admission: factorial tensor provenance and multiscale soft-belief backoff remain audit-
only, while online transition adaptation enters Candidate.predict(PredictContext) and is scored through a genuinely nested train/validation contract. Protocol
candidates currently admitted: 1; predictive gate clears: no. Across 5 distinct synthetic generator/noise realizations sharing the locked split rule, the adaptive
candidate improves the separately tuned fixed-transition AIF by a mean 0.146 nats (range 0.068 to 0.280), with traveller-clustered separation on 4 realizations.
It beats the predeclared online-base-rate comparator with clustered separation on 0 realizations, so the repeated predictive gate remains no. This advances the
generative model and localizes the remaining gap without clearing promotion.
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Figure 9: Source aif_deepening_candidates.json tracks active-inference deepening surfaces by predictive admission: factorial tensor provenance, multiscale soft-
belief backoff, and online adaptation. Rows show whether each surface has entered the locked Candidate.predict(PredictContext) protocol and whether any
predictive gate clears. Online adaptation is now a scored candidate that improves the fixed AIF ablation but not the predeclared online-base-rate comparator;
audit-only rows remain visible so tensor, EFE, and VFE ideas cannot substitute for prediction. Evidence: a predictive-admission map where online adaptation
is scored while factorial and multiscale surfaces remain audit-only. Boundary: predictive improvement, SOTA promotion, or operational claims from EFE, VFE,
tensor, or adaptation surfaces alone.
4.2 The F air Ladder Assigns Most Gain to Soft Marginalization
The active-inference lane uses the same locked, traveller-disjoint split as the transparent baselines and is scored by prequential next-cell loss [ Dawid, 1984, Luca
et al. , 2023, Gneiting and Raftery , 2007]. Across the structural sweep, no active-inference configuration beats the strongest baseline: the best inference loss
is 0.909 nats, above the strongest baseline’s lower confidence bound, and the claim gate stays sota_not_cleared. That comparison is information-asymmetric
because the baselines receive the true previous cell. The fair ladder instead gives every predictor the same locked split and transition source, varying only how the
previous cell is inferred from the emission (fig. 10). A hard MAP estimate scores 0.936 nats; full soft marginalization scores 0.788 nats; recursive active inference
scores 0.835 nats; and the oracle-fed reference scores 0.606 nats.
Soft Bayesian marginalization supplies the dominant inference gain, about 0.147 nats over the hard point estimate. Recursive temporal belief contributes
conditionally: single-step marginalization leads at the clean setting, while recursion turns positive as the channel degrades and reaches about 0.356 nats at the
noisiest setting.
The direction of that crossover is what estimation error predicts. At a clean emission the single-step posterior is already nearly one-hot, so the recursive prior
contributes no information the observation lacks but does inject the smoothing mass and finite-sample error of the learned transition into every step. Once the
emission degrades, the prior carries information the observation no longer supplies, and recursion’s contribution turns positive. Recursive belief therefore earns
its keep specifically under observation noise, not in general.
At the clean setting, single-step soft marginalization leads the recursive active-inference filter (0.788 versus 0.835 nats). The per-traveller visited-cell return prior
worsens both predictors on the regenerated fixture (soft 1.129 nats; filter 1.085 nats), although the recursive filter absorbs less of that penalty.
Positive controls verify the comparison: an identity emission collapses every inferring predictor onto the oracle, and the oracle-fed baseline remains the ceiling.
The fair ladder therefore assigns most of the gain to single-step soft marginalization and the remaining noise-dependent gain to recursion. The broader benchmark
gate remains sota_not_cleared.
Figure 10: Source fair_inference.json scores an oracle-stripped ladder in which every predictor learns the same transition from the same observed cells. The left
panel ranks oracle, hard argmax, soft marginalization, return-boosted soft prediction, and recursive active inference with bootstrap whiskers. The right panel traces
recursion’s incremental advantage as emission noise rises. Most of the gain comes from soft marginalization; recursion adds value conditionally as the observation
channel degrades. Evidence: a fair, transition-source-matched comparison of how much latent-cell inference helps, decomposed into soft marginalization and
recursion. Boundary: a state-of-the-art claim, an oracle-access result, or real-mobility validity.
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4.3 The Regime Map Keeps the Advantage Sparse and Noisy
The fair question has a measured answer, but it must be read from the tokens, and with its sample size in the same breath. Scored under the pre-specified locked
next-cell loss, chosen before this comparison and not to favor any predictor, and aggregated across multiple seeds at a holdout whose power the next paragraph
qualifies, the artifact reports the number of seeds in which an active-inference predictor is the lowest-loss fair predictor as 0/8. Its mean advantage is -0.348 nats
over the best non-active-inference fair predictor, where a negative advantage means the active-inference predictor trails that baseline.
Those seeds reshuffle the same handful of travellers, with as few as 2 distinct held-out travellers per split. Only a unanimous fixture-local rate with a positive
advantage would support even bounded wording about this fixture’s tested predictor set. The current hydrated values do not support that wording: they report
a non-unanimous rate and a negative mean advantage, consistent with the fair-ladder finding above that the active-inference filter is not the best fair predictor.
Either way the comparison is directional and provisional, does not beat the oracle, and is not an operational claim.
We deliberately report no confidence interval. Per-step bootstrap intervals treat within-traveller-correlated steps as independent and overstate precision, while a
traveller-clustered interval is degenerate at this distinct-traveller count. No valid interval exists, so CI-separation is withheld rather than merely wide. A positive
control confirms the oracle-fed baseline is still lower in every seed, so the comparison is non-degenerate; the prerequisite for a precision claim is more held-out
travellers and larger, more strongly regime-structured synthetic data, not a cleverer filter.
Independently of where that between-predictor comparison lands, the predictor’s own calibration can still be improved. Precision-weighting the active-inference
belief ( 𝛾 = 1.500, fixture-selected rather than held out) lowers its mean fair loss from 0.958 to 0.759 nats in 8/8 seeds with lower expected-calibration error observed
on this fixture (mean ECE 0.367 to 0.148), because the over-smoothed base belief is under-confident. This is an in-sample inference-internal improvement, not a
generalization claim, and it is deliberately excluded from the between-predictor comparison above so it cannot inflate the active-inference margin. Cross-vendor
audit is a constraint in this project record: the confound taxonomy marks 2 apparent advantages caught only by that audit, so the responsible reading is constraint,
not confirmation.
The session’s central limitation — too few held-out travellers to interval the advantage — is itself testable. We generate deterministic synthetic streams at a fixed
spatial resolution with up to 32 travellers and interval the fair advantage with a traveller-clustered bootstrap, resampling whole travellers as the correlated unit
rather than steps. Because that bootstrap still only sees one generator draw, we repeat the whole sweep across 5 independent draws and call a cell a seed-robust
win only when its clustered interval separates from zero in every draw. The across-draw spread is the between-dataset variance the bootstrap alone cannot capture.
The result is a regime map over traveller count and observation noise. With few travellers the active-inference filter’s advantage over a return-boosted soft
Markov is large and seed-robust (0.408 nats at a clean emission). In this smallest column the holdout contains only 2 travellers per draw — too few for a valid
traveller-clustered interval, which is why we withhold CI-separation language for this column (see the power analysis above). Its seed-robust designation should
therefore be read as across-draw sign unanimity with a large margin (worst draw 0.378 nats across 5 independent draws), not as within-draw interval precision;
the interval-backed cells are those with more travellers and at least four holdout clusters.
As travellers grow the clean-emission advantage shrinks to the noise floor and slightly reverses (-0.005 nats at the largest count, not a seed-robust win). At a fixed
cell grid, traveller count and per-cell density are deliberately coupled, and the vanishing advantage is the shared population transition model becoming sufficient
as data-per-cell grows — a density effect, not a count-intrinsic law. Its onset is resolution-dependent: a finer grid delays it, but it is not a fixed-box artifact, since
it persists when anchor density is held constant.
The advantage re-emerges under observation noise as a monotone gradient across the noise axis even at that scale, reaching a seed-robust 0.054 ± 0.003 nats at
the noisiest emission (noise restores the advantage: yes). Because these cells are selected from a 2D sweep, the monotone gradient, not any single cell clearing
zero, is the claim. The magnitudes are kept distinct: the few-traveller effect (0.408 nats) is roughly an order of magnitude larger than the at-scale-noisy one
(0.054 nats).
For the target sparse-waypoint regime, recursive temporal belief earns its keep when the emission is uninformative, while a simpler boosted Markov suffices when
locations are dense and clean. The oracle-fed baseline remains the ceiling, and the advantage follows the noise gradient rather than extending across regimes
(fig. 11).
Figure 11: Source power_analysis.json maps active inference minus return-boosted soft Markov across traveller count and observation noise on deterministic
synthetic streams. Color reports signed advantage in nats. Solid rings mark traveller-clustered interval separation when enough holdout clusters exist; dashed
rings mark cross-seed sign stability where within-draw intervals are underpowered. The map shows large small-sample margins, vanishing clean-emission margins
at scale, and renewed advantage as observation noise rises. Evidence: a clustered-bootstrap regime map showing the fair AIF advantage is large with few
travellers, vanishes at scale under a clean emission, and re-emerges under observation noise. Boundary: a blanket state-of-the-art claim, an oracle-access result,
or real-mobility validity.
4.4 Oracle Asymmetry and Cross-Generator Nulls Block Promotion
The same discipline marks the boundaries of the claim as sharply as its centre. The persistence null of sec. 3.2.1 is an oracle baseline: it is handed the true
previous cell. The current location-blind lane therefore loses under an explicitly weaker information set; this is a benchmark-specific information-asymmetry
bound, reported plainly as a synthetic-regime fact rather than reframed as an artifact.
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The higher-power, 4-lane benchmark of sec. 6.3 tests cross-regime generality. Against strong fair baselines on locked splits with traveller-clustered intervals across
fractalrabbit, gravity, reporting_gap, regime_stressor, its gate stays sota_program_not_cleared.
The synthesis is precise. Under the declared noisy emission, active inference achieves the lowest implemented point estimate and participates in a replicated hidden-
state filtering advantage: 0.739 nats on the primary fixture draw and 0.495 nats on average across 10 higher-power draws. Its margin over the strongest non-AIF
belief filter remains statistically unresolved, and the oracle-fed baseline remains lower. On the default observed-state surface, pymdp contributes interpretability
through its variational and policy diagnostics (sec. 7.3). These are synthetic software results; a separate empirical protocol covers real-data evaluation (sec. 6.5).
4.5 Bayesian Mechanics F rames the W aypoint Particle as a Bounded Analogy
Bayesian mechanics gives this result a useful conceptual grammar, but not a stronger evidential warrant. In that literature, systems with a particular partition can
be described in terms of internal states whose trajectories encode beliefs about external states, mediated by blanket states and interpreted through variational free
energy [ Ramstead et al. , 2023, Da Costa et al. , 2021, Friston, 2019]. Related Markov-blanket work connects this partition vocabulary to autonomy, information
geometry, and stochastic thermodynamics [ Kirchhoff et al. , 2018, Parr et al. , 2020], while the path-integral formulation treats particle trajectories as paths subject
to a variational principle [ Friston et al. , 2023b]. The analogous object here is deliberately smaller: a synthetic waypoint belief over a hidden cell path, updated
through sparse reports and a declared observation model. Calling that object a waypoint particle or cognitive-particle analogue is therefore a metaphor for an
abstract belief-carrying trajectory in a controlled state space, not a claim that the synthetic trace is cognitive, living, sentient, autonomous, or empirically tracked.
The formal analogy is a typed bookkeeping device, not an ontology. A Bayesian-mechanics partition is often written as external, sensory, active, and internal
states; in this benchmark the only defensible mapping is: hidden cell (x_t) as the external variable of interest, sparse report (o_t) as the sensory channel, no
embodied active state, and the software posterior (q_t(x_t)) as the internal coordinate. The operative update is the ordinary discrete filter:
𝑞𝑡(𝑥𝑡) = 𝑝𝑚(𝑥𝑡 ∣ 𝑜1∶𝑡) ∝ 𝑝𝑚(𝑜𝑡 ∣ 𝑥𝑡) ∑
𝑥𝑡−1
𝑝𝑚(𝑥𝑡 ∣ 𝑥𝑡−1)𝑞𝑡−1(𝑥𝑡−1). (17)
where (m) is the synthetic model contract. This is enough to say that the waypoint particle is a belief path over latent cells. It is not enough to assert a
realized Markov blanket, a conditional synchronization map from internal to external states, a nonequilibrium steady state, a path integral over an organism, or
a strange-particle/sentience claim. Those stronger readings require assumptions the current artifact neither states nor tests, and scope critiques of the FEP make
that caution substantive rather than merely rhetorical [ Aguilera et al. , 2022].
The analogy is still useful because it sharpens the role of sporadic waypoints. The report stream is not a dense path; it is a sparse coupling between hidden
movement and observed categorical evidence. The filter’s internal state is the posterior over the latent cell, and the successful noisy-emission regime is precisely
the case where preserving that distribution is better than committing to a point estimate. Read this way, the benchmark is a toy path-tracking problem: the
internal belief path follows a hidden stochastic process only through the information the synthetic report channel supplies. That is compatible with the broader
free-energy and active-inference vocabulary already used for the formal model [ Friston, 2010, Friston et al. , 2017, 2023a, Parr et al. , 2022], while staying below a
full Bayesian-mechanics derivation. The manuscript does not define a biological Markov blanket, prove a nonequilibrium steady state, or infer any actual mental
state; it defines a software generative model and measures how belief updates behave under its synthetic evidence.
That boundary prevents the attractive but wrong conclusion. Bayesian Mechanics can motivate asking whether sparse observations let an internal state track
a hidden process; it cannot turn a synthetic waypoint fixture into real cognition, real mobility validation, or a promotion claim. The right claim is therefore
conceptual and local: this benchmark offers a source-bound example of belief-state path tracking under sparse synthetic reports, and its result remains the same
bounded one stated above — uncertainty-preserving inference helps only in the noisy partial-observability regime and stays below the oracle-fed ceiling.
4.6 Governance Sources Bound Interpretation, Not Deployment
The governance lesson is a boundary discipline, not a new empirical result. Sparse waypoint traces are policy-relevant because location data can be unique,
matched across datasets, aggregated, sold, repurposed, or recombined, and because commercially available information and sensitive-location enforcement sources
treat trace provenance and minimization as live governance questions [ de Montjoye et al. , 2013, Kondor et al. , 2020, Haggerty and Ericson , 2000, Office of the
Director of National Intelligence , 2022, 2024, Federal Trade Commission , 2024, 2026]. Those sources support the relevance of the problem setting only. They do
not validate FractalRabbit, do not establish legal compliance, and do not turn the synthetic benchmark into an operational or surveillance-ready system. Formal
privacy mechanisms and trajectory-specific privacy evaluations remain separate from this benchmark’s synthetic risk proxies [ Dwork, 2006, Buchholz et al. , 2024,
National Institute of Standards and Technology , 2020].
The responsible interpretation is therefore analyst-facing and uncertainty-preserving, not deployment-facing. The model should be read as a structured aid to
inference: it exposes posterior uncertainty, null failures, calibration gaps, and minimization costs, while keeping human judgment responsible for problem framing
and for any decision to seek empirical data [ Heuer, 1999]. Automation-bias work makes the same caution sharper: a clean trace, a calibrated probability, or a
low-loss row can become misleading when readers over-trust an automated aid or mistake a bounded benchmark for deployment evidence [ Horowitz and Kahn ,
2024]. Human oversight is necessary, but it is not a magic solvent; the manuscript’s stronger safeguard is that the artifacts keep uncertainty and non-claims
visible.
Official AI, cyber, and responsible-AI frameworks supply vocabulary for that discipline: governability, traceability, reliability, risk mapping, and measurement are
useful labels for the code gates, ledgers, and artifact provenance [ National Institute of Standards and Technology , 2023, 2024, U.S. Department of Defense , 2021].
They are conceptual anchors, not certification. In this manuscript, governance means refusing to let a regime-qualified AIF advantage outrun its evidence: no
global SOTA claim, no real-trace claim, no tasking claim, and no claim that policy sources certify the model.
5 Limitations: Synthetic Evidence Does Not Promote Real-T race Claims
5.1 The Generator and Lanes Bound Reproducibility
The following limitations concern the synthetic-data substrate and the gap between latent-state recovery and ground truth. Active FractalRabbit: A Synthetic
Benchmark for Belief Filtering Under Sparse Waypoint Observations has deliberate limitations. Although the external lane now builds and runs the full stochastic
simulator at the pinned commit, the upstream CSV parameter surface exposes no random seed, so individual external runs are not bit-reproducible; reproducibility
at that boundary is statistical (replicate dispersion is reported) rather than exact. The checked fixture remains the deterministic regression substrate.
The latent state is a discretized spatial cell. It is useful for a discrete POMDP analysis, but it is not a recovered FractalRabbit internal state, a real location
semantic, or a cognitive state. In the default configuration location remains an observation modality, so the flagship lane stays close to an observed-state filter; the
deep-latent configuration ( model.modalities without location, exercised by the sensitivity lane and a checked config fixture) removes direct location evidence
and demonstrably raises posterior uncertainty, but it is a configuration option rather than the default reporting lane.
The spatial-resolution frontier narrows this limitation rather than removing it. Its current verdict is default_resolution_not_best_feasible_loss : the 4x4
default remains fully occupied and auditable, but the canonical fixture no longer makes it the best feasible observed-location loss among the measured candidates.
The deterministic sample-size ladder (2, 4, 8 times the canonical reports per traveller, largest n=19200) is useful because it retests the same frontier under larger
synthetic samples; it reports larger_sample_changes_frontier_decision at the largest run and a guardrail-stable status of yes across the ladder. It refines the
observed-location fit verdict, so it must be read as sensitivity evidence rather than population replication. It is still generated from the same fixture family and
is not a population confidence interval or empirical validation. Because the ladder has strict feasible candidate counts 2, 0, 0, its selected-bin series 4, 8, 4 is a
fallback best-measured-loss series wherever that count is zero, not proof that the larger lanes satisfy the canonical occupancy floor. The no-location guardrail still
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moves against fine-cell recovery (canonical default-vs-coarse mass change -0.045; largest-sample change -0.036), so the model gains nominal cell granularity only
where location is observed; it does not gain an unsupported ability to infer fine-grained cells from metadata alone.
The active-inference, fixed-transition, and pymdp traces are synthetic-data software diagnostics. The external sensitivity lane now resimulates stochastic waypoints
per variant, which broadens the evidence beyond a single fixture, but nothing here shows that FractalRabbit output reproduces empirical human-mobility
regularities such as recurrent returns, scaling laws, population-level trajectory structure, or task- and aggregation-dependent predictability limits [ Barbosa et al. ,
2018, Gonzalez et al. , 2008, Song et al. , 2010a,b, Ikanovic and Mollgaard , 2016].
5.2 Performance Language Remains Blocked by SOT A Gates
The pymdp lane is not a state-of-the-art performance result. The benchmark matrix reports not_demonstrated, and the measured predictive-loss delta versus the
reference filter is 0.428 nats. The present evidence supports implementation validity and interpretability, not predictive superiority. A performance claim would
need the baselines and empirical gates listed in sec. 6.3.
The closed-loop selector is a transparent heuristic for comparing declared synthetic simulator configurations. It does not optimize a real collection policy, and
it should not be used as operational guidance without an empirical design that defines sampling, harms, privacy, and validation endpoints independently of this
scaffold [ de Montjoye et al. , 2013, Kondor et al. , 2020]. The same boundary applies to commercially available or connected-vehicle location-data debates: official
policy and enforcement sources make the governance context visible, but they do not transform this scaffold into a CAI workflow, legal-compliance result, or
operational system [ Office of the Director of National Intelligence , 2022, 2024, Federal Trade Commission , 2024, 2026].
5.3 Scoring and Holdout Limits Keep Nulls Local
The remaining limitations concern measurement uncertainty, the distinction between internal validation and real-world generalization, and honest null findings
that do not extend beyond their measurement regime. The fixture sensitivity lane is a deterministic reprocessing lane and its normal-approximation intervals
summarize configured variants only. The external sensitivity lane does resimulate stochastic waypoints per variant, but its replicate family is small and the
upstream seed is uncontrollable, so its dispersion numbers are descriptive spread, not calibrated sampling uncertainty.
The holdout and negative-control lanes are software-falsification evidence, not external validity. Holdout scoring re-estimates tensors on training rows but shares
discretization bin edges with the full lane, so it bounds tensor-estimation generalization only. The negative controls confirm that the pipeline responds to destroyed
structure in the configured direction; they do not show that intact structure corresponds to any real mobility process.
Several program-extension findings (sec. 14.7, sec. 14.6) are honest nulls rather than capability wins, and the limitation is precisely that they do not generalize
beyond the regime in which they were measured. Structure recovery does not beat its dynamics-only baseline on the expanded fixture lane (the only lane the
current structure-recovery artifact contains): the deep-latent occupancy total variation (0.171) does not improve on propagating the trained transition model
alone (0.042), so the sparse non-location metadata adds little to the preferred-place structure a fitted dynamics model already encodes. Mission-conditioned active
sensing is scored against a pure mission-pragmatic selection rule on the expanded benchmark (0.590 for expected-free-energy selection versus 0.554 for pragmatic
selection), and the budgeted information-gain schedule beats only a fraction 0 of blind random schedules. We report these regenerated values without reframing
nulls as wins.
The claim-level evaluation contract (sec. 8) has a deliberately narrow reach, and that narrowness is itself a limitation rather than a guarantee. The static contract
catches only the statically-encodable share of this project’s honesty failures, through its five shipped guards: wrong-regime persistence skill (G1), undisclosed
speed cues (G2), unsupported leaderboard rhetoric (G3), unbounded active-inference-help or uniqueness wording (G4), and deployment, surveillance-readiness, or
real-mobility-transfer wording that is not explicitly negated (G5). A learned model underperforming its own baseline, headline numbers that did not reproduce
on real data, a fabricated library call, and a scoring artifact visible only on full re-scoring were all caught only by executing the analysis. The contract is therefore
the smaller, claim-level tier of a two-tier honesty stack; a clean contract pass does not certify the analysis is honest, only that the statically-checkable claim-level
errors are absent. As with every result here, all of these remain synthetic-data software measurements on the pinned generator within the oversight-positive,
no-operational-tasking boundary, never empirical mobility validation.
5.4 Roadmap Artifact Boundaries Block Deployment Evidence
The new robustness and roadmap artifacts are still software evidence, not deployment evidence. Cross-realization variance bands summarize repeated synthetic
draws, not population uncertainty; upstream sensitivity can block when no comparable prior commit builds; the fractal-dimension sweep varies a generator control
rather than estimating a real trajectory dimension; and the circadian-phase artifact tests a candidate prior rather than real circadian behavior. The sequence-
baseline ladder is a stronger prequential null, not a complete movement-model benchmark. The reporting-process gate tests synthetic inter-report timing; without
empirical evidence about the observation mechanism, it cannot establish missing-at-random assumptions or rule out informative reporting [ Rubin, 1976, Lin et al. ,
2004]. The privacy frontier reports unicity and co-travel coincidence only as synthetic minimization-risk proxies, not k-anonymity, differential privacy, or any
other formal privacy guarantee. The hardened anomaly probes improve the baseline, but they remain perturbation tests over generated data rather than an
alerting or investigation method. The privacy-utility frontier now reports a synthetic monotone minimization frontier and a source-cleared minimum-collection
operating point on the larger canonical fixture, but that still does not imply an operational minimization recommendation, real-mobility evidence, or privacy
guarantee; synthetic mobility utility itself still requires task-based checks before it can be generalized [ Sweeney, 2002, Dwork, 2006, Kapp and Mihaljevic , 2023].
Privacy-preserving synthetic daily-trajectory pipelines are useful future comparators, but their aggregation assumptions, mechanism design, and deployment
claims do not transfer to this sparse waypoint fixture [ Ozaki et al. , 2025]. Cross-domain synthetic-data reviews make the same caution sharper: privacy and
utility metrics are task-dependent, not interchangeable certification labels, and many synthetic-data evaluations understate privacy risk when privacy is not tested
directly [ Kaabachi et al. , 2025]. The timing-channel integrity probe is read from its regenerated artifact rather than from a fixed null narrative: on the current
hardened-anomaly artifact the timing-manipulation probe shows a modest above-chance variational-free-energy separation while the online Markov baseline stays
near chance, and that is a synthetic perturbation-response diagnostic on this fixture, not a detector to deploy and not a timing-integrity capability claim.
6 Roadmap: Promotion Stays Blocked by Evidence Gates
This roadmap is a work queue, not a changelog. Current results, audits, and release artifacts set the boundary conditions for future work; historical sequencing
belongs in tasks.yaml, the claim ledger, generated manifests, and git history. The open gates below are therefore framed as falsifiable next questions: what
evidence would be needed to promote a claim, what would kill it, and which synthetic-only boundary remains in force.
6.1 Current Evidence Stops at Synthetic Artifacts
The current evidence surface is already reported with provenance-checked tokens in Results and Discussion: fixture diagnostics and spatial-resolution choice in
sec. 13.3, sequence/reporting/model gates in sec. 14.2 and sec. 14.3, forward gates in sec. 14.4, safety and minimization boundaries in sec. 15.2, pymdp diagnostics
in sec. 13.2, and synthesis in sec. 4. This section deliberately does not repeat verdicts. Its role is to keep the future bar visible without turning open work into a
delivered-work recap.
6.2 Near-T erm Model Gates Need F resh External Evidence
• External-realization model gates. Promote any fixture-positive sequence, reporting-process, return-plus-phase, forward-gate, or safety-boundary result
beyond fixture language only after fig. 34 and fig. 35 show current-run external evidence instead of an unavailable lane.
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• Multiscale spatial state. Replace the measured single-grid default with a hierarchy of coarse-to-fine states, so uncertainty can be interpretable at multiple
resolutions rather than forced into one cell size. This should extend spatial_resolution_frontier.json, not bypass it.
• Continuous or state-space dynamics. Add continuous, multiscale, or particle-filter dynamics only as regenerated artifacts with the same null hierarchy,
runtime surface, and interpretability audit used by the current gates.
6.3 State-of-the-Art Gates Remain Uncleared
The current status is not a state-of-the-art performance claim. The first stronger-baseline rung, the lane-resolved matrix, the factorial pymdp comparison in
sec. 15.1, and the promoted forward gates mostly narrow the claim space. A latent-regime hidden Markov model overfits out of sample; the dependency-light
neural sequence model does not beat the particle/state-space mixture; and learned Dirichlet or two-level hierarchical priors are refuted, with only a marginal
persistence-rate survivor whose paired bootstrap interval (-0.016 to -0.001) excludes zero but does not clear the pre-registered promotion threshold, so its verdict
remains honest_regime_null. Those negative gates remain claim blockers in the artifact surface, so a future claim cannot quietly resurrect a refuted direction.
First principles make the future bar simple: a method would need to assign a better predictive distribution to the next sparse waypoint cell on a locked task.
Lower variational free energy, richer expected-free-energy diagnostics, or a more legible policy posterior can make the model easier to audit, but those surfaces do
not by themselves establish predictive leadership. The primary future contract should therefore be prequential next-cell loss under sparse reports, with calibration,
Brier/ECE, persistence-relative gap filling, runtime, and minimization or integrity regressions carried as secondary gates. The artifacts that should eventually
encode this contract are sota_task_contract.json, sota_benchmark_matrix.json, sota_leaderboard.csv, and sota_claim_gate.json.
The canonical fixture locked-split contract partitions travellers disjointly into train and holdout so no traveller identity crosses the split, scores the transparent
baseline ladder under prequential next-cell loss with calibration, runtime, location-minimization, and integrity columns, and emits all four artifacts above. The
claim gate currently reports sota_not_cleared : no implemented candidate beats the strongest honest baseline, whose mean predictive loss is 0.606 nats on
the locked split, and the required foundation-model and language-model baseline families are declared but unavailable, so performance-leading language stays
blocked. The false-claim oracle makes this guard legible rather than asserted: a leakage probe that peeks at the true next cell reaches mean loss 0.000 nats —
far below every honest baseline — yet is excluded by the leakage guard, so a leakage-driven win cannot clear the gate. The same gate rejects a fixture-only
win, a single-metric win that loses on calibration, and any win that depends on direct location or fails the poisoning-integrity diagnostics. A positive control
confirms the gate is not vacuous: a clean, calibrated, externally confirmed win with no minimization or integrity regression would clear it, which is exactly the
condition no current method meets. This matrix remains a leakage and null guard; it is not the direct active-inference comparison because its rows do not score
the active-inference candidate on that same expanded program surface.
A higher-power, robustness-expanded instance of this contract sharpens the verdict rather than softening it. The locked benchmark was re-run in the partial-
observability regime with 64 travellers (26 held out) across 4 canonical lanes ( fractalrabbit, gravity, reporting_gap, regime_stressor), so that every candidate
faces the same traveller-disjoint split, known noisy-emission channel, train-only transition source, and traveller-clustered interval. The stronger sequence and
state-space candidates — a switching-noise HMM and a particle filter — are scored directly on the locked split rather than marked ineligible, and the roster now
includes dependency-light recency and multi-horizon attention sequence baselines alongside the improved active-inference candidate (a precision-weighted belief
with a calibrated return prior selected on a train-internal split only). fig. 12 is the direct FractalRabbit-lane comparison: it places precision_return_aif and the
soft_filter active-inference reference on the same locked-split surface as switching HMM, particle filtering, neural and attention comparators, Markov variants,
persistence, and base rate. The gate stays sota_program_not_cleared (clears: no). On the FractalRabbit lane, the active-inference row is 1.139 nats against
the strongest fair baseline switching_noise_hmm at 1.144 nats, with paired clustered interval [-0.002, 0.012] nats; on the gravity lane it is 3.030 nats against on
line_base_rate at 2.771 nats. The reporting-gap lane is scored: yes, and the larger regime-stressor lane is scored: yes. A separate diagnostic robustness grid
now scores high-motion adversarial missingness and an independent repeated regime-stressor realization through the same candidate interface, but it is an audit
surface, not an expanded claim gate. The bounded reading is set by the artifact itself: Reporting-gap and regime-stressor lanes are scored synthetic robustness
evidence, not empirical transfer, operational readiness, or SOTA clearance. The oracle-fed reference is excluded as a ceiling rather than a competitor, no baseline
was weakened to manufacture the comparison, and the candidate was calibrated on training travellers only — so the blocked gate is the evidence speaking, not a
missing implementation.
Figure 12: Source sota_program_leaderboard.csv ranks every locked-split synthetic FractalRabbit row by mean next-cell predictive loss. Bootstrap whiskers share
one loss axis; the annotation adds Brier score, ECE, top-1 accuracy, runtime, paired delta, one-sided p-value, and holdout-traveller count. Precision-return AIF
and soft-filter AIF are scored beside switching HMM, particle, neural, attention, Markov, persistence, and base-rate comparators. The comparison is direct: active
inference is scored directly, and the strongest fair baseline and blocked program gate remain visible. Evidence: a direct locked-split SOTA-program comparison
that includes active inference and the strongest fair baselines on the same FractalRabbit lane. Boundary: a global state-of-the-art performance claim, operational
tasking, or real-mobility validity.
A separate regime-qualified active-inference search asks the narrower question the global gate is not allowed to answer: are there specific synthetic latent-emission
regimes where the best active-inference family candidate beats the strongest implemented non-AIF fair baseline under the same locked split, train-only transition
source, known observation channel, and traveller-clustered CI rule? fig. 13 maps that local gate by regime and realization seed. Its status is regime_qualified_
sota_not_cleared (clears: no; cleared regimes: 0). The artifact’s cleared-regime fields hydrate as: best cleared regime none; best AIF candidate(s) unavailable;
strongest fair baseline unavailable; minimum advantage (nats) unavailable; conservative CI edge (nats) unavailable. When no regime clears, those fields render their
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explicit none/unavailable sentinels — the bounded null — rather than numbers. Either way the boundary is fixed by the artifact: This gate is separate from the
canonical global SOTA program. A positive regime result is limited to the exact synthetic regime IDs, realization seeds, candidate roster, and observation-channel
contract in this artifact; it does not imply external, empirical, operational, surveillance, foundation-model, or global SOTA performance.
Figure 13: Source aif_regime_sota_gate.json maps the separate regime-qualified synthetic search for active-inference advantage. Each cell is loss(strongest fair
baseline) minus loss(best AIF-family candidate) for one synthetic regime and realization seed on a common signed scale; positive values favor AIF. Green rings
mark traveller-clustered CI-separated local wins that also clear the oracle/leakage floor, while the side panel reports p/max-CI clearance and the Holm-adjusted
familywise failure from multiplicity_ledger.json. Evidence: a regime-local synthetic search for where AIF-family belief marginalization beats the strongest
implemented fair baseline with clustered-CI separation. Boundary: global SOTA, external simulator SOTA, empirical transfer, operational readiness, or real-
mobility validation.
The baseline map also needs to become wider than the current fixture gate. Future comparison work should re-check the mobility-prediction literature at
implementation time rather than freezing this manuscript’s date-stamped view of the field. Useful seed families include deep-learning mobility surveys, memory-
and-competition mobility models, pretrained and continual-learning mobility transformers, universal mobility predictors, self-supervised disentangled next-POI
models, sparse transformer-style trajectory predictors, GPT-style mobility generation, trajectory-LLM taxonomies, spatially aware mixture-of-experts foundation
models, instruction-tuned and open-source mobility language models, intention-guided and coordinate-regression next-location systems, training-free LLM-agent
evidence-gathering predictors, LLM-agent synthetic-trajectory generators, reversible trajectory-to-CNN generators, systematic synthetic-urban-mobility generator
taxonomies, large-scale diffusion-style synthetic mobility datasets, aggregated-input privacy-preserving daily-trajectory synthesis, cross-city LLM-guided mobility
generators, train/test-overlap-aware benchmark protocols, HuMob/GISCUP-style sparse-challenge systems, higher-order path-validity checks, semantic mobility
question-answering benchmarks, plausibility-versus-realism audits for LLM-based urban simulators, and task-based synthetic-mobility privacy/utility evaluations
[Luca et al. , 2021, Yan et al. , 2017, Wu et al. , 2024, Haydari et al. , 2024, Gao et al. , 2022, Xu et al. , 2025, Shi et al. , 2026, Long et al. , 2024, Solatorio, 2023, Yuan
et al., 2025, Han et al. , 2025, Tang et al., 2024, Qin et al. , 2026, Liu et al. , 2026b, 2024, Chen et al. , 2026, Li et al. , 2026, Merhi et al. , 2024, Kapp et al. , 2023, Yuan
et al. , 2026, Ozaki et al. , 2025, Liu et al. , 2026a, Luca et al. , 2023, Fang et al. , 2025, LaRock et al. , 2026, Asano et al. , 2025, Santos et al. , 2026, Deng et al. , 2025,
Wu et al. , 2025, Kapp and Mihaljevic , 2023, Mishra et al. , 2025]. Inside this project, those references are not evidence that the current scaffold is competitive,
privacy-preserving, realistic, or useful in real-life downstream tasks; they define external baseline categories, leakage/overlap checks, synthetic-validity checks,
semantic-evaluation gaps, and task-utility/privacy checks that any future state-of-the-art or release-utility claim would need to face.
The remaining forward positives stay bounded. Cross-generator transfer shows persistence strength is a self-transition-rate regime property across synthetic
generators, while the expanded held-out reporting-process gate demotes the earlier burst-cadence survivor to an honest null. What the study still lacks is
consented empirical traces under the separate validation protocol, plus enough repeated external and stressor realizations to stress the negative gates fairly.
The fair-ladder external-realization manifest records this block explicitly: fixture language cannot be promoted until every required current external realization
is present and agrees on the oracle-boundary controls. Each future candidate must report predictive loss, calibrated recovery, persistence-null skill, runtime,
interpretability surface, failure modes, locked-split performance, and current-lane external evidence. Only a method that improves performance while preserving
the claim-level null discipline should be described as performance-leading.
The claim guard is stricter for national-security-adjacent language. Synthetic performance, even if improved, cannot unlock real waypoint, deployment, surveillance-
readiness, or operational tasking claims. Those remain blocked by the empirical-validation protocol, consent and provenance records, minimization endpoints,
privacy review, and a non-operational publication plan.
6.4 AIF Deepening Must Admit Predictive Candidates
The active-inference lane remains under the prototype-before-claim discipline. Two current methodology surfaces bound future work. First, the generative
model is an auditable artifact rather than a side effect of construction code: a machine-checkable specification (the generative model card ) states the factor and
observation structure, the dependency graph, the column-stochastic normalization invariants, and the conditional-independence approximation, and a conformance
validator confirms that the implemented tensors are the model the manuscript describes. Second, the location-minimization question is answered in the free-energy
machinery’s own currency: metadata_recovery_not_above_structure_null , with location share 1.000, metadata null p-value 0.417, and residual localization 0.
The oversight-positive reading, scoped to this generative model and offered as neither a universal claim nor a collection-priority recommendation, is narrower after
the 4x4 expanded fixture: the artifact verdict decides whether metadata clears the structure null, while withholding location still sharply reduces localizability.
Real mobility may couple metadata and place far more strongly, so the result does not transfer without the empirical protocol.
Current active-inference scholarship sharpens that discipline rather than relaxing it. Scalable POMDP planning variants such as Active Inference Tree Search,
sparse-reward/world-model R-AIF agents, and formal-equivalence reviews of active inference all motivate richer future candidates; none is a scored row here,
none makes the present proxy canonical, and none upgrades a local synthetic regime result into global SOTA language [ Maisto et al. , 2025, Nguyen et al. , 2024,
Sweeney et al. , 2026].
Two further active-inference levers were prototyped and returned honest nulls. Multi-step expected-free-energy planning does not improve recovery: when the cell
is observed the chosen control is moot, and in the location-withheld regime any apparent gain is not robust and does not survive a smoothing sweep — a synthetic
control where multi-step planning provably should help confirms the machinery works, so the result is a genuine null rather than a power failure. Policy precision
is performance-inert under deterministic selection, and an apparent gain under stochastic selection is explained away by a random-action confound rather than
by precision itself; precision is retained only as an interpretive readout, never to sharpen any location inference.
The lane was then made eligible on the same locked split the transparent baselines use, by scoring the POMDP filter’s prequential next-cell loss under a traveller-
disjoint train/holdout split. The measured answers that follow from that eligibility — the fair-comparison ladder (how much principled latent-cell inference helps
once every predictor shares the transition source, and how that help splits between single-step soft marginalization and recursion) and the traveller ×noise regime
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map that bounds where the advantage lives — are reported in the Discussion (sec. 4.2 and sec. 4.3, with fig. 10 and fig. 11). What remains genuinely forward here
is everything those results do not settle: a cross-vendor audit of the single-vendor result, more held-out travellers and more strongly regime-structured synthetic
data to interval the advantage, and the multiscale and continuous-dynamics extensions below.
The noise-conditional reading of those results is where an earlier session overclaimed, via the retracted observation-noise frontier described above. The corrected
settlement uses soft versus hard predictors that differ only in marginalize-versus-commit under an emission matched to the generator by construction, so no knob
can be asymmetric; the protocol is specified in sec. 2.6.2 and the result, with its robustness band, is reported as a measured result in sec. 3.1.1 (fig. 3). It remains
a synthetic software measurement that does not beat the oracle-fed baseline and is not a real-mobility claim, and the benchmark gate is unchanged.
The completed online-adaptation ablation and its remaining fair-baseline deficit are reported in sec. 4.1.1. What remains forward is narrower: admit factorial or
multiscale candidates only after they implement Candidate.predict(PredictContext), use the same nested estimation contract, and plausibly address a measured
residual rather than adding audit-only complexity. EFE, VFE, and tensor surfaces cannot substitute for locked-split predictive improvement.
6.5 Real-T race Claims Require a Separate Empirical Gate
The empirical-validation protocol remains separate ( docs/empirical_validation_protocol.md). It is the prerequisite for any real waypoint-data claim, requiring
consent, provenance, sampling, minimization endpoints, and privacy review defined independently of this scaffold [ Patterson et al. , 2017, Deng et al. , 2025,
de Montjoye et al. , 2013]. The synthetic numbers here settle nothing about real mobility and are not a step toward an operational system.
Throughout, the boundary is unchanged: these are synthetic-data directions on the pinned FractalRabbit generator, oversight-positive and location-minimization-
framed, with no operational surveillance, tasking, or evasion surface. Each item is a falsifiable question with a kill-gate, not an intended capability claim.
7 Conclusion: A Synthetic Benchmark Can Clarify Without Promoting
7.1 Recovery and Minimization Stay Null-Bounded
The signature contribution of Active FractalRabbit: A Synthetic Benchmark for Belief Filtering Under Sparse Waypoint Observations is a claim-bounded
benchmark discipline for the public NSA-hosted FractalRabbit synthetic generator. The discipline rests on a hierarchy of synthetic nulls: uniform chance, base-
rate prediction, and temporal persistence handed the true previous cell (sec. 3.2.1). That last null is an oracle baseline, and the central methodological lesson
is an information-asymmetry bound: the location-blind filter is scored with less state information than the baseline receives for free. This bound is reported in
Results as a synthetic-regime fact, not reframed as an artifact or limitation to bypass.
The same discipline applies across three front-line tests. Routine-break detection clears its synthetic positive controls, with VFE surprise AUC 0.649 for rare-cell
breaks and 0.667 for random-cell breaks. Structure recovery from non-location metadata remains regime-contingent, depending on learned transition structure
rather than on metadata alone. Mission-conditioned collection advances from prose to executable comparison on the expanded fixture, not to an operational
workflow.
The minimization frontier gives the main synthesis: with all modalities the filter holds mean mass 0.995 on the true cell, but withholding location collapses it to
0.069, an oversight-positive statement of what location minimization protects on this generator. Its utility-side dual (sec. 15.4, fig. 48) now reports a monotone
synthetic frontier on the larger canonical fixture: the endpoint pair moves from 3.933 bits and 0.389 risk to 1.747 bits and 0 risk, with a minimum-collection
operating point at grid_2x2.
That operating point is not a privacy guarantee; it is a generated-task frontier that would need separate k-anonymity, differential-privacy, legal, and empirical
utility analyses before any real-data use [ Sweeney, 2002, Dwork, 2006, Kapp and Mihaljevic , 2023].
The spatial-resolution result follows the same rule. The default 4x4 grid remains auditable because all 16 default cells are occupied, but the frontier now reports d
efault_resolution_not_best_feasible_loss: the default is not the best feasible observed-location loss in the canonical run, and its full-location loss changes by
0.867 nats versus the coarse comparator. A deterministic synthetic sample-size ladder (2, 4, 8 times the canonical reports per traveller; largest n=19200) reports
larger_sample_changes_frontier_decision at the largest run, with selected bins 4, strict feasible candidate count 0, and default-vs-coarse loss change -1.069;
that ladder refines the observed-location fit verdict rather than turning it into population replication. The no-location guardrail moves by -0.045 in the canonical
run and -0.036 in the largest check, with guardrail stability yes across the ladder, so the paper does not claim improved fine-cell recovery from metadata-only
evidence.
7.2 Roadmap Advances Still Leave Performance Gates Closed
The new roadmap artifacts advance the paper from “future work” to executable research gates. The spatial-resolution frontier reports default bins 4, best feasible
bins 3, and pymdp sentinel agreement 3.20e-07. The return-structure gate reports 0.186 nats of move-step entropy reduction and verdict promote_return_condi
tioned_prior. Cross-realization bands place gap-filling skill between 0.219 and 0.268 across synthetic draws. The fractal-dimension sweep reports status fixtur
e_control_unvaried; the circadian-phase analysis reports verdict honest_null; the sequence-baseline gate reports best model first_order_markov and gate str
onger_sequence_baseline_beats_pymdp_on_this_run; and the lane-resolved model-gate matrix reports status partial.
The promoted forward gates narrow the next-performance story. Latent-regime HMM is latent_regime_hmm_does_not_beat_markov_null_em_overfits ; neural
sequence is neural_sequence_beats_weak_nulls_not_particle_mixture ; learned stay-rate is honest_regime_null ; held-out reporting is honest_null; and
cross-generator persistence is regime_dependent_on_self_transition_rate . The safety-boundary gates report metadata_recovery_not_above_structure_nu
ll, location_carries_relink_risk_that_minimization_removes , and poisoning_detection_regime_changed . The future roadmap for moving this toward
state-of-the-art performance is now narrower and more concrete: current-run external evidence for the fixture positives, multiscale or continuous dynamics, and
consented empirical validation under the separate protocol.
The benchmark’s clearest answer concerns noisy partial observability. Holding model, emission, observations, and priors fixed while varying marginalize-versus-
commit, soft Bayesian marginalization ties the point estimate when the latent cell is directly observed and gains strictly as the emission degrades (1.860 nats per
unit 𝜀, R 2 = 0.995). Every one of the 15 resamplings is positive at every nonzero noise level.
Active inference realizes this mechanism through recursive belief updating. In the full noisy-emission comparison it ranks 1 of 14, leads the best point-estimate/raw-
observation family by the belief-cluster gap of 0.192 nats, and leads the strongest non-AIF belief filter by 0.005 nats with a clustered interval crossing zero. Active
inference is therefore the implemented point leader and a statistical member of the top belief-preserving cluster. HMM, particle, state-space, and soft-filter
methods share the core marginalization mechanism.
The wider model map completes the answer. Under latent regime switching, online transition adaptation improves fixed AIF by 0.146 nats on average, while the
adaptive online base-rate comparator remains strongest. Under reporting gaps, persistence and disclosed kinematic controls anchor the comparison (sec. 14.2).
With location withheld, occupancy and trained dynamics explain broad structure while specific-cell recovery collapses. The practical rule is conditional: commit
when the state is effectively observed, marginalize when it is genuinely hidden, and adapt when the generating regime changes.
The oracle-fed baseline remains the predictive ceiling. The higher-power, 4-lane program scores 64 travellers across fractalrabbit, gravity, reporting_gap,
regime_stressor and reports sota_program_not_cleared. The present contribution is therefore a regime-specific synthetic model result: Active Inference leads
the implemented noisy hidden-state lane, shares that lead statistically with the strongest non-AIF belief filter, and supplies an auditable variational account of
the uncertainty that produces the gain.
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7.3 pymdp Adds Interpretability Rather Than Performance Leadership
The pymdp lane provides a validated variational active-inference implementation. It agrees with the exact Bayes posterior under matched priors to maximum
absolute difference 3.99e-07 and exposes variational free energy, policy posterior, expected free energy per policy, runtime, and action-conditioned prior divergence.
Relative to the transparent reference filter, the benchmark matrix reports status not_demonstrated, predictive-loss delta 0.428 nats, and posterior-entropy delta
0.009 nats. Its established contribution on the default observed-state surface is therefore interpretability; its predictive advantage appears in the separate noisy
hidden-state comparison above.
7.4 The Final Boundary Is an Honesty Stack
Holding the whole arc together is a two-tier honesty stack. The execution tier supplies checked fixtures, negative controls, holdout scoring, a checksummed
release manifest, tokenized quantities, and source-artifact provenance. The claim tier uses five guards (G1-G5) to bind every performance statement to its regime,
information set, cue disclosure, and evidence class [ Sandve et al. , 2013, Wilson et al. , 2017, Smith et al. , 2016].
Active FractalRabbit: A Synthetic Benchmark for Belief Filtering Under Sparse Waypoint Observations therefore delivers an auditable synthetic model map:
Active Inference records its clearest predictive result under noisy hidden-state observations; simpler predictors lead when the state is clean or the generator changes
faster than the fixed model; and location minimization materially constrains recovery. That map is the basis for the next empirical contract.
8 Supplementary S1 - V alidation Gates Preserve Synthetic-Only Claims
8.1 T ests Protect Artifacts Before Prose Claims
The validation strategy is artifact-first: every manuscript-facing claim is meant to remain tied to retained inputs, scripts, generated artifacts, and software
identifiers rather than to an unrecorded analyst session [ Sandve et al. , 2013, Wilson et al. , 2017, Smith et al. , 2016]. The synthetic validation suite uses unit
tests to validate config parsing, FractalRabbit parameter ordering, CSV parsing, first-observation sentinel handling, observation determinism, stochastic-matrix
normalization, JAX-compatible tensor shapes, policy-proxy component sums, fixed-transition baseline trace emission, holdout split and scoring behavior, seeded
negative-control mutations, candidate-score ordering, figure registry completeness, PNG integrity, release-manifest checksums, manuscript token coverage, fractal-
dimension sweep summaries, circadian-phase signal formulas, sequence-baseline loss formulas, reporting-process log-loss formulas, and the pymdp benchmark
matrix. Fixture tests run without Java or Maven; the external FractalRabbit integration test is explicitly marked and skips with an explicit reason naming the
missing tool or Java version.
8.2 Guardrails Block Claim Drift and Evidence Laundering
The primary failure modes are concrete:
Table 3: Validation threat model for the synthetic waypoint analysis.
risk guardrail
FractalRabbit source drift pinned commit 9933449c4f4fe1b26b6ac7bfdeeac76583085df5 and config
validation
CSV contract drift parser tests for ID, Days, x(km), y(km)
observation category drift deterministic feature-table tests
invalid probability tensors column-sum tests for eq. 1 and eq. 2
ambiguous temporal prior explicit eq. 4 and trace-level baseline comparison
selector opacity emitted tbl. 5 and deterministic tie-breaks
manuscript stale numbers token-generation gate and rendered-output checks
manuscript stale source artifacts token provenance tuples from eq. 30 with checksum and value matching
pipeline insensitive to destroyed structure seeded negative-control lane with directional probes (fig. 14, tbl. 7)
in-sample-only scoring additive per-traveller chronological holdout metrics in metrics.json
roadmap artifact overpromotion fractal-dimension, circadian-phase, sequence-baseline, reporting-process,
forward-gate, and pymdp benchmark artifacts carry explicit status and caveats
claim-ledger stale artifacts scripts/12_check_claim_ledger_artifacts.py parses generated output/
paths cited in docs/claim_ledger.md and fails on missing artifacts
release bundle drift checksummed release_manifest.json over configs, fixtures, run artifacts,
variables, figures, and rendered PDF
8.3 Real T races Require Empirical and Privacy Review
The red-team boundary is also explicit. A persuasive plot is not sufficient evidence for real-world mobility inference. The project therefore treats fig. 17 through
fig. 26 as software diagnostics over generated or fixture data. Any future empirical study must introduce separate consent, provenance, sampling, privacy, and
external-validity checks before reusing the manuscript language for real traces, especially because human mobility data can remain re-identifiable after coarse
spatiotemporal reduction and can be vulnerable to cross-dataset trace matching [ de Montjoye et al. , 2013, Kondor et al. , 2020, Mishra et al. , 2025]. Formal
privacy guarantees are separate mechanism claims, not something produced by this benchmark automatically [ Dwork, 2006]. Synthetic trajectory generation also
should not be treated as a privacy guarantee by itself without explicit privacy evaluation: recent trajectory-generator work separates utility from adversarial
privacy testing, studies memorization mitigation in diffusion generators, and shows that differential privacy can impose measurable utility costs under constrained
mechanisms [ Wang et al. , 2023, Buchholz et al. , 2024, Bouras et al. , 2026, Cherigui et al. , 2026, Guepin et al. , 2026, Buchholz et al. , 2025, Yadav et al. , 2024].
Cross-domain synthetic-data metric reviews reinforce that privacy and utility must be evaluated separately and that untested privacy dimensions should remain out
of claim scope rather than inferred from utility or resemblance [ Kaabachi et al. , 2025]. The manuscript’s “minimization” language follows the data-minimization
principle and privacy-by-design posture codified in data-protection law and risk-management guidance [ European Parliament and Council , 2016, National Institute
of Standards and Technology , 2020], but its minimization and linkage numbers are synthetic risk proxies on generated traces, not compliance determinations,
formal guarantees, or differentially private releases. AI risk, cyber-governance, responsible-AI, commercially available information, and location-data enforcement
sources extend that policy framing only: they support provenance, minimization, oversight, and responsible interpretation language, not technical validity, legal
compliance, operational readiness, or a real-trace workflow [ National Institute of Standards and Technology , 2023, 2024, U.S. Department of Defense , 2021, Office
of the Director of National Intelligence , 2022, 2024, Federal Trade Commission , 2024, 2026].
8.4 Risk and Integrity Gates Stay Synthetic Proxies
Three defensive, oversight-positive analyses sharpen the privacy and integrity boundary, each gated with the project’s structure-null plus positive-control discipline
so that a reassuring number means “the synthetic proxy passed its structure-null and positive-control check”, not “the test was too weak” . The EFE location
frontier in fig. 43 reports verdict metadata_recovery_not_above_structure_null : location carries share 1.000 of the joint epistemic value, the metadata null
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p-value is 0.417, and the residual fraction localized without location is 0. That artifact is a minimization boundary for this synthetic generator: the current
verdict determines whether the metadata residual clears the structure null, while withholding location still collapses localization and is not a collection-priority
recommendation.
The linkage-risk frontier in fig. 44 reports verdict location_carries_relink_risk_that_minimization_removes. Full-location linkage is 1, while the no-location
regime exceeds its null band: no. The statistic is an aggregate per-regime risk number over synthetic identities, computed to show what data-minimization buys
back; it is not, and does not yield, a re-identification, surveillance, or tasking capability over any real person. The boundary is gated in code: the data-loading
entry point derives and validates a synthetic-generator provenance marker, so running on real data requires a deliberate, auditable misrepresentation rather than
an accident.
The poisoning gate in fig. 45 asks whether the analyst’s own active-inference generative model notices tampered input. Its verdict is poisoning_detection_re
gime_changed: gross teleport poisoning detected no, subtle-drift null versus Markov yes, and the teleport mid-rate VFE AUC is 0.636. The defensive reading
is verdict-bound: the 4x4 artifact reports which crude stressors separate from the Markov baseline in this configuration, not a general label-flip or subtle-drift
assurance. The stressors are integrity probes, never an attack technique, and no operational capability is produced.
8.5 The Claim Contract Catches Manuscript Overreach
FractalRabbit exists so that sparse-mobility-analytics algorithms can be developed and compared on a controlled, reproducible, ground-truth-bearing synthetic
testbed without real traces [ Darling, 2018, National Security Agency , 2026a]. The central methodological hazard for any such benchmark is the one this project
was built to detect: a number that looks like recovered structure but is an artifact of the wrong null, the wrong regime, a self-selected coverage subset, or an
undisclosed cue.
We therefore promote the project’s honesty discipline from prose to a machine-checkable evaluation contract (src/active_fractal_rabbit/eval_contract.py ,
enforced by tests/test_eval_contract.py ). It is a static linter over the manuscript and its token bindings, encoding the discipline as falsifiable claim-level
guards: a null-regime guard (G1) that flags any sentence asserting positive skill against the persistence null while citing a location-blind token — the precise error
this manuscript itself avoids, since persistence receives the true previous cell and the location-blind filter does not; a cue-disclosure guard (G2) that requires any
recovery claim leaning on the speed cue to disclose that speed is derived from inter-report displacement; a performance-claim guard (G3) that requires state-of-
the-art or performance-leading wording to be explicitly negated, future-scoped, or bound to a cleared gate-status token; an active-inference-help guard (G4) that
requires active-inference help or uniqueness wording to be negated or bounded to its measured regime and comparator family; and a deployment/surveillance-claim
guard (G5) that requires deployment, surveillance-readiness, or real-mobility-transfer wording to be explicitly negated, so synthetic progress cannot unlock that
language.
The contract is the same negative-control philosophy that gates the pipeline, lifted to the level of the claim: it complements, and does not replace, the execution-
level harness (negative controls, full-trajectory scoring, the binding gate, the no-hardcoded-numbers guard) that catches honesty failures visible only by running
the analysis.
We apply the project’s own prototype-before-claim rule to the contract itself, and report its reach honestly rather than overstating it: of this project’s documented
honesty failures, only the wrong-regime class was statically catchable from prose and token bindings, while the others — a learned model that underperformed
its own baseline, headline numbers that did not reproduce on real data, a fabricated library call, a scoring artifact visible only on full re-scoring, and external
simulator and render-readiness failures that only appear when the full artifact pipeline runs — were caught only by executing the analysis. The static contract is
therefore the smaller, claim-level tier of a two-tier honesty stack, and it says so. It ingests nothing but this project’s own manuscript and artifacts — a reusable,
oversight-positive evaluation layer rather than an instrument over any real data.
8.6 T oken Provenance Runs Before Rendering
The execution tier now includes fail-loud manuscript-variable provenance. scripts/11_check_manuscript_variable_provenance.py rebuilds the selected token
map, verifies that every result-critical source artifact and JSON path exists, checks the source checksum, and byte-compares the formatted artifact value to the
rendered token. Missing optional external quantities are allowed only as explicit unavailable text; silent zeros are not an acceptable fallback. This is narrower
than full semantic review, but it closes the stale-token class before the PDF render is trusted.
9 Supplementary S2 - Reproducibility Runs Through Artifacts and Render Checks
9.1 Fixture-First Commands Rebuild the Study Surface
The reproducibility design is artifact-first and executable, following computational-research and software-citation guidance that favors versioned inputs, retained
intermediates, scriptable workflows, plain-text project structure, and specific software identifiers [ Sandve et al. , 2013, Wilson et al. , 2017, Smith et al. , 2016]. The
default reproducibility lane is fixture-first:
uv run python scripts/00_preflight.py
uv run python scripts/02_run_pipeline.py --config configs/default.yaml
uv run python scripts/03_run_sweep.py --config configs/sweep.yaml
uv run python scripts/05_run_negative_controls.py --config configs/default.yaml
uv run python scripts/08_run_sparsity_analysis.py --config configs/default.yaml
uv run python scripts/04_generate_figures.py --run output/runs/default
uv run python scripts/14_check_visual_quality.py
uv run python scripts/20_run_aif_regime_search.py
uv run python scripts/z_generate_manuscript_variables.py
uv run python scripts/11_check_manuscript_variable_provenance.py
uv run python scripts/15_check_claim_audit.py
uv run python scripts/16_check_visual_claim_audit.py
uv run python scripts/12_check_claim_ledger_artifacts.py
uv run pytest tests/ --cov=src --cov-fail-under=90
# or run both lanes end to end (external lane runs when JDK 21 + Maven resolve):
uv run python scripts/07_run_full_study.py --lane both
The render lane runs from the sibling template checkout:
uv run python -m infrastructure.orchestration link-projects
uv run python scripts/03_render_pdf.py --project working/active_fractal_rabbit
# back in the project checkout, bind the rendered outputs to their exact inputs:
uv run python scripts/29_finalize_publication_package.py
uv run python scripts/29_finalize_publication_package.py --verify-only
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9.2 Code and Data A vailability
The full source tree, checked fixtures, manuscript source, and generated release manifest are public at github.com/ActiveInferenceInstitute/active_fractal_rabbit
under the licenses recorded in LICENSE (code, MIT) and LICENSE-DOCS.md (documentation and scholarly outputs, CC-BY-4.0). Third-party notices for the pinned
external simulator and installed dependencies are recorded in THIRD_PARTY_NOTICES.md . A tagged GitHub release and an archival Zenodo deposit provide a
versioned, citable snapshot; citation metadata is recorded in CITATION.cff and, once minted, the archival digital object identifier appears on the manuscript cover
and in the Zenodo record linked from the repository.
9.3 Inventories and Checksums Bind the Release Surface
The primary generated artifacts are grouped by role:
• Run traces and tensors: observations.csv, discrete_features.csv, tensor_summary.json, posterior_states.csv, inference_trace.csv, policy_tra
ce.csv, baseline_trace.csv, baseline_metrics.json, candidate_scores.json, pymdp_trace.csv, ground_truth.csv, and provenance_manifest.json.
• Fixture, robustness, and diagnostic analyses: sensitivity_summary.json, sensitivity_summary_external.json, negative_controls_summary.json,
sparsity_analysis.json , spatial_resolution_frontier.json , anticipatory_analysis.json , active_sensing_analysis.json , anomaly_analysis.json ,
structure_recovery_analysis.json, mission_collection_analysis.json, frontier_analysis.json, partial_observability_analysis.json, return_str
ucture_analysis.json, variance_bands.json, upstream_sensitivity.json, fractal_dimension_sweep.json, circadian_phase_analysis.json, canonical
sequence_baseline_analysis.json, lane-qualified sequence_baseline_analysis_*.json, canonical missingness_model_analysis.json, and lane-qualified
missingness_model_analysis_*.json, return_phase_prior_analysis*.json, model_gate_matrix.json, model_conformance.json, forward_gates_summary
.json, latent_regime_hmm.json, neural_baseline.json, learned_stay_rate.json, heldout_reporting_process.json, and cross_generator_transfer.js
on.
• Safety , minimization, benchmark, and challenge surfaces: efe_location_frontier.json, linkage_risk_frontier.json, poisoning_robustness.js
on, pymdp_benchmark_matrix.json, sota_task_contract.json, sota_benchmark_matrix.json, sota_leaderboard.csv, sota_claim_gate.json, sota_progr
am_gate.json, sota_program_leaderboard.csv, sota_program_robustness_grid.json, sota_program_robustness_grid.csv, aif_regime_search.csv, aif
_regime_search.json, aif_regime_sota_gate.json, aif_sweep.json, aif_deepening_candidates.json, fair_inference.json, fair_inference_external
_realizations.json, power_analysis.json, open_challenge_pack.json, multiplicity_ledger.json, confound_taxonomy.json, model_comparison_leade
rboard.json, privacy_frontier_analysis.json, privacy_utility_frontier.json, privacy_utility_frontier_repeats.json, synthetic_task_utility_p
rivacy.json, and hardened_anomaly_analysis.json.
• Manuscript, visual, and release contracts: figure_registry.json, active_fractal_rabbit_cover.png, visual_quality_audit.json, claim_audit.j
son, visual_claim_audit.json, manuscript_variables.json, manuscript_variable_provenance.json, and release_manifest.json.
The manuscript values in sec. 3 are hydrated from these artifacts. If a metric changes, the rendered manuscript changes with it, and the provenance check fails
if a token source is missing, stale, incomplete, or byte-mismatched. The release manifest additionally records a SHA-256 checksum and byte size for source
modules, scripts, tests, documentation, configs, fixtures, default-run artifacts, cover art, figures, variable files, required release artifacts, and rendered outputs, so
a shipped bundle can be verified byte-for-byte and fails when a required or discovered release entry is absent. The resolved manuscript embeds a content-addressed
input fingerprint into both PDF and HTML; final verification recomputes that fingerprint, so changing a manuscript or visual input and merely updating output
timestamps cannot re-certify an unchanged render. For reviewers who want to rebuild the headline scalars without rerunning the whole simulator, scripts/z_ge
nerate_manuscript_variables.py rehydrates every manuscript token from the retained run artifacts and scripts/11_check_manuscript_variable_provenance.
py verifies the source path, JSON key, checksum, and rendered value behind each token.
The visual-quality audit reports pass for 53 registered figures. Its minimum rendered extent is 1339 x 724 pixels, its minimum normalized pixel standard deviation
is 0.129, and 53 captions carry source or boundary language. The audit also records aspect-ratio extremes and names the shortest, narrowest, lowest-variance,
and widest/tallest-aspect figures so the contact sheet can be manually inspected where static layout risk is highest. This is not an aesthetic proof, but it prevents
blank, undersized, caption-orphaned, source-orphaned, or silently hard-to-read figures from entering the manuscript unnoticed.
The figure layer treats visual design as part of the reproducibility contract rather than decoration. Quantitative comparisons use aligned axes, common-position
encodings, and generated source tables where possible; comparison patterns are graphed only when the plot clarifies a relation that would be harder to read in a
dense table; and uncertainty marks are paired with source artifacts plus explicit non-claim boundaries [ Cleveland and McGill , 1984, Gelman et al. , 2002, Munzner,
2014, Hullman, 2020, Spiegelhalter et al. , 2011]. These sources justify the visual audit’s reader-task, data-shape, encoding, and uncertainty checks. They do not
make a figure self-validating: the manuscript claim still has to survive the artifact, variable-provenance, claim-ledger, and visual-claim audits.
The claim and visual-claim audits add the RedTeam layer above those mechanical checks. claim_audit.json inventories manuscript claims by section and verifies
high-risk families against the claim ledger. visual_claim_audit.json records a mini-brief for every registered figure plus the cover, checking story job, reader
task, source artifact, data shape, encoding, caption support, and explicit non-claim boundary before render.
Table 4: Figure registry sources for the default generated figure set.
figure key source artifact
evidence_atlas output/runs/default/metrics.json
waypoint_paths output/runs/default/observations.csv
spatial_bins output/runs/default/discrete_features.csv
spatial_resolution_frontier output/runs/spatial_resolution_frontier.json
reporting_bursts output/runs/default/discrete_features.csv
speed_categories output/runs/default/discrete_features.csv
transition_heatmap output/runs/default/discrete_features.csv
likelihood_panels output/runs/default/discrete_features.csv
posterior_entropy output/runs/default/inference_trace.csv
policy_proxy output/runs/default/policy_trace.csv
candidate_scores output/runs/default/candidate_scores.json
negative_controls output/runs/negative_controls_summary.json
pymdp_agreement output/runs/default/pymdp_trace.csv
pymdp_diagnostics output/runs/default/pymdp_trace.csv
state_recovery output/runs/default/ground_truth.csv
sparsity_recovery output/runs/sparsity_analysis.json
calibration output/runs/default/calibration.json
anticipatory output/runs/anticipatory_analysis.json
efe_decomposition output/runs/active_sensing_analysis.json
anomaly_detection output/runs/anomaly_analysis.json
recoverability_frontier output/runs/frontier_analysis.json
return_structure output/runs/return_structure_analysis.json
variance_bands output/runs/variance_bands.json
upstream_sensitivity output/runs/upstream_sensitivity.json
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figure key source artifact
fractal_dimension_sweep output/runs/fractal_dimension_sweep.json
circadian_phase_signal output/runs/circadian_phase_analysis.json
partial_observability output/runs/partial_observability_analysis.json
sequence_baselines output/runs/sequence_baseline_analysis.json
missingness_model output/runs/missingness_model_analysis.json
model_gate_matrix output/runs/model_gate_matrix.json
m10_forward_gates output/runs/forward_gates_summary.json
factorial_pymdp_modes output/runs/factorial_pymdp_analysis_fixture.json
latent_mode_recovery output/runs/factorial_pymdp_analysis_fixture.json
factorial_model_gate_matrix output/runs/factorial_pymdp_analysis_fixture.json
efe_location_frontier output/runs/efe_location_frontier.json
linkage_risk_frontier output/runs/linkage_risk_frontier.json
poisoning_robustness output/runs/poisoning_robustness.json
privacy_frontier output/runs/privacy_frontier_analysis.json
hardened_anomaly_detection output/runs/hardened_anomaly_analysis.json
sota_leaderboard output/runs/sota_program_leaderboard.csv
aif_regime_map output/runs/aif_regime_sota_gate.json
fair_inference output/runs/fair_inference.json
fair_power_regime output/runs/power_analysis.json
multiplicity_ledger output/runs/multiplicity_ledger.json
confound_taxonomy output/runs/confound_taxonomy.json
regime_mechanism_synthesis output/runs/regime_mechanism_synthesis.json
regime_switch_phase_diagnostic output/runs/regime_switch_phase_diagnostic.json
privacy_utility_frontier output/runs/privacy_utility_frontier.json
privacy_utility_repeats output/runs/privacy_utility_frontier_repeats.json
synthetic_task_utility_privacy output/runs/synthetic_task_utility_privacy.json
model_comparison_under_noise output/runs/model_comparison_leaderboard.json
aif_deepening_candidates output/runs/aif_deepening_candidates.json
dataflow source pipeline modules
9.4 The External T oolchain Boundary Stays Stochastic and Pinned
External FractalRabbit runs require the toolchain boundary documented by preflight: Maven plus a JDK 21 runtime, which the boundary layer resolves
automatically from the environment, PATH, Homebrew keg locations, or java_home. The external integration tests skip with explicit named reasons when that
resolution fails, and run for real when it succeeds. Because the upstream simulator exposes no seed, external waypoint outputs are stochastic; the release manifest
checksums pin the exact artifacts behind any given rendered manuscript.
Render input fingerprint: f9a806b2a7e62501c1c237224f4b5052.
10 Supplementary S3 - F ractalRabbit Becomes Categorical Evidence, Not Real Mobility
This supplement documents the exogenous FractalRabbit generator contract and the observation-discretization pipeline that converts raw waypoints into the
categorical evidence consumed by the main-line inference layer (sec. 2).
10.1 The Pinned Upstream Contract Defines the Fixture Lane
FractalRabbit is treated as an upstream stochastic data generator, not as project-local source. The pinned external lane writes the published parameter rows
with labels matching parameters.csv, invokes the built jar as java -cp fractalrabbit-1.0-jar-with-dependencies.jar fractalRabbitGenerator.MainClassFR
parameters.csv <output_prefix> (the simulator appends XY.csv and PLACES.csv to the prefix rather than taking an output filename), and parses only the
documented output record shape [ National Security Agency , 2026a,c,b]. Because the upstream repository currently has no release archive, the manuscript cites
commit-specific URLs and stores the exact commit in the generated provenance manifest, following software-citation principles of specificity and persistence
[Smith et al. , 2016]. The fixture lane uses a checked CSV with the same columns, allowing Python tests and manuscript generation to run when Java and Maven
are unavailable. The boundary layer resolves a JDK 21 runtime explicitly (environment override, PATH, Homebrew keg locations, then java_home) and exports
JAVA_HOME to the Maven and Java subprocesses, because Homebrew installs openjdk@21 keg-only. On the current host the external lane status is: completed
on this host with the pinned upstream build — an artifact-presence status derived from the retained pinned-build metrics file, not a statement that the lane
completed within the current full-study invocation (the current-run gate artifacts report their own external-lane status independently).
10.2 F ractal Dimension Is a Generator Knob, Not a Real-T rajectory Estimate
The simulator-facing parameter vector is:
𝜃FR = (𝑑, ℎ, 𝑁pts, 𝑁trav, 𝑐, 𝑇days, 𝑁rep), (18)
where 𝑑 is the ambient space dimension, ℎ the fractal dimension, 𝑁pts the generated point count, 𝑁trav the traveller count, 𝑐 the co-traveller count, 𝑇days the
duration in days, and 𝑁rep the mean report count. eq. 18 is a wrapper around the upstream CSV surface; it is not a fitted statistical parameter vector in this
project.
The dimension parameter obeys the generator-side range:
0 < ℎ ≤ 𝑑, (19)
with this scaffold restricted to the upstream two-dimensional waypoint output. We use ℎ as a controlled synthetic roughness knob: lower values concentrate
generated support into a thinner set of places, while higher values spread the support through more of the ambient plane. Movement-ecology and human-mobility
models make clear why this distinction matters: generator controls, individual movement mechanisms, and observation processes are different objects even when
their outputs can be plotted as trajectories [ Nathan et al. , 2008, Barbosa et al. , 2018]. The project therefore asks how downstream inference diagnostics respond
when ℎ changes; it does not estimate a box-counting, Hausdorff, or correlation dimension from observed traces, and it does not claim that any generated ℎ matches
real movement.
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10.3 CSV Parameters Expose Only Part of the Upstream Simulator
The pinned upstream source implements three explicit tiers, each with its own parameters. The retro-preferential tier is useful benchmark context for exploration-
and-return mobility ideas, but this project treats it as a simulator boundary rather than a fitted empirical law [ Song et al. , 2010a, Darling, 2018]. The CSV
interface exposes seven of these parameters; the remaining internals are fixed constants in the upstream main class, documented here so the configurability
boundary is exact rather than implied:
tier (upstream class) role CSV-exposed parameters upstream-fixed internals
AgoraphobicPoints heavy-tailed fractal place process space dimension 𝑑, fractal dimension ℎ,
point count 𝑁pts
clump restart rate 𝜃 = 0.75
Retropreferential retro-preferential trajectory process
over places
traveller count 𝑁trav, co-traveller
count 𝑐
distance exponent −2.0, exploration
mean 𝜙 = 10, trajectory-length mean
100
SporadicReporter sporadic report-time process along
trajectories
duration 𝑇days, mean report count
𝑁rep
speed bound 50 units/day, 200
km/unit, Pareto cutoff 0.001, tail −1.5
Every CSV-exposed parameter is configurable through fractalrabbit.params; the upstream-fixed internals cannot be changed without forking the pinned commit,
and this project deliberately does not fork it. The simulator emits two row-aligned output streams per run: the waypoint stream *XY.csv consumed as observations,
and the ground-truth stream *PLACES.csv (Traveler ID,Days,Place ID ) naming the true AgoraphobicPoints place behind every report. The pipeline ingests
both: places feed the revisit-structure statistics and the ground-truth state recovery evaluation in sec. 3.
10.4 The Parser Consumes a Narrow W aypoint Record Contract
The parser accepts rows of the form:
𝑤𝑖 = (id𝑖, 𝑡𝑖, 𝑥𝑖, 𝑦𝑖), (20)
with 𝑡𝑖 measured in days and positions measured in kilometers. The parser sorts by traveller and time and writes output/runs/*/observations.csv as the raw
sorted post-parser artifact; the downstream observation-discretization step (sec. 10.5) subsequently validates nonnegative time before any categorical features are
derived.
10.5 The Observation Model Converts W aypoints into Finite Evidence
With the simulator boundary fixed, the observation layer turns the raw waypoint stream above into the finite categorical evidence the generative model of sec. 2.6
consumes.
10.5.1 Categorical F eatures Bound the Evidence Surface
The observation layer maps continuous, irregular waypoint records into finite categorical modalities. The default emitted feature table has columns ID, Days,
x(km), y(km), is_first_observation, x_bin, y_bin, spatial_state, time_bin, speed_km_per_day, interval_days, speed_category, burst_category and is the
source for the spatial, temporal, speed, and burst figures in sec. 3.
10.5.2 Spatial States Are Analysis Cells, Not Simulator Internals
For each sorted waypoint, spatial discretization maps coordinates into a finite cell:
𝑠𝑖 = 𝑏𝑦(𝑦𝑖) ⋅ 𝐺 + 𝑏𝑥(𝑥𝑖), (21)
where 𝐺 is the configured spatial bin count per axis and 𝑏𝑥, 𝑏𝑦 are the configured spatial binning functions. The current implementation supports equal-width
grids, fixed-bound grids, and empirical quantile bins. The latent state in eq. 21 is a categorical analysis state, not the hidden point identity inside FractalRabbit;
because location is also emitted as an observation modality, the default fixture is close to a directly observed-state filter rather than a deep latent-uncertainty
benchmark.
10.5.3 T emporal, Kinematic, and Burst F eatures Remain Heuristic Cues
Time-of-day is represented as:
𝑏𝑡 ∶ [0, 1) → {0, … , 𝐺𝑡 − 1}, 𝜏 𝑖 = 𝑏𝑡(𝑡𝑖 mod 1), (22)
where 𝐺𝑡 is the configured number of time-of-day bins and 𝑏𝑡 is the explicit temporal binning map. Within each traveller, inter-report interval and speed are:
Δ𝑡𝑖 = 𝑡𝑖 − 𝑡𝑖−1, 𝑣 𝑖 =
⎧{
⎨{⎩
√(𝑥𝑖 − 𝑥𝑖−1)2 + (𝑦𝑖 − 𝑦𝑖−1)2
Δ𝑡𝑖
Δ𝑡𝑖 > 0,
0 Δ𝑡𝑖 ≤ 0.
(23)
Non-positive intervals are not floored to a positive denominator; the implementation instead leaves 𝑣𝑖 at its zero-initialized sentinel value, distinct from the
observation-noise probability in sec. 2.6.2. The first waypoint for each traveller has no previous within-traveller report, so the emitted feature table marks 5
rows with is_first_observation=1 and assigns the zero interval, zero speed, and non-burst sentinel. This sentinel convention keeps all waypoint rows in the
categorical summaries while avoiding an artificial positive interval.
Speed categories are thresholded from 𝑣𝑖, while burst categories are assigned by the configured interval rule. In the default run, the burst rule is median_positive,
so short intervals are defined relative to the positive-interval median rather than a universal biological or operational threshold. We use “burst” in the temporal-
dynamics sense of clustered reporting separated by longer waiting times; the current median-positive rule is a heuristic discretizer, not a full burstiness statistic,
and finite event sequences require particular caution before treating a burst score as stable [ Barabasi, 2005, Goh and Barabasi , 2008, Kim and Jo , 2016].
10.5.4 F ractal-Dimension Sweeps Shift Occupancy Through the Same Discretizer
The sweep introduced in sec. 10.2 changes the upstream support before this observation layer sees any rows. The downstream state count, occupancy profile,
revisit rate, and predictive losses are therefore consequences of the same discretizer applied to generator outputs with different support roughness. This is why
the sweep is reported as generator sensitivity rather than a direct fractal-dimension estimator.
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## Page 27

11 Supplementary S4 - F ormal Diagnostics Stay Proxies and Provenance Checks
This supplement collects the implementation-level formalisms — robustness, privacy-proxy, and provenance contracts, plus the pymdp performance/interpretability
boundary — that underpin but are not part of the main-line generative-model argument (sec. 2.6).
The robustness extensions keep the same artifact discipline as the generative model of sec. 2.6. A return-conditioned prior introduces a visited-destination feature
𝑟𝑖 = 𝟙{𝑠𝑖 ∈ 𝑉 𝑖−1}, 𝑉 𝑖 = 𝑉 𝑖−1 ∪ {𝑠𝑖}, (24)
and promotes it only when the move-step conditional entropy reduction
Δ𝐻return = 𝐻(𝑠𝑖 ∣ 𝑠𝑖−1) − 𝐻(𝑠𝑖 ∣ 𝑠𝑖−1, 𝑟𝑖) (25)
clears the predeclared artifact gate. Otherwise the result remains an explicit null rather than a hidden negative result. Cross-realization robustness uses empirical
bands over repeated synthetic-generator realizations:
ℬ𝛼(𝑧) = [𝑄𝛼({𝑧𝑗}), 𝑄1−𝛼({𝑧𝑗})] , (26)
where 𝑧𝑗 is a scalar verdict metric from realization 𝑗. These bands are descriptive synthetic-realization intervals, not population confidence intervals. They should
be read like bootstrap-style uncertainty summaries over generated software runs, not like a guarantee that the same interval would cover a real-world population
quantity [Efron and Tibshirani , 1994].
The privacy frontier reports only oversight and minimization quantities. For traveller 𝑎, a coarsened signature is
Γ𝑎(𝑀 ) = {(𝜏𝑖, 𝑐𝑀
𝑖 ) ∶traveller(𝑖) = 𝑎}, (27)
where 𝑀 is a modality-minimization regime and 𝑐𝑀
𝑖 is the retained categorical code. Synthetic unicity and co-travel coincidence are then
𝑈 (𝑀 ) =|{Γ𝑎(𝑀 )}|
|{𝑎}| , 𝐶(𝑀 ) = 1
|𝒫| ∑
(𝑎,𝑏)∈𝒫
𝟙{Γ𝑎(𝑀 ) ∩ Γ𝑏(𝑀 ) ≠ ∅}. (28)
The set-valued signature is intentional: it discards multiplicity and ordering to make a coarse oversight proxy, not a full reconstruction attack, k-anonymity
mechanism, differential-privacy mechanism, or formal privacy proof [ Sweeney, 2002, Dwork, 2006, Buchholz et al. , 2024]. If a later analysis prices repeated visits,
ordered routines, or temporal sequence alignment, Γ𝑎(𝑀 )must become a multiset or sequence and the corresponding frontier must be regenerated.
The hardened anomaly probe compares pymdp-style surprise with a fair online Markov-surprise baseline:
𝒮Markov
𝑖 = − log ̂𝑃𝑖−1(𝑠𝑖 ∣ 𝑠𝑖−1), (29)
and reports both AUC and operating-point metrics so separability is not summarized by area alone. Finally, result-critical manuscript tokens are bound to source
artifacts by a provenance tuple
𝜋𝑘 = (𝑘, 𝑝𝑘, 𝜂𝑘, ℎ𝑘, 𝑣𝑘), (30)
where 𝑘 is the token, 𝑝𝑘 the source artifact path, 𝜂𝑘 the JSON key path, ℎ𝑘 the source checksum, and 𝑣𝑘 the rendered value. Rendering is trusted only if the
artifact exists, the key resolves, the checksum is current, and the formatted artifact value byte-matches the token.
11.1 pymdp Adds Interpretability Without Predictive Leadership
The same A, B, C, and D arrays are also consumed by the actual pinned pymdp agent. The benchmark matrix reports not_demonstrated for state-of-the-art
performance and diagnostic_gain_demonstrated for diagnostic value — a distinction that is load-bearing. pymdp currently helps by exposing variational free
energy, policy posteriors, and expected-free-energy terms in a common active-inference grammar; reaching performance leadership would require clearing the
sequence-baseline gate in sec. 14.2 and the broader roadmap gates in sec. 6.3, not just replacing the transparent reference filter with the library agent.
When model.engine is both, the pipeline constructs a batched JAX Agent from the tensors above and runs a sequential perception-action loop: variational
state inference under the current empirical prior, policy inference returning the policy posterior and expected free energy, deterministic action selection, and an
empirical-prior update through the selected control’s transition slice [ Heins et al. , 2022, infer-actively, 2026a,b]. Two comparisons are emitted. First, a matched-
prior validation: at every step the pymdp variational posterior is compared against the exact Bayes posterior computed from the same prior and tensors; on the
default run the maximum absolute difference is 3.99e-07, which validates the inference implementations against each other. Second, a closed-loop comparison: the
full trajectories diverge (maximum absolute posterior difference 0.044 on this run) through policy-induced prior divergence — differing action-selection criteria
(expected free energy versus the preference-cross-entropy proxy score of eq. 11) select different controls, which propagate different empirical priors, so subsequent
posteriors legitimately differ. Because the posteriors agree under matched priors at every step, the closed-loop divergence is fully explained by differing action
sequences rather than any latent inference discrepancy. Its magnitude is trajectory-specific, not a stable property of the implementations. Both traces are emitted
side by side in output/runs/default/pymdp_trace.csv and output/runs/default/policy_trace.csv. The pymdp trace additionally records, per timestep, the
agent’s own variational free energy (the final fixed-point iterate returned by infer_states), the wall-clock step runtime, the policy posterior, and the expected
free energy of every policy, so the full diagnostic surface of the pinned library is a run artifact rather than an internal quantity.
12 Supplementary S5 - Closed-Loop Ranking Remains a Non-Controller
This supplement describes the closed-loop candidate-ranking heuristic, the recovery-versus-sparsity lane, and the additive holdout-scoring protocol — secondary
experimental lanes extending the main-line evaluation.
12.1 Candidate Ranking Is a Heuristic, Not a Controller
The closed loop is an experiment-level feedback loop: simulate or load waypoints, infer latent-state beliefs, score the run, then rank declared candidate simulator
configurations. It is not an online controller acting on a real mobility system.
For a configured objective 𝐽 and candidate 𝑘, the selector records:
score𝑘 = 𝐽 (run) ⋅𝑟current
𝑟𝑘
, (31)
when the objective direction is minimization. Here 𝑟 is the configured mean report count. eq. 31 is a transparent ranking heuristic for comparing declared
simulator candidates under the current objective: denser reporting is favored when the measured inference objective is high. Every candidate score is written
26

## Page 28

to candidate_scores.json and candidate_scores.csv . It is not presented as an optimal experimental-design rule; formal active-inference treatments connect
expected free energy to Bayesian optimal design and expected utility under assumptions that this scalar fixture diagnostic does not satisfy [ Sajid et al. , 2021b].
The current default ranking is:
Table 5: Candidate scores emitted by the default closed-loop run.
rank candidate metric value reporting ratio score
1 higher_reports 5.718819 0.500000 2.859410
2 lower_reports 5.718819 1.500000 8.578229
The selected next candidate is higher_reports, with score 2.859410 and reporting ratio 0.500000. Because tbl. 5 is generated from run artifacts, it changes when
the objective, candidate set, or simulator parameters change.
12.2 Sporadic-Observation Fit Stays Synthetic
The modeled situation deserves explicit statement. FractalRabbit was published by NSA Research as a sparse-mobility synthetic generator; this project uses it
only as a pinned software benchmark. Its traces are observed through sporadic, irregular reports, where most of a trajectory is never seen [ Darling, 2018, National
Security Agency , 2026a]. The analytic question that situation poses — how much latent movement structure is recoverable from sparse reports, with what
calibrated uncertainty, and which next data-collection configuration would be most informative — is exactly the shape of problem a discrete active-inference agent
addresses: state estimation under partial observability, uncertainty quantified per step as posterior entropy and variational free energy, and candidate evaluation
through expected free energy [ Da Costa et al. , 2020, Sajid et al. , 2021b]. The ground-truth recovery evaluation in sec. 3 makes this concrete: it measures, against
the simulator’s own latent structure, how much of that structure each configured model actually recovers. Two boundaries hold throughout. The evaluation is
synthetic-only software evidence, and the same recoverability that makes sparse analytics tractable is what makes coarse spatiotemporal data re-identifiable —
which is why the privacy threat model of sec. 8 and the separate empirical protocol are load-bearing parts of this project rather than disclaimers [ de Montjoye
et al. , 2013, Kondor et al. , 2020].
12.3 Recovery Is Measured Across the Sparsity Lane
A dedicated sparsity lane turns the question into a quantitative check. Each traveller’s reports are deterministically subsampled (seeded by the root seed) to
a configured fraction of the full set; at every level the full and deep-latent models are re-estimated from scratch and scored against the exact ground-truth cell,
and the pymdp lane validates the released state updater on deterministic sentinel rows at each sparsity level rather than running a full deep-latent agent pass.
The result is a recovery-versus-sparsity curve rather than a single operating point — and the curve’s direction is read from the artifact, not assumed: under this
deterministic subsampling the deep-latent recovery mass does not fall monotonically as reports thin (densest-level mean mass on the true cell 0.069 against 0.118
at the sparsest level, which currently scores highest), so the lane measures how sparsity reprices the available evidence rather than demonstrating degradation.
12.4 Holdout Scoring Remains Additive Under Fixed Discretization
The experiment layer also supports holdout scoring as an additional pass. When experiment.holdout_fraction is positive, the last configured fraction of each
traveller’s chronologically ordered waypoints is held out (each traveller always keeps at least two training rows), the A/B/D tensors are re-estimated from the
training rows only, and the filter is re-run over the full ordered sequence while aggregating predictive loss and posterior entropy only at holdout indices. The
primary full-data metrics are never replaced by this pass; the holdout keys are additive. Discretization bin edges remain shared with the full lane, so the holdout
numbers measure out-of-sample tensor estimation under a fixed discretization rather than a fully leakage-free protocol; this boundary is restated in sec. 5.
13 Supplementary S6 - Fixture Diagnostics Bound Sensitivity and pymdp Agreement
This supplement audits the experimental fixture — sensitivity sweeps, negative controls, and pymdp implementation agreement — verifying the setup without
advancing the headline claim (sec. 3).
13.1 Sensitivity and Negative Controls F alsify Easy Wins
The fixture sensitivity lane emits 10 runs across deterministic repetitions, report-count variants, spatial-bin settings, burst-rule settings, smoothing, and transition-
control choices. This lane runs the sweep configuration ( configs/sweep.yaml), which deliberately differs from the canonical default configuration: among other
declared differences it configures a third identity transition control alongside the two canonical controls and uses a different spatial discretizer, seed, and holdout
setting. Its policy-entropy and loss summaries therefore audit the sweep configuration and are not directly comparable to the canonical run’s values reported later
in this supplement. This deterministic sensitivity lane reprocesses the checked fixture. Simulator parameter variants affect declared run metadata and candidate
scoring, but they do not resimulate waypoint rows unless the external FractalRabbit lane is available. Fixture-lane replicates are bit-identical reruns: their spread
is exactly zero by construction, so std and normal_approx bounds in this lane are determinism checks, never sampling uncertainty. Sensitivity variants use the
reference engine; the canonical lane carries the full pymdp trace. The interval column in tbl. 6 is a normal-approximation interval over deterministic variants, not
an inferential population confidence interval. Policy entropy is summarized across 10 run(s) with 3 control(s), max entropy 1.099 nats.
Table 6: Sensitivity summary emitted by scripts/03_run_sweep.py.
metric n mean std min-max normal-approx interval
mean_predictive_loss 10 5.112 1.003 [3.392, 6.360] [4.490, 5.734]
mean_posterior_entropy 10 0.321 0.842 [0.005, 2.710] [-0.201, 0.842]
mean_policy_entropy 10 1.099 0 [1.099, 1.099] [1.099, 1.099]
baseline_delta_mean_pr
edictive_loss
10 1.357 0.893 [-0.006, 2.335] [0.803, 1.910]
The default run also reports per-traveller chronological holdout scoring with configured fraction 0.250: 600 of 2400 waypoint rows are scored by tensors estimated
only from the remaining 1800 training rows, yielding holdout mean predictive loss 5.774 nats and holdout mean posterior entropy 0.068 nats. Because the holdout
pass is additive, the headline full-data metrics above are identical whether or not the knob is enabled.
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## Page 29

Figure 14: Source negative_controls_summary.json reports 4/4 directional expectations held. Loss changes under shuffled report times and shuffled identities
test destroyed structure, while occupancy-collapse probes test degenerate bounds and misspecified speed thresholds. Because collapsed modalities can be easier
to predict, the oracle is control-specific rather than a universal loss direction. Fixture-lane software diagnostics, not empirical mobility evidence. Evidence:
artifact-level falsification checks for destroyed or degenerate structure. Boundary: empirical mobility evidence.
The negative-control lane intentionally destroys one structural property at a time and checks a directional expectation against the resulting artifacts. fig. 14 and
tbl. 7 report the current outcome: 4 of 4 controls behaved as their falsification hypotheses require. Negative controls falsify pipeline insensitivity to destroyed
structure. They are software diagnostics on the fixture lane, not empirical mobility evidence.
Table 7: Negative-control outcomes emitted by scripts/05_run_negative_controls.py.
control probe delta mean predictive loss passed
shuffled_time speed_km_per_day column differs
from the intact run
-1.135 yes
shuffled_ids speed_km_per_day column differs
from the intact run
-0.390 yes
degenerate_bounds occupied spatial states == 1 (observed
1)
-2.256 yes
misspecified_speed occupied speed categories == 1
(observed 1)
-1.343 yes
13.2 pymdp Agreement Is an Implementation Check, Not a Win
Figure 15: Sources pymdp_trace.csv and inference_trace.csv compare the pinned pymdp agent with the transparent reference on identical tensors. Under matched
priors the state posteriors agree to max abs delta 3.99e-07, validating the inference implementation; closed-loop posteriors diverge to 4.41e-02 through policy-
induced prior divergence because expected-free-energy action selection and the proxy-score rule propagate different priors. This is a synthetic action-selection
diagnostic, not an inference bug. Evidence: implementation agreement and policy-induced prior divergence diagnostics. Boundary: a state-of-the-art performance
claim.
The real pymdp agent lane (fig. 15) reports mean predictive loss 6.147 nats and mean posterior entropy 0.055 nats on the default run. The matched-prior validation
gives a maximum absolute state-posterior difference of 3.99e-07 against the exact Bayes posterior, so the two independent inference implementations agree at
numerical precision; the closed-loop traces nevertheless diverge (maximum absolute posterior difference 0.044 on this run) through the policy-induced prior
divergence mechanism described in sec. 2.6. The matched-prior control localizes that divergence entirely to action selection.
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## Page 30

Figure 16: Source pymdp_trace.csv makes the pinned agent’s internal surface visible. variational free energy per step (mean 6.147 nats) shows fit-plus-complexity
surprise, wall time (median 18.159 ms) reports computational cost, and expected free energy per policy shows the quantity used for policy ranking. The panel
supports interpretability claims, not state-of-the-art predictive performance on synthetic waypoints. Evidence: interpretability of the real pymdp lane through
VFE, EFE, policy, and runtime surfaces. Boundary: predictive-performance leadership.
fig. 16 exposes the full per-step diagnostic surface of the pinned agent: variational free energy (mean 6.147 nats on the default run), wall-clock runtime (median
18.159 ms per step, maximum 2430.487 ms, 48.486 s total against 0.988 s for the reference filter), and the expected free energy of every policy at every timestep.
These numbers make the computational cost and the policy-evaluation dynamics of the active-inference layer auditable artifacts.
The performance-versus-interpretability answer from sec. 11.1 is summarized in tbl. 8. The current state-of-the-art performance status is not_demonstrated :
pymdp changes predictive loss by 0.428 nats and posterior entropy by 0.009 nats relative to the transparent reference filter, so the current contribution is not
a predictive-performance win. The diagnostic status is diagnostic_gain_demonstrated , because the library lane exposes VFE, policy posterior, expected free
energy, and action-conditioned prior dynamics as inspectable artifacts. The roadmap gates are: use the lane-resolved model gate matrix before performance-
leading language; learn hierarchical or continuous-space dynamics instead of fixed cells only; calibrate missingness and reporting processes explicitly; validate on
consented empirical traces before real-world claims.
Table 8: Current pymdp performance and interpretability matrix, emitted by pymdp_benchmark_matrix.json.
model implemented current role interpretability surface
reference_filter yes transparent Bayes-style performance
baseline
posterior trace, tensor provenance,
calibration
pymdp_agent yes variational active-inference
implementation and policy diagnostic
VFE, policy posterior, expected free
energy, action-conditioned prior
factorial_pymdp_agent yes multi-factor latent-mode
active-inference diagnostic
cell, movement-mode, and
cognitive-proxy posteriors plus
VFE/EFE per step
persistence_and_base_rate_nulls yes honesty floor for autocorrelated
waypoint recovery
explicit null hierarchy
markov_surprise_baseline yes transition-aware anomaly comparator online transition surprise
prequential_sequence_baselines yes stronger next-cell
predictive-performance gate
named online nulls and per-baseline
loss/skill rows
lane_resolved_model_gate_matrix yes fixture/external evidence gate for
model claims
lane status, unavailable handling, and
per-gate verdict rows
return_plus_phase_prior yes first promoted-or-null prior extension
after return and phase gates
pooled, phase, return, combined,
persistence, and permuted comparator
rows
future_sota_baselines planned required before any state-of-the-art
performance claim
to be compared under the same null
hierarchy
13.3 Spatial-Resolution Diagnostics Choose the Reporting Grid
The remaining sections are the supporting battery — the diagnostics, null hierarchy, gate verifications, and safety boundaries against which the headline result
was tested. They begin with the fixture and discretization diagnostics that every later lane depends on.
The default fixture run writes 18 run artifacts and 53 registered figures. From this baseline, the measured summary is: 2400 observations, 16 latent states, mean
predictive loss 5.719, final posterior entropy 0.001, and mean policy entropy 0.693. The fixed-transition baseline filter uses empirical_continuation , yielding
mean predictive loss 3.845 and an active-minus-baseline loss delta of 1.874. On this fixture, the fixed-transition baseline has lower mean predictive loss than the
active policy-proxy trace, so the current active layer should be read as an auditable diagnostic rather than a performance improvement — and the delta has a
mechanical explanation: with the proxy exactly tied under uniform preferences (sec. 2.6.3), tie-breaking selects the uniform high_entropy_exploration transition
on a fraction 0.818 of steps, flattening the temporal prior that the fixed empirical_continuation baseline keeps sharp.
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## Page 31

Figure 17: Source observations.csv is shown as 2400 synthetic sporadic waypoint reports for 5 travellers. Lines connect reports only in report order; they are a
visual index, not reconstructed continuous tracks. Color encodes report time, the open triangle marks each first report, and the star marks the final report. The
visible clustering and gaps define the sparse-observation regime that the benchmark scores, not empirical mobility. Evidence: inspection of sparse report ordering
and coverage gaps. Boundary: continuous-track reconstruction, surveillance, or empirical mobility inference.
fig. 17 shows that the fixture preserves the FractalRabbit-style sparse waypoint contract while remaining small enough for deterministic tests.
Figure 18: Source discrete_features.csv maps all n=2400 reports from continuous coordinates into the model’s latent spatial cells. Color and printed cell labels
show the configured grid that the location modality actually observes: reports sharing a cell become equivalent evidence even when their coordinates differ. This
figure fixes the analysis resolution before inference and is a synthetic discretization audit, not a map of real places. Evidence: the fixed synthetic analysis-cell
boundary used by the tensors. Boundary: geographic interpretation of places or real-world map validity.
fig. 18 audits the spatial discretization used in eq. 21. The plotted cells are analysis bins, not FractalRabbit internal point-process states.
30

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Figure 19: Sources spatial_resolution_frontier.json and spatial_resolution_larger_sample_confirmation.json compare candidate square grids on occupancy,
transition sparsity, full-location predictive loss, no-location recovery, real-pymdp agreement, and deterministic sample-size sensitivity. The selected default is the
canonical guardrail survivor. When the larger lane has no strict-feasible grid, the marked bin is explicitly a best-measured fallback. The two recovery rows keep
observed-location fit separate from metadata-only recovery. Evidence: the grid-selection guardrail for observed-location fit and metadata-only recovery. Boundary:
promotion of no-location recovery beyond the artifact frontier.
fig. 19 makes the discretization choice first-class. In fig. 19, the artifact evaluates candidate square grids against occupancy, transition sparsity, full-location
predictive loss, location-withheld recovery, and bounded real- pymdp matched-prior agreement. The default grid is 4x4: 16 states with 0 empty cells, full-location
loss 5.719, and default-vs-coarse loss change 0.867. On the canonical fixture the emitted verdict is default_resolution_not_best_feasible_loss , with best
feasible bins 3. A deterministic sample-size ladder then regenerates 2, 4, 8 times the canonical reports per traveller from the same fixture generator family, with
the largest 8x lane at n=19200 (3840 per traveller); the parallel largest-sample tokens resolve to n=19200 and 3840 reports per traveller for the same lane. The
largest lane reports larger_sample_changes_frontier_decision: status changed, strict feasible candidate count 0, selected bins 4, default-vs-coarse loss change
-1.069, and default-vs-coarse no-location mass change -0.036. Across the ladder, verdict stability is no, no-location guardrail stability is yes, selected bins are 4, 8,
4, strict feasible candidate counts are 2, 0, 0, and the generated interpretation is guardrail_stable_but_fit_selection_changes . When a strict feasible count
is zero, the selected bins are the best measured loss among the candidate grids rather than a strict occupancy claim. The ladder refines the observed-location
fit verdict at larger synthetic report counts, while the no-location guardrail keeps the same direction against fine-cell recovery (canonical default-vs-coarse mass
change -0.045). It is not evidence that time, speed, and reporting-burst metadata recover fine spatial cells better, and it is no longer phrased as a universal best-fit
grid.
That no-location guardrail is a change between the default and coarse discretizers. It is not the same scalar as the absolute deep-latent recovery mass in fig. 5 or
the densest sparsity recovery mass in fig. 7, so those values should not be compared as if they measured one regime.
Table 9: Spatial-resolution frontier emitted by spatial_resolution_frontier.json ; the pymdp column is the matched-prior agreement check on deterministic
sentinel rows. The sample-size ladder is emitted separately as spatial_resolution_larger_sample_confirmation.json so it can test the qualitative decision
without changing the canonical fixture rows in this table.
bins states occupied empty full loss no-location mass pymdp delta
3 9 9 0 4.852 0.114 2.08e-07
4 16 16 0 5.719 0.069 3.20e-07
5 25 25 0 5.254 0.045 2.68e-07
6 36 36 0 4.292 0.051 4.82e-07
8 64 63 1 5.211 0.021 3.62e-07
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Figure 20: Source discrete_features.csv exposes the reporting process rather than treating missingness as background noise. The left panel plots positive inter-
report intervals against the configured burst cutoff; the right panel counts burst labels after the 5 first observations are assigned zero-interval non-burst sentinels.
The heavy tail and short-interval cluster are the synthetic SporadicReporter texture that later missingness gates must explain. Evidence: the synthetic reporting-
process texture used by later missingness gates. Boundary: a behavioral account of real reporting cadence.
Figure 21: Source discrete_features.csv converts consecutive reports into speed evidence for n=2400 synthetic reports. Bars summarize category counts; the trace
shows each derived speed against thresholds (10, 50, 150 km/day), with first observations fixed at zero by convention. This is one non-location modality used
by the deep-latent configuration, and it remains derived evidence rather than direct ground truth about unobserved movement. Evidence: the derived kinematic
evidence channel used by the deep-latent lane. Boundary: ground-truth claims about unobserved movement between reports.
fig. 20 and fig. 21 inspect the derived temporal and motion categories from eq. 23. They are category diagnostics, not empirical claims about real movement
speed.
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## Page 34

Figure 22: Source discrete_features.csv estimates the empirical latent-cell transition surface before tensor smoothing, excluding traveller-boundary (first-
observation) pairs exactly as the model’s B-tensor estimator does. Each column is P(next cell | previous cell), with raw counts printed over the diagonal
and the largest off-diagonal cells; the diagonal makes dwell-and-return structure visible, while off-diagonal mass carries movement evidence. This panel is the
normalization and sparsity audit for downstream synthetic B tensors before smoothing=0.05 is applied. Evidence: normalization and sparsity checks for the
synthetic B-tensor surface. Boundary: external movement-model validation.
Figure 23: Source discrete_features.csv builds column-normalized observation likelihoods P(observation | latent cell) for location, time, speed, and reporting-burst
modalities. The near-diagonal location panel is expected by construction; the time, speed, and burst panels are the evidence channels the deep-latent configuration
uses when location is withheld. The panels are the audit point for the conditional-independence approximation before Model A smoothing=0.05 is applied, not
empirical sensor validation. Evidence: the likelihood-audit boundary for location, time, speed, and burst modalities. Boundary: empirical sensor validation or
independence claims outside the configured approximation.
fig. 22 and fig. 23 expose the empirical structure that feeds eq. 2 and eq. 1. These diagnostics are useful because normalization bugs in A or B can otherwise
produce plausible-looking posterior traces.
33

## Page 35

Figure 24: Source inference_trace.csv records the transparent reference filter over n=2400 reports. The top panel shows one-step predictive loss, the negative
log prior-predictive probability assigned to the observed report, against the uniform-chance joint-loss floor; the bottom panel shows posterior entropy after
updating. Spikes identify synthetic reports that surprise the model, while low sustained entropy marks confident cell tracking rather than proof of real trajectory
reconstruction. Evidence: reference-filter surprise and uncertainty diagnostics over synthetic reports. Boundary: proof of real trajectory reconstruction.
Figure 25: Source policy_trace.csv exposes the proxy policy diagnostic for the 2 configured transition control(s). Total score, score spread, entropy and preference
components, and the softmax policy posterior show whether candidate controls separate under the current preferences; identical proxy scores are drawn as one
line when the loaded artifact makes the tie exact. Near-uniform posteriors are reported as a synthetic observational-equivalence finding, not as a controller
failure or operational recommendation. Evidence: candidate-control separability under the proxy scoring rule. Boundary: operational control advice or controller
validation.
fig. 24 reports the measured loss and uncertainty sequences from eq. 7 and eq. 8. fig. 25 reports the configured-control diagnostics from eq. 11 and eq. 14. For
the default fixture, near-maximal policy entropy; under the default uniform preferences the proxy score is constant across controls by algebra, so the configured
policies are exactly tied rather than empirically close.
34

## Page 36

Figure 26: Source candidate_scores.json ranks the n=2 declared next-run simulator candidates by the measured objective scaled by relative reporting density.
Rank labels and scores make the closed-loop choice recomputable from artifacts. This is an audit trail for candidate selection inside the synthetic fixture lane,
not an external simulator-performance benchmark. Evidence: recomputable closed-loop candidate ranking inside the fixture lane. Boundary: external simulator
performance leadership.
fig. 26 visualizes tbl. 5. The selected next candidate is higher_reports; the displayed formula is minimize predictive_loss: score = 5.718819 x 0.500000 =
2.859410. It is deliberately a score explanation figure: it supports auditability of the next-run choice, not an external performance benchmark.
14 Supplementary S7 - Program Extensions Add Gates, Not Promotion
This supplement holds the secondary result lanes — anticipatory gap-filling, expected-free-energy decomposition, program extensions, robustness probes, sequence
baselines, and roadmap-gate verifications — that support but do not constitute the main-line findings (sec. 3).
14.1 Robustness Artifacts Record Synthetic Realization Spread
The robustness expansion asks whether those verdicts survive stronger nulls and broader software checks. The return-structure probe in fig. 27 applies eq. 24
and eq. 25 on move steps only. The measured move-step entropy reduction is 0.186 nats, persistence headroom is 0, and the current verdict is promote_return
_conditioned_prior; this either promotes a return-conditioned prior as a concrete next model component or records a bounded null in the same artifact. The
figure’s third bar, return_skill_vs_persistence, is a secondary, prototype-only Brier-skill diagnostic of the return-conditioned predictive prior itself, not of the
location-observed POMDP posterior; it is negative on the current run and plays no role in the promotion gate above, which is decided solely by the entropy
reduction and the persistence-headroom sign, so a negative bar underneath a promote_return_conditioned_prior title is expected rather than a contradiction of
that verdict. Cross-realization bands in fig. 28 repeat the expanded configuration across 10 synthetic realizations. The gap-filling skill band spans 0.219 to 0.268
(interquartile range 0.230–0.246, SD 0.014 — min–max over ten draws is extreme-value-dominated, so the rank- and moment-based spreads are reported alongside
it), so single-run conclusions can be read against an empirical synthetic-realization spread rather than treated as if one draw were a stable law. The same repeated-
realization pass also plots five further verdict metrics discussed at the single-run level elsewhere in this document: the location-blind-limit skill against persistence
(blind_limit_skill, sec. 14.5), the no-location frontier recovery mass ( frontier_no_location_mass, sec. 14.7), the deep-latent structure-recovery total variation
(structure_deep_latent_tv , sec. 14.7), the random-cell anomaly ROC AUC ( anomaly_random_auc, sec. 14.7), and the mission EFE-minus-pragmatic recovery
margin ( mission_efe_minus_pragmatic, sec. 14.7). Because blind_limit_skill is the Brier-type skill score in the harder location-blind limit, already reported as
strongly negative in sec. 14.5. Unlike the other four metrics (which stay within a bounded unit-scale range), it is unbounded below — so its band sits roughly an
order of magnitude beneath the rest of the figure due to its scale, not a plotting error or a stale realization. These bands are robustness summaries over generated
software realizations, not population confidence intervals [ Efron and Tibshirani , 1994]. Upstream sensitivity in fig. 29 reports blocked after 5 attempted prior
commits; a blocked result is rendered as evidence about build comparability, not as a missing figure.
35

## Page 37

Figure 27: Source return_structure_analysis.json tests whether a visited-cell return feature lowers move-step next-cell entropy beyond persistence headroom.
The bars show entropy reduction, available null headroom, and the prototype-before-claim score. A promoted result becomes a candidate prior; a null remains an
explicit bound on this synthetic trace rather than a hidden failure. Evidence: whether return features merit promotion to a candidate prior. Boundary: a hidden
behavioral law of movement.
Figure 28: Source variance_bands.json repeats key analyses across synthetic-generator realizations and plots medians with min-max bands. Gap-filling skill,
anomaly separability, and minimization-frontier recovery are shown as realization-sensitive program diagnostics. These bands describe synthetic reruns, not
population confidence intervals or empirical uncertainty. Evidence: sensitivity of key diagnostics across synthetic-generator reruns. Boundary: population
confidence intervals.
36

## Page 38

Figure 29: Source upstream_sensitivity.json records whether a second buildable FractalRabbit commit produced comparable tensor or recovery distances under
the current JDK/Maven toolchain. If no comparable build completes, the blocked state is rendered explicitly. The captioned artifact prevents silent upstream
drift from masquerading as validated simulator robustness. Evidence: explicit blocking or comparison of buildable upstream simulator commits. Boundary: silent
robustness to upstream drift.
The implemented roadmap probes from sec. 6.1 extend that robustness layer. The fractal-dimension sweep in fig. 30 varies the generator control introduced in
sec. 10.2; its status is fixture_control_unvaried, the best predictive-loss dimension is 1.100, the highest revisit-rate dimension is unavailable, and the predictive-
loss sweep range is 5.719 to 5.719. The circadian-phase signal in fig. 31 tests whether a phase-conditioned occupancy prior is worth promoting: the current verdict
is honest_null, with phase gain 0.011, permuted gain 0.007, and maximum Jensen-Shannon separation 0.004. Against a 200-permutation label null (floored at
one over the draw count plus one), the phase gain carries permutation p-value 0.199 and the maximum Jensen-Shannon separation p-value 0.214, so neither clears
at the conventional threshold. Both artifacts are roadmap gates, not behavioral claims.
Figure 30: Source fractal_dimension_sweep.json varies the FractalRabbit dimension parameter while holding the expanded configuration fixed, then reports filter
diagnostics (left panel) and, when the lane populates it, place-return texture (right panel; an explicit ‘no revisit data in this lane’ marker is drawn when the
return texture is unavailable). The parameter is treated as a synthetic generator knob over support roughness and revisit structure. It is not estimated fractal
dimension for real mobility. Evidence: a fixture-replay invariance check over the nominal dimension knob (the external generator was unavailable, so metrics are
constant by construction). Boundary: estimation of real-mobility fractal dimension.
37

## Page 39

Figure 31: Source circadian_phase_analysis.json tests whether phase-conditioned occupancy carries predictive structure. The heatmap shows cell occupancy
by phase, and the bars compare phase-conditioned gain with a permuted-phase null plus Jensen-Shannon separation. A positive result can become a candidate
prior; a null remains bounded synthetic evidence rather than a behavioral claim. Evidence: phase-conditioned prior candidacy against a permuted-phase null.
Boundary: a behavioral circadian claim.
14.2 Sequence and Reporting Gates Strengthen the Nulls
The sequence-baseline gate in fig. 32 implements a prequential ladder of transparent next-cell predictors: base-rate, persistence, first-order Markov, phase-
conditioned Markov, metadata-conditioned Markov, and return-boosted variants [ Dawid, 1984]. Its current best model is first_order_markov , with mean
predictive loss 0.570 nats and skill 0.787 against the online base-rate null. Relative to the default reference filter, the best sequence baseline changes predictive
loss by -5.149 nats; relative to the pymdp lane, it changes predictive loss by -5.577 nats. The current performance gate is stronger_sequence_baseline_beats_py
mdp_on_this_run, which is deliberately harder than asking whether pymdp agrees with a matched-prior Bayes implementation.
Table 10: Prequential next-cell sequence baselines emitted by sequence_baseline_analysis.json.
model mean predictive loss (nats) skill vs base-rate
base_rate 2.677 0
persistence 0.839 0.687
first_order_markov 0.570 0.787
phase_markov 0.680 0.746
metadata_markov 1.111 0.585
return_boost_markov 0.592 0.779
phase_return_markov 0.782 0.708
Figure 32: Source sequence_baseline_analysis.json implements the prequential baseline ladder before any stronger performance language is allowed. Online
base-rate, persistence, Markov, phase-conditioned, metadata-conditioned, and return-boosted variants are scored on next-cell predictive loss before observing the
current report. pymdp must clear these transparent synthetic sequence nulls before the manuscript can claim predictive leadership. Evidence: the prequential
baseline ladder required before performance language. Boundary: pymdp predictive leadership until the gate is cleared.
The reporting-process gate in fig. 33 asks whether sparse reporting itself has phase or traveller structure. Treating observation timing as ignorable requires explicit
assumptions: classical missing-data theory conditions ignorability on the missingness mechanism, and irregular outcome-dependent observation can bias ordinary
38

## Page 40

marginal analyses when visit intensity and the outcome process are associated [ Rubin, 1976, Lin et al. , 2004]. The synthetic gate scores 2395 positive inter-report
intervals, defines short gaps from the generated interval distribution, and reports verdict honest_null. The short-gap rate is 0.500, interval coefficient of variation
is 1.316, phase gain over a pooled reporter is -0.005, traveller gain is -0.007, combined phase-traveller gain is -0.029, and permuted-phase gain is -0.006. It tests
report timing in generated waypoints; it neither establishes ignorability nor characterizes real nonresponse behavior.
Table 11: Reporting-process log-loss gains emitted by missingness_model_analysis.json.
reporting context log-loss gain vs pooled
phase -0.005
traveller -0.007
phase + traveller -0.029
permuted phase -0.006
Figure 33: Source missingness_model_analysis.json models reporting cadence as its own synthetic process. Phase-conditioned short-gap probabilities and online
log-loss gains for phase, traveller, and combined contexts are compared with a pooled Bernoulli reporter and a permuted-phase null. A promoted result is
a candidate reporting-process model, not a claim about real nonresponse or missingness behavior. Evidence: reporting-process structure against pooled and
permuted nulls. Boundary: claims about real nonresponse behavior.
14.3 Lane-Resolved Gates Keep Fixture and External Evidence Separate
The singleton sequence and reporting-process artifacts remain for backward compatibility, but the manuscript-facing comparison surface is now the lane-resolved
model gate matrix. fig. 34 and tbl. 12 put fixture and external readiness side by side for the sequence-baseline ladder, the synthetic reporting-process gate, and
the return-plus-phase prior gate. The matrix status is partial; on the external lane the sequence gate is unavailable, the missingness verdict is unavailable,
and the return-plus-phase verdict is unavailable. If the external lane did not complete in the current invocation, the external cells render explicit unavailable
statuses rather than stale numbers or numeric zeroes.
Table 12: Lane-resolved model gate matrix emitted by model_gate_matrix.json.
lane gate status model metric verdict
fixture sequence_baseline_ladd
er
completed first_order_markov 0.570 stronger_sequence_base
line_beats_pymdp_on_th
is_run
fixture reporting_process_miss
ingness
completed phase_traveller_report
er
-0.029 honest_null
fixture return_plus_phase_prio
r
completed return_plus_phase_prio
r
-1.797 honest_null
fixture factorial_pymdp_latent
_modes
completed particle_state_space 5.296 factorial_pymdp_cleare
d_current_lane
external sequence_baseline_ladd
er
unavailable unavailable unavailable unavailable
external reporting_process_miss
ingness
unavailable phase_traveller_report
er
unavailable unavailable
external return_plus_phase_prio
r
unavailable unavailable unavailable unavailable
external factorial_pymdp_latent
_modes
unavailable unavailable unavailable unavailable
39

## Page 41

Figure 34: Source model_gate_matrix.json puts fixture and external lanes on one readiness contract for the sequence baseline ladder, reporting-process structure,
and return-plus-phase prior. Completed cells show current-lane metrics and verdicts; unavailable lanes render unavailable rather than zero. The matrix preserves
lane honesty while newer promoted synthetic families move to the forward-gates artifact. Evidence: lane readiness for promoted fixture and external evidence
families. Boundary: treating unavailable external lanes as failures or successes.
The return-plus-phase prior is the first concrete M9 model idea. In tbl. 13, it compares pooled, phase-only, return-only, and return-plus-phase priors against
persistence and permuted-phase nulls before promotion. The current canonical-lane verdict is honest_null; the best model is return_plus_phase_prior with
mean predictive loss 2.636, gain -1.797 over persistence, and gain 0.004 over the permuted-phase comparator. A promoted verdict would justify adding the factor
to the generative prior; an honest null keeps the manuscript from treating return and circadian texture as a model improvement merely because they are plausible.
Table 13: Return-plus-phase prior gate emitted by return_phase_prior_analysis.json.
prior mean predictive loss (nats) skill vs base-rate
base_rate_null 2.677 0
persistence_null 0.839 0.687
pooled_prior 2.677 0
phase_prior 2.738 -0.023
return_prior 2.658 0.007
return_plus_phase_prior 2.636 0.015
permuted_return_plus_phase_prior 2.640 0.014
14.4 F orward Gates Promote Only Bounded Synthetic Positives
The forward gates in fig. 35 promote the deeper roadmap analyses from prototype claims into regenerated artifacts. The summary status is completed, with 8
completed fixture gates; external rows are either current-lane evidence from the same full-study invocation or explicit unavailable records. The latent-regime
HMM remains a bounded null: its gate is latent_regime_hmm_does_not_beat_markov_null_em_overfits , best honest held-out loss 2.615, and overfit gap 0.492
[Rabiner, 1989, Zucchini et al. , 2016]. The neural sequence baseline reports neural_sequence_beats_weak_nulls_not_particle_mixture, with loss 0.618 against
particle/state-space loss 0.550 [ Patterson et al. , 2008, Doucet et al. , 2001, Arulampalam et al. , 2002].
The learned-prior and reporting gates separate positives from nulls. The learned-stay-rate verdict is honest_regime_null ; the best variant is stay_move, with
best-minus-particle difference -0.008 and bootstrap interval -0.016 to -0.001. The held-out reporting-process verdict is honest_null, with runlen gain 0.001 on
leave-one-traveller-out scoring and 0.002 on the temporal split. Cross-generator transfer reports persistence as regime_dependent_on_self_transition_rate ,
particle-vs-hard-persistence as transfers, and return structure as transfers; this keeps broad mechanism language bounded to the two synthetic generators
actually tested.
The table deliberately keeps lane disagreements visible rather than merging lanes: an external row that did not complete in the current invocation renders an
explicit unavailable record instead of inheriting a fixture value or a stale prior-run number, and the manuscript conclusion follows the fixture-scoped token unless
a current-run external result is explicitly named.
Table 14: Promoted forward-gate summary emitted by forward_gates_summary.json.
lane gate status metric verdict artifact
fixture latent_regime_hmm completed 2.615 latent_regime_hmm_does
_not_beat_markov_null_
em_overfits
output/runs/latent_reg
ime_hmm.json
fixture neural_baseline completed 0.618 neural_sequence_beats_
weak_nulls_not_particl
e_mixture
output/runs/neural_bas
eline.json
fixture learned_stay_rate completed -0.008 honest_regime_null output/runs/learned_st
ay_rate.json
fixture heldout_reporting_proc
ess
completed 0.001 honest_null output/runs/heldout_re
porting_process.json
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## Page 42

lane gate status metric verdict artifact
fixture cross_generator_transf
er
completed 30 persistence regime_dep
endent_on_self_transit
ion_rate; particle tra
nsfers; return transfe
rs
output/runs/cross_gene
rator_transfer.json
fixture efe_location_frontier completed 1.000 metadata_recovery_not_
above_structure_null
output/runs/efe_locati
on_frontier.json
fixture linkage_risk_frontier completed 1 location_carries_relin
k_risk_that_minimizati
on_removes
output/runs/linkage_ri
sk_frontier.json
fixture poisoning_robustness completed 0.636 poisoning_detection_re
gime_changed
output/runs/poisoning_
robustness.json
external latent_regime_hmm unavailable unavailable external lane was not
completed in this run
output/runs/latent_reg
ime_hmm_external.json
external neural_baseline unavailable unavailable external lane was not
completed in this run
output/runs/neural_bas
eline_external.json
external learned_stay_rate unavailable unavailable external lane was not
completed in this run
output/runs/learned_st
ay_rate_external.json
external heldout_reporting_proc
ess
unavailable unavailable external lane was not
completed in this run
output/runs/heldout_re
porting_process_extern
al.json
external cross_generator_transf
er
unavailable unavailable external lane was not
completed in this run
output/runs/cross_gene
rator_transfer_externa
l.json
external efe_location_frontier unavailable unavailable external lane was not
completed in this run
output/runs/efe_locati
on_frontier_external.j
son
external linkage_risk_frontier unavailable unavailable external lane was not
completed in this run
output/runs/linkage_ri
sk_frontier_external.j
son
external poisoning_robustness unavailable unavailable external lane was not
completed in this run
output/runs/poisoning_
robustness_external.js
on
Figure 35: Source forward_gates_summary.json summarizes the promoted M10+ artifact families: latent-regime HMM, neural baseline, learned stay-rate, held-
out reporting process, cross-generator transfer, EFE location frontier, linkage-risk frontier, and poisoning robustness. Metrics and verdicts are shown together,
including honest nulls. External rows count only same-run synthetic evidence, not stale simulator results. Evidence: current M10+ synthetic gate outcomes
including honest nulls. Boundary: stale or empirical simulator-validation conclusions.
14.5 Gap Filling Still F aces the Persistence Oracle
The persistence null deserves a closer look, because it is a deceptively strong baseline: it is handed the true previous cell and simply predicts it again.
Two regimes separate cleanly. In the location-blind limit — the location modality removed at every step — the filter’s information set is not handed the true
previous cell, while persistence receives that cell by construction. There the deep-latent skill against persistence is strongly negative under this weaker information
set — the filter does not beat the persistence oracle, and the deficit is large rather than marginal (reference lane -19.745 on the fixture; the current pinned-fixture
resimulation gives flat -3.422 and speed-conditioned -3.467): non-location evidence narrows the gap but does not close it. This is an honest benchmark-specific
information asymmetry, not a universal theorem about location-blind methods; a different generator or target could make a location-blind predictor competitive.
The target synthetic gap-filling regime is sporadic-reporting interpolation : location is observed at sparse reports and missing in between, so both the filter
and persistence know the last reported cell and the question is what happens across a gap. fig. 36 reports recovery scored on the 1199 held-out gap steps of the
current pinned-fixture run (location hidden there). Persistence rigidly holds the last reported cell (Brier 0.304). Against that oracle the regenerated run scores
skill 0.133 for the flat belief filter and 0.219 for the speed-conditioned variant (positive = clears persistence; speed-clamp edge 0.086) — on the current canonical
regeneration both are positive, so both variants clear the persistence oracle here, with the speed-conditioned filter strongest. We do not promote these margins
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as a win: they are single-run synthetic software measurements that lean on the disclosed displacement-derived speed cue, they sit outside the clustered-bootstrap
multiplicity family of sec. 3.2.1.1, and the controlled harness’s role remains proving the machinery can detect a planted speed-to-move coupling. Speed is derived
from inter-report displacement, so it is a strong kinematic cue for whether the cell changed — we disclose this rather than hide it, report the speed-free flat filter
alongside, and confine all of these to synthetic-data software measurements on the pinned simulator, never empirical mobility validation.
Figure 36: Source anticipatory_analysis.json tests whether belief propagation fills sparse gaps better than persistence. The left panel shows speed-conditioned
off-diagonal transition mass; the middle panel reports gap-filling recovery skill against the persistence null, and the right panel keeps the location-blind limit on
its own scale. Positive bars would support gap filling beyond the oracle previous-cell baseline, while negative bars are retained as bounded nulls. Speed is derived
from reports, and the result is a synthetic software measurement. Evidence: gap-filling skill or bounded nulls against the persistence oracle. Boundary: claims
that propagation predicts real hidden paths.
14.6 Expected F ree Energy Separates Epistemic and Pragmatic V alue
The active-sensing analysis ranks candidate location fixes by expected information gain / expected-free-energy components, which decompose into an epistemic
term (the expected information gain about the latent cell from an observation) and a pragmatic term (the expected log-preference of the predicted observation
under the preference vector 𝐶) [ Millidge et al. , 2021, Sajid et al. , 2021b, Champion et al. , 2024]. fig. 37 makes that decomposition explicit. This is separate from
the transparent closed-loop simulator-candidate selector of sec. 12, which ranks declared simulator configurations from measured artifact metrics.
Because this project runs with uniform preferences ( 𝐶 all zero), the pragmatic term is identically zero and the agent’s sensing value is purely epistemic : the
mean epistemic share of a location fix is 1. Sharpening 𝐶 toward a preferred observation introduces a pragmatic drive and the epistemic share falls — to 0.820
at preference strength 4 — which confirms the decomposition is a genuine measurement that separates the two value components rather than a constant. Under
this project’s synthetic, preference-free generative model, then, “active” inference here means purely information-seeking sensing, not operational collection.
We also tested whether that epistemic value is useful for scheduling: under a fixed observation budget, does ranking steps by expected information gain (spending
location fixes where they most reduce cell uncertainty) recover the latent cell better than spending the same budget on a blind, budget-matched random schedule?
Scored honestly on the full non-first trajectory — every schedule covers the identical evaluation set, so the metric cannot be flattered by a schedule that leaves
only easy steps unobserved — the answer is an honest null: epistemic-led acquisition beats only a fraction 0 of random schedules on the current pinned-fixture run.
The speed-conditioned dynamics already anticipate where the cell will change, so most of the uncertainty an information-greedy fix would target is uncertainty
the transition model has already resolved; choosing which step to observe by information gain therefore adds little over choosing blindly. We report this null
rather than search for a framing that inverts it.
Figure 37: Source active_sensing_analysis.json decomposes expected free energy into epistemic and pragmatic value. As preferences sharpen, the location-fix
epistemic share changes rather than remaining constant; the budgeted sensing panel compares information-led acquisition with a budget-matched random schedule.
Near-zero or negative margins are reported as an active-sensing null, showing that information gain does not robustly beat blind acquisition on this synthetic
trace. Evidence: the separation of epistemic and pragmatic value in synthetic active sensing. Boundary: a robust collection or sensing recommendation.
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14.7 Detection, Structure Recovery , and Minimization Stay Program Extensions
Three further analyses map what the sparse-mobility benchmark can and cannot do, each reported against its honest baseline.
For routine-break detection, fitting the generative model on the clean routine and scoring per-step surprise (variational free energy) on a stream with injected
breaks separates anomalies from normal steps with ROC AUC 0.649 for a rare-cell break and 0.667 for a random-cell break, against a first-occurrence novelty
baseline of 0.500 (fig. 38). Surprise wins because it folds in the transition model, making an unreachable jump surprising in a way mere novelty cannot see; the
comparison is a synthetic anomaly-as-surprise diagnostic, not a deployed detector [ Pimentel et al. , 2014].
For pattern-of-life structure recovery, the target is occupancy total-variation and preferred-place-set overlap rather than next-cell prediction. The deep-latent lane
recovers the broad occupancy structure (preferred-set Jaccard 0.500) above a uniform null, but its honest baseline is dynamics-only propagation: on the current
pinned-fixture run the non-location evidence (occupancy TV 0.171) does not beat simply propagating the trained dynamics (TV 0.042), so sparse metadata adds
little to the preferred-place structure a fitted transition model already encodes. A between-draw check repeats this comparison on 10 independent synthetic
generator draws (16 travellers each, mean occupancy TV 0.076 deep-latent vs. 0.075 dynamics-only): the deep-latent lane beats dynamics-only on only 0.500 of
draws, corroborating rather than contradicting the single-fixture result above — this is a genuine coin-flip across independent draws, not a robust win or a robust
loss, consistent with a trained transition model already carrying most of the preferred-place signal.
For mission-conditioned collection, allocating a fixed location-fix budget by expected free energy under mission-weighted preferences is scored against a mission-
pragmatic comparator, not operational tasking, on the expanded benchmark: mission-weighted recovery is 0.590 for EFE versus 0.554 for pragmatic. The text
should be read from the regenerated values rather than a fixed prior verdict.
Composing these, the recoverability frontier (fig. 39) maps recovery against the observed modality set: with all modalities the filter holds mean mass 0.995 on the
true cell, but withholding location collapses it to 0.069 — an oversight-positive statement of how protective location-minimization is and how little the specific
cell is recoverable from time, speed, and reporting-burst metadata alone. All of these are synthetic-data software measurements on the pinned generator, not
empirical mobility findings.
Figure 38: Source anomaly_analysis.json injects routine breaks into the synthetic observation stream after fitting the clean routine. Filter surprise, measured by
variational free energy, is scored by ROC AUC against injected labels and compared with first-occurrence novelty for rare-cell and random-cell breaks. The result
is a software diagnostic of synthetic perturbations, not empirical anomaly detection. Evidence: VFE surprise behavior under injected synthetic routine breaks.
Boundary: deployment-ready anomaly detection.
Figure 39: Source frontier_analysis.json compares observation-modality subsets on point recovery and occupancy-structure recovery. Mean posterior mass on
the true cell shows what direct location buys; occupancy total-variation distance shows which aggregate structure survives minimization. The frontier is an
oversight-positive map of synthetic recoverability, not evidence about real populations. Evidence: oversight-positive accounting of recovery versus minimization.
Boundary: claims about real populations or individual recoverability.
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15 Supplementary S8 - Safety and Privacy Analyses Stay Synthetic Risk Proxies
This supplement covers multi-factor pymdp interpretability, location-minimization and linkage-risk safety gates, privacy-utility analysis, and external-lane run
evidence — diagnostic and data-governance surfaces underpinning the honest-negative thesis.
15.1 F actorial pymdp Diagnostics Expose Modes Without Cognitive Claims
The single-factor lanes treat the latent cell as the only hidden variable. The factorial pymdp lane adds interpretable structure: across its 3 hidden factors —
the spatial cell, a movement mode, and a synthetic reporting mode — it factorizes the generative model so that movement texture and report-timing texture
are inferred as separate, inspectable posteriors. The reporting-mode factor is a synthetic reporting-process construct derived from gap and burst structure; it
represents synthetic cognitive-proxy states, not real cognition or intent , not a behavioral or psychological claim. fig. 40 shows the per-factor posterior
entropy and the movement and reporting-mode confidence and label stability.
A multi-factor mean-field posterior is an approximation, and the lane reports the cost of that approximation rather than hiding it [ Jordan et al. , 1999, Blei et al. ,
2017]. The released pymdp variational engine is validated against an independent analytic mean-field solver: the pymdp-versus-mean-field agreement is 0.000,
near machine precision, so the two implementations cross-validate. The mean-field-versus-exact marginal gap is 0.044 — the honest price of factorizing a posterior
whose likelihoods couple factors — and it is reported as a diagnostic rather than folded into the agreement check. fig. 41 places these two quantities side by side
with per-factor recovery sharpness.
Multi-factor interpretability is not a performance claim. fig. 42 and tbl. 15 compare the factorial lane against the transparent reference filter, single-factor pymdp,
and stronger switching-HMM and particle/state-space baselines on mean next-observation predictive loss [ Zucchini et al. , 2016, Doucet et al. , 2001, Arulampalam
et al. , 2002]. The factorial mean predictive loss is 5.296 nats, against 0.635 for the switching-HMM baseline and 0.550 for the particle/state-space baseline; the
current best model is particle_state_space and the performance gate reports factorial_pymdp_cleared_current_lane. A non-leading gate is reported as such:
the factorial lane earns its place through interpretable latent-mode diagnostics, not through a state-of-the-art predictive claim.
Table 15: Factorial pymdp model comparison emitted by factorial_pymdp_analysis_fixture.json.
model implemented mean predictive loss (nats) interpretability surface
reference_filter yes 5.719 posterior trace and tensor provenance
single_factor_pymdp yes 6.147 VFE, EFE, policy posterior
factorial_pymdp yes 5.296 cell, movement-mode, cognitive-proxy
posteriors plus VFE/EFE
switching_hmm yes 0.635 online transition regime baseline
particle_state_space yes 0.550 transparent persistence/Markov
mixture state-space baseline
neural_sequence planned blocked until explicit prequential
training gate
future comparator only
Figure 40: Source factorial_pymdp_analysis_fixture.json exposes the factorial pymdp hidden-factor diagnostics. Posterior entropy is shown against each factor’s
computed maximum entropy (all three factors), while mode confidence and label stability are shown for the movement-mode and synthetic cognitive-proxy
reporting factors only. The cognitive-proxy factor is derived from gap and burst texture; it is not a claim about real cognition, intent, or mental state. Evidence:
factor-specific posterior diagnostics in the factorial pymdp lane. Boundary: claims about real cognition, intent, or mental state.
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Figure 41: Source factorial_pymdp_analysis_fixture.json validates the factorial lane and reports the cost of factorizing coupled likelihoods. The pymdp variational
posterior is checked against an independent analytic mean-field solver, the mean-field-versus-exact marginal gap is shown separately, and recovery sharpness is
plotted per factor. Synthetic software measurements, not empirical claims. Evidence: mean-field agreement, exact-marginal gap, and factor recovery costs.
Boundary: empirical latent-mode validation.
Figure 42: Source factorial_pymdp_analysis_fixture.json compares predictive loss for the transparent reference filter, single-factor pymdp, factorial pymdp,
switching-HMM, and particle/state-space baselines, with persistence marked as a null. The performance gate reports whether the factorial lane leads; a non-
leading verdict is part of the synthetic result. Multi-factor interpretability does not establish state-of-the-art predictive performance. Evidence: performance-gate
comparison between factorial, single-factor, and sequence baselines. Boundary: state-of-the-art predictive performance when the gate is non-leading.
15.2 Location-Minimization and Integrity Gates Stay Oversight-Positive
The promoted safety-boundary artifacts in sec. 14.4 sharpen the old privacy and anomaly summaries. They are the point where model diagnostics become explicit
minimization, linkage-risk, and data-integrity gates rather than general-purpose safety prose.
fig. 43 prices location in expected-free-energy terms: the location joint share is 1.000, the metadata-bundle structure-null p-value is 0.417, the residual fraction
localized without location is 0, and the verdict is metadata_recovery_not_above_structure_null . The 4x4 expanded fixture therefore demotes any blanket
metadata-recovery claim: the artifact verdict, not prior prose, decides whether the metadata residual clears the structure null, and withholding location still
sharply reduces localizability on this generator.
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Figure 43: Source efe_location_frontier.json prices location in the model’s epistemic currency. The figure compares the expected cell-information value of direct
location with the non-location metadata bundle, checks metadata against a structure-destroyed null, and includes a positive control for test power. This is an
oversight-positive synthetic boundary, not a collection recommendation. Evidence: the epistemic value and positive-control boundary for location minimization.
Boundary: a collection recommendation.
The linkage-risk frontier in fig. 44 measures aggregate synthetic traveller re-linkability under minimization regimes. Full location has linkage 1 and verdict lo
cation_carries_relink_risk_that_minimization_removes ; the no-location regime exceeds its structure-null band: no. This is a defensive data-minimization
statistic over synthetic IDs, not a matcher, re-identification product, formal privacy mechanism, or real-population claim [ de Montjoye et al. , 2013, Dwork, 2006,
Buchholz et al. , 2024].
Figure 44: Source linkage_risk_frontier.json measures aggregate synthetic traveller re-link accuracy under full-location and minimized-metadata regimes, with
structure-null bands and a positive control showing the weak linker can detect injected identity structure. The output is a defensive minimization-risk statistic,
never a per-person linkage product or real-population claim. Evidence: defensive aggregate relink-risk accounting under minimization. Boundary: per-person
linkage, tasking, or real-population inference.
The poisoning-robustness gate in fig. 45 checks whether the analyst’s own VFE surprise flags corrupted inputs before downstream interpretation trusts them.
Its verdict is poisoning_detection_regime_changed : gross teleport poisoning detected no, subtle drift remains a null against the Markov baseline yes, and
the teleport mid-rate VFE AUC is 0.636. The 4x4 regeneration changes the prior fixture conclusion, so the verdict is deliberately reported as a regime-change
diagnostic rather than a generalized assurance claim; which stressors separate from the Markov baseline is read from the artifact’s per-mode gates, not carried
over from an earlier fixture. The stressors are crude synthetic data-integrity probes and the output is a defensive self-monitoring diagnostic.
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Figure 45: Source poisoning_robustness.json tests VFE surprise as a defensive data-integrity monitor under crude synthetic stressors. VFE is compared with a
Markov-surprise baseline and structure-null plus positive-control checks; separated corruptions and remaining nulls are reported by the generated verdict. This
is robustness triage, not a generalized assurance claim. Evidence: defensive VFE-integrity triage under crude synthetic corruptions. Boundary: generalized
robustness assurance.
15.3 Privacy F rontier and External Evidence Do Not Certify Deployment
The older privacy and hardened-anomaly extensions complement the promoted artifact-bound safety checks in sec. 15.2. fig. 46 reports eq. 28: synthetic unicity
is 1 with all modalities and 1 without location, while location-blind co-travel coincidence is 1. These are data-minimization risk indicators on synthetic traces,
not association claims about people, privacy proofs, compliance determinations, or complete adversarial evaluations [ Buchholz et al. , 2024, Bouras et al. , 2026,
Cherigui et al. , 2026]. fig. 47 compares filter surprise to the online Markov-surprise baseline from eq. 29 on subtler probes: the speed-regime shift scores VFE
AUC 0.666 versus Markov AUC 0.923, and preferred-set drift scores VFE AUC 0.637. The point is not to produce an alerting system; it is to ensure the anomaly
result still has signal when novelty is replaced by a transition-aware null.
Figure 46: Source privacy_frontier_analysis.json quantifies what minimization buys back on the synthetic trace. Unicity under coarsened modality sets and
co-travel coincidence rates are shown side by side for the same regimes. On this fixture unicity remains at the ceiling across every rendered coarsening, and
co-travel coincidence does too except for the full ‘all’-modality set, which dips slightly below ceiling (0.89) - an honest, near-no-relief finding rather than a uniform
one. The figure supports oversight-positive risk accounting, not association tasking or claims about real people. Evidence: synthetic minimization accounting for
unicity and co-travel coincidence risk. Boundary: association tasking or claims about real people.
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Figure 47: Source hardened_anomaly_analysis.json re-tests VFE surprise against an online Markov-surprise baseline on every hardened synthetic perturbation
present in the artifact, including speed-regime shifts, preferred-set drift, timing manipulation, and adversarial missingness. Operating-point metrics live in the
artifact. The figure strengthens the routine-break diagnostic while keeping anomaly claims inside synthetic software evaluation. Evidence: harder synthetic
routine-break checks against an online Markov-surprise baseline. Boundary: deployment-ready anomaly monitoring.
The integrity boundary here is read from the regenerated artifacts rather than from a fixed narrative. On the hardened-anomaly artifact (fig. 47), distinct
from the poisoning gate above, the timing-manipulation probe is not a null on this fixture: its VFE surprise shows a modest above-chance separation while the
online Markov baseline stays near chance; that artifact carries no positive-control field, so no positive-control claim is attached to the timing probe, and the
separation is reported as a synthetic perturbation-response diagnostic rather than a detector. On the poisoning gate, the transition-aware comparison is the
negative one reported above: at the mid-rate gate neither teleport nor label-flip separates from the online Markov baseline (gross teleport poisoning detected no),
with label-flip clearing only the above-chance floor, so no poisoning mode currently carries signal above the transition-aware null. Timing-channel integrity as a
designed capability would still require a generative model in which report timing is itself informative.
The external stochastic lane status is: completed on this host with the pinned upstream build. That status is derived from the presence of the retained pinned-build
metrics artifact ( output/runs/fractalrabbit_external/metrics.json ) on this host, not from the current full-study invocation. The current-run forward-gate
and external poisoning artifacts record their own lane status independently and can simultaneously report the external lane as not completed in this run (sec. 14.4),
in which case every external number in this paragraph describes that retained prior pinned-build run rather than same-invocation evidence. From that retained
artifact, the pinned simulator build generated 5737 waypoint rows from 8 travellers over 16 latent cells, with mean predictive loss 2.920 nats, mean posterior
entropy 0.128 nats, holdout mean predictive loss 3.029 nats, and a pymdp matched-prior agreement of unavailable. The external sensitivity lane resimulates
waypoints for each of its 10 runs, so its replicate family reflects genuine simulator stochasticity: the replicate spread in mean predictive loss is 0.783 nats. The
simulator’s ground-truth place stream is also ingested: the external run reports 165 unique places with revisit rate 0.976 and 34.770 reports per place on average,
and external-lane recovery (reference mean mass 0.972) is scored the same way as the fixture lane, with the same objective decomposition applied (external
reference joint-loss skill 0.561 against its own uniform-chance floor). These numbers exercise the full stochastic simulator; they remain synthetic-data software
evidence, not empirical mobility validation.
15.4 The Privacy-Utility F rontier Shows What Survives Minimization
The privacy frontier of sec. 15.3 measures only the risk side of minimization. Its dual is the governance question that matters for a minimization policy: as location
is coarsened or withheld, how much useful next-cell prediction survives, and is that surviving utility bought back in privacy? fig. 48 pairs the two. Predictive
utility is reported on a resolution-fair, shuffle-corrected axis — bits of next-location pinned beyond chance ( log2(n_states) minus the loss in bits), minus a
label-shuffle static-occupancy floor — because two confounds otherwise make a naive utility axis dishonest: a coarser grid is intrinsically easier to predict (target
cardinality), and even a temporally-shuffled predictor scores on a peaked occupancy marginal. Controlling both, the endpoint comparison moves from 3.933 bits
and 0.389 event-uniqueness risk at the finest grid to 1.747 bits and 0 risk at the coarsest grid, while withholding location entirely drives surviving location utility to
zero by construction. On the larger canonical fixture, the full-grid ladder is monotone and clears the graceful-degradation gate; the minimum-collection operating
point is grid_2x2, with 1.747 excess utility bits and 0 event-uniqueness risk against the configured 0.100 utility floor and 0.200 risk ceiling. The reading is the
honest governance one: this is a source-cleared synthetic minimization frontier, not a free lunch and not a transferable real-mobility or operational claim. The
risk axis is an oversight-positive minimization diagnostic over synthetic identifiers, never association capability over real people, k-anonymity, differential privacy,
or a trajectory-privacy certification; the utility axis remains task-specific synthetic utility, not evidence of downstream real-life usefulness [ Sweeney, 2002, Dwork,
2006, Buchholz et al. , 2024, Deng et al. , 2025, Kapp and Mihaljevic , 2023].
Reading the tradeoff as a minimum-collection operating point sharpens the governance question into a falsifiable one: what is the coarsest grid — the least
location disclosed — that still clears a 0.100-bit predictive-utility floor while holding re-identification event-uniqueness below 0.200? On this larger synthetic
generator the answer is source-positive (operating point found: yes): grid_2x2 preserves 1.747 excess utility bits while reducing event-uniqueness risk to 0. The
binding caveat is scope, not threshold failure. This is a precise statement about this generated fixture, this grid ladder, and this next-cell prediction task; it is not
evidence that the same minimization policy would preserve utility or privacy under real mobility, different tasks, temporal coarsening, suppression, k-anonymity,
or deployment constraints [ European Parliament and Council , 2016, National Institute of Standards and Technology , 2020, Sweeney, 2002]. The thresholds remain
deliberately strict so future regenerated artifacts can fail rather than inherit this positive.
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Figure 48: Source privacy_utility_frontier.json pairs surviving next-cell utility with per-event uniqueness risk across location-minimization regimes. Utility is
measured as bits beyond chance and corrected for the shuffled static-occupancy floor, making grids comparable. The current artifact reports a monotone graceful-
degradation gate and minimum-collection operating point grid_2x2. Evidence: a synthetic governance audit showing surviving predictive utility, re-identification
risk, a source-cleared monotone graceful-degradation gate, and the current minimum-collection operating point as location is minimized. Boundary: a state-of-
the-art claim, association over real people, or a real-mobility claim.
The repeated-draw audit in fig. 49 keeps this privacy-utility reading honest across available generated observations. It records 11 completed repeat rows and 0
unavailable variance-realization rows. Unavailable rows are not imputed and do not count as failures or successes; they block repeat-stability wording until the
source observations exist and the regenerated gate clears. Completing every row does not by itself clear the claim: the audit content-hashes each completed source
and flags any realization byte-identical to the canonical fixture as a determinism rerun rather than an independent draw, and a repeated-draw claim requires
more than one genuinely distinct draw among the completed rows. When the completed rows are almost entirely byte-identical reruns of the canonical fixture,
the repeat-stability wording stays blocked for that reason — lack of independent draws — even with zero unavailable rows, and the figure attests determinism
rather than independent-sample stability in that case.
Figure 49: Source privacy_utility_frontier_repeats.json reruns the privacy-utility frontier over the canonical fixture and any generated variance-realization
observation files that are present. Completed rows show finest and coarsest shuffle-corrected utility spread; unavailable realization rows are counted explicitly
rather than imputed. The figure supports only a repeated-draw audit surface: when required rows are unavailable or the full repeated gate does not clear, stability
and graceful-degradation wording remain blocked. Evidence: a repeated synthetic privacy-utility audit with explicit unavailable-row accounting. Boundary:
repeat-stability wording when required realization rows are missing, empirical privacy evidence, or real-mobility claims.
The task-utility/privacy screen in fig. 50 makes release-utility language thresholded rather than rhetorical. It joins surviving predictive utility with re-identification
event uniqueness, co-travel, recoverability, and linkage-minimization context. Current joint operating points: 4; release-utility wording allowed: yes. This remains
a synthetic governance screen, not a privacy guarantee or operational usefulness claim.
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Figure 50: Source synthetic_task_utility_privacy.json joins predictive utility, event uniqueness, co-travel coincidence, recoverability, and linkage-minimization
status. Bars compare utility with the configured utility floor and risk with the risk ceiling; each regime states whether both thresholds define a joint operating
point. The synthetic artifact contains such points, so utility wording remains conditional on joint clearance. Evidence: a thresholded synthetic task-utility/privacy
screen that blocks release-utility wording unless utility and privacy thresholds jointly clear. Boundary: release utility, operational usefulness, privacy guarantees,
or real-world utility claims when the joint gate is blocked.
16 Supplementary Confound T axonomy Keeps Apparent Wins Auditable
This supplement records the confound taxonomy behind the main-text claim discipline. Across development, apparent model wins were raised and then checked
against live artifacts, null models, and cross-vendor audit. The resulting taxonomy is included here as an audit trail rather than as a main-line performance result.
fig. 51 maps 7 catalogued apparent advantages onto 7 confound classes: data density, spatial confinement, in-sample selection, knob or measurement asymmetry,
no signal, family misclassification, and instrumentation bug — the last added when a reporting-artifact miscomputation, not any model-level effect, was found
to have manufactured an apparent regime clearance. The taxonomy reports 7 currently verified entries out of 8, with any missing-artifact cases left explicitly
unverified rather than treated as dissolved. It also marks the fair-by-construction partial-observability positive as the surviving non-confound, because it varies
only marginalize-versus-commit under a matched emission and grants no oracle access.
Figure 51: Source confound_taxonomy.json maps every apparent active-inference advantage this synthetic benchmark raised and then checked onto the confound
class that explains it, with each entry marked as live-verified, documentation-verified, or explicitly unverified when the current external trace needed by the
hook is absent. Markers sit on confound-class rows; diamonds flag confounds caught only by cross-vendor audit, and a star marks the single fair-by-construction
surviving positive. The panel turns the project’s pattern of dissolved naive wins into an auditable map rather than a performance result. Evidence: an auditable
map of which confound class explains each dissolved active-inference advantage and which catches required cross-vendor review. Boundary: a state-of-the-art
claim, an operational capability, or a real-mobility claim.
The taxonomy is bound to current repository state rather than asserted from memory. Each entry carries a verification hook that re-derives its status from an
artifact, a code invariant, a gate result, an explicitly weaker documentation check for historical events, or an explicit unverified marker when the required current
artifact is absent. Read with the multiplicity correction in sec. 3.2.1.1, the supplement explains why apparent active-inference wins are not promoted unless they
survive the same evidence contract as the partial-observability result. It does not support an oracle-beating claim, a global state-of-the-art claim, an operational
claim, or a real-mobility claim.
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16.1 Where, How Much, and Why: A Per-Regime Mechanism Map
The confound taxonomy above and the multiplicity ledger in sec. 3.2.1.1 each answer part of a single question this benchmark keeps returning to: not just whether
active inference beats a fair baseline, but where it does so, how much it wins or loses by, and why. fig. 52 joins them, adding a diagnostic that aif_regime_searc
h.py itself never ran: this project’s own confound-control battery (dominant-cell, pooled-Markov, return-boosted-soft, and oracle-previous-cell baselines), applied
per regime rather than only on the default fixture. Across 5 synthetic regimes, no directional signal (the traveller-clustered confidence interval straddles zero) is
found in 3 regime(s), and active inference loses outright to the strongest implemented fair baseline in 1 regime(s). The one negative-control regime (zero-noise
emission) is trivial by construction, as designed.
The mechanism map’s finding is more precise than a blanket “AIF reduces to a confound. ” 3 of the 4 non-trivial regimes see the best AIF candidate beat every
confound-battery baseline (dominant-cell, pooled-Markov, and return-boosted-soft, all scored against the same noisy observations AIF itself has to work from), so
an apparent AIF signal on those regimes is not reducible to those simpler naive or pooled effects. What still blocks a promoted claim differs by regime, not by one
shared mechanism: on the symmetric-noise and burst-reporting-gap regimes the AIF-vs-fair-baseline advantage is nominally positive but the traveller-clustered
confidence interval straddles zero, so no direction is established; on the latent-regime-switching lane, AIF clears the confound battery yet still loses outright to
online_base_rate , a fair baseline whose adaptive tracking fits this regime’s switching structure better than AIF’s fixed generative model does — a loss to a
stronger adaptive competitor, not to a naive confound. The remaining regime fails the confound battery outright, beating neither the pooled-Markov nor the
return-boosted-soft baseline. A regime can therefore clear this project’s own confound battery and still not earn a promoted claim, for structurally different
reasons (statistical insufficiency versus a loss to a stronger adaptive competitor outside the battery); collapsing that distinction into a single verdict would have
hidden exactly the mechanism this map exists to surface. Every gate at once (fair-baseline win, confound-battery clearance, and Holm-survival) is cleared by 0
regime(s) in the current grid — the mechanism-map methodology’s bar for a claim this benchmark would call a robust, regime-local, still-synthetic win.
Figure 52: Source regime_mechanism_synthesis.json joins three checks per regime: AIF-versus-strongest-fair magnitude and traveller-clustered interval from
aif_regime_search.json, Holm survival from multiplicity_ledger.json, and the dominant-cell, pooled-Markov, return-boosted-soft, and oracle-previous-cell con-
found battery. Dot and whisker encode magnitude and interval; color encodes the mechanism verdict; the margin labels confound clearance and spatial confinement.
Each row names its current blocker, keeping directional loss, confounding, and multiplicity as separate reasons. Evidence: a per-regime join of AIF-vs-fair mag-
nitude and CI, multiplicity-survival status, and confound-battery/mobility standing into one mechanism verdict per regime. Boundary: a state-of-the-art claim,
a global or operational capability, or a real-mobility claim.
This map is a diagnostic layered on top of the canonical regime-search gate in sec. 3.2.1.1, not a replacement for it: it uses a single generator realization and a
smaller bootstrap resample count than aif_regime_search.json ’s own multi-realization average, so its confound-battery and mobility columns are directional,
not the headline gate’s own publication-grade estimate. Like every other synthetic result in this manuscript, it supports no state-of-the-art claim, no global or
operational capability claim, and no real-mobility claim.
16.2 A Structural Diagnostic: Where Within the T rajectory the Loss Sits
The mechanism map above answers WHERE ( latent_regime_switch_035) and HOW MUCH (a pooled loss to online_base_rate), but not WHY within that
one trajectory. This regime is the only one in the grid whose generator has a named, 3-segment movement-mode schedule per traveller — a low-variance,
high-return “commute” segment, a high-variance, low-return “explore” segment (the movement scale jumps sixfold at this boundary), and an intermediate
“return_stabilization” segment — so it is the one regime where a within-trajectory structural breakdown is possible without inventing a new generator. fig. 53
re-slices the exact same per-step losses aif_regime_search.py already computes for its best AIF candidate and the strongest fair baseline, this time grouped by
movement-mode segment instead of pooled, with a traveller-clustered bootstrap CI computed separately within each segment.
The one-sentence version going in would have been a guess: does AIF’s disadvantage concentrate in the volatile “explore” segment, where a fixed generative
model might be expected to struggle most? The regenerated artifact answers without forcing that story. Its uniform_disadvantage flag is False; the worst
segment is return_stabilization, the best is commute, and their magnitude ratio is n/a. The ratio deliberately renders n/a whenever segment intervals do not
support a common disadvantage sign, rather than dividing incomparable effects. The current non-uniform result localizes the loss: the adaptive online-base-rate
comparator’s advantage is strongest in the return-stabilization phase, present in exploration, and unresolved in commute. Online transition adaptation improves
the fixed-transition AIF ablation, but does not erase that phase-structured deficit or beat the adaptive fair baseline. This is evidence against both blanket
explanations — neither “AIF fails only during volatility” nor “AIF is uniformly worse everywhere” survives the phase decomposition.
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Figure 53: Source regime_switch_phase_diagnostic.json partitions the AIF-versus-strongest-fair per-step losses from latent_regime_switch_035, the one syn-
thetic regime with named commute, explore, and return_stabilization segments. Bars report AIF advantage with traveller-clustered bootstrap intervals. CI-
separated negative segments: explore, return_stabilization; zero-crossing unresolved segments: commute; uniform disadvantage: False; worst-to-best magnitude
ratio: n/a. Evidence: a structural, per-movement-phase breakdown of an AIF-vs-fair-baseline loss on one regime, showing whether the loss is uniform or concen-
trated across phase segments. Boundary: a state-of-the-art claim, an operational capability, or a real-mobility claim.
This diagnostic is scoped to one regime and one generator realization, with a smaller bootstrap resample count than the canonical gate. It supports a structural,
per-phase account of where within this one synthetic trajectory a fair-baseline loss sits; it does not support global capability, state-of-the-art standing, deployment,
surveillance readiness, operational use, or real mobility.
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*Extraction method: pypdf*