# Full Text: DuckRabbit: Typed Multimodal Illusion Generator

> Extracted from `Friedman_2026_Duckrabbit_3afefaee.pdf`

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DuckRabbit: Typed Multimodal Illusion Generator
Deterministic visual, auditory, temporal, and audio-visual stimulus construction
Daniel Ari Friedman
Active Inference Institute
ORCID: 0000-0001-6232-9096
DOI: 10.5281/zenodo.21419693
2026-07-15

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Contents
1 Abstract 2
2 Introduction 3
3 Methodology 4
3.1 Request and canonical artifact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.2 Typed parameter domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.3 Canonical serialization and provenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.4 Encoding and verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.5 Objective metric definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.5.1 Synthetic psychophysics boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 Results 6
4.1 Generated catalog, metrics, and outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4.2 Typed domains and delivery profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.3 Pipeline and provenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.4 Visual constructions and parameter sweeps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.5 Temporal and auditory constructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.6 Audiovisual timing and encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.7 Objective metric results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.8 Observer estimands and verification controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.9 Synthetic psychophysics model diagnostic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
5 Experimental and Computational Setup 16
6 Reproducibility and Provenance 17
6.1 Data availability and software citation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
7 Scope, Related W ork, and Limitations 18
7.1 Scope and epistemic boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
7.2 Visual families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
7.3 Auditory families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
7.4 Audiovisual and temporal binding families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
7.5 From literature to engineering contract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
7.6 Limitations and future observer work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
8 Publication Atlas, Caption Contract, and Scholarship Audit 21
8.1 Claim-level visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
8.2 Scholarship map and lineage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
8.3 Formal traceability and objective metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
8.4 Observer-design boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
8.5 Generated audit tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
9 Discussion and Conclusion 48
9.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
10 Appendix A. Complete catalog, source tiers, and evidence/implementation boundaries 49
10.1 How to read the matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
10.2 Evidence boundary and future expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

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1 Abstract
DuckRabbit is typed, deterministic research software by Daniel Ari Friedman (Active Inference Institute) for constructing reproducible
visual, auditory, temporal, and audiovisual stimulus families. The intended public release will be available at the following repository:
https://github.com/docxology/DuckRabbit
DuckRabbit is released under the MIT License.
Its basic unit is an immutable request containing an illusion identifier, validated parameters, a seed, and an encoding specification.
The request yields a canonical artifact, objective media measurements, and a versioned provenance manifest before any delivery codec
is selected. This separation makes the stimulus a testable computational object while reserving claims about perception for controlled
observer protocols.
The release situates its engineering choices within a deliberately broad historical foundation spanning Greek, Arabic/Islamicate,
Chinese, and early-modern work on optics, visual inference, and cross-sensory knowledge, alongside later psychophysics and illusion
research. These traditions motivate questions about construction, observation, and evidence; they are contextual precedents, not
evidence that a generated file reproduces an ancient, early-modern, or clinical observation.
Version 0.5.0 contains 17 implemented generators and 18 catalog entries, supported by 36 source records and 18 evidence records in
a checked-in audit snapshot. The package generates 15 publication figures and 10 machine-derived tables from the live registry. It
also provides a typed observer-study harness and a transparent synthetic diagnostic: a hand-specified feature observer with serialized
weights, temperature, analytic calibration, and human_data=false . No participant data are bundled; synthetic model output is
explicitly nonhuman.
DuckRabbit verifies physical stimulus properties, media round trips, hashes, timing, and declared provenance. It does not infer a
universal percept, effect size, or cross-device perceptual equivalence from a generated artifact. Its contribution is a reproducibility and
epistemic boundary: source-backed family descriptions, deterministic media facts, and future observer hypotheses remain different
typed records rather than being collapsed into one claim. DuckRabbit is software for reproducible stimulus construction and audit,
not a claim that a generated file alone produces a universal perceptual effect.
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2 Introduction
An illusion stimulus is not the same thing as an illusion report. A stimulus can be physically specified, generated, encoded, and
inspected without establishing what every observer will see or hear. This distinction is central to reproducible cognitive science: the
physical manipulation must be auditable, while observer-level effects require a task, calibrated presentation conditions, randomization,
and data.
Visual illusion classifications are useful maps rather than exhaustive or universally agreed ontologies [ Gregory, 1997]. Auditory and
audiovisual families add spectral structure, channel separation, temporal coincidence, and spatial alignment. The Sound-Induced
Flash literature illustrates the boundary particularly clearly: the physical contrast is a flash paired with different beep counts, while
the perceptual claim requires a listener, timing, and a response task [ Hirst et al. , 2020, Shams et al. , 2000].
DuckRabbit therefore treats an illusion as a typed stimulus-construction problem. Each catalog entry declares modality, mechanism,
perceptual signature, cognitive process, requirements, evidence status, output kind, and implementation status. The taxonomy is
orthogonal and explicitly provisional; it is an engineering index linked to sources, not a replacement for domain-specific theory.
The release also treats the package as research software rather than as an unannotated collection of media files. Reproducible
computational research depends on preserving the code, inputs, environment assumptions, and execution path needed to recreate a
result [ Sandve et al. , 2013, Wilson et al. , 2014]. The F AIR literature extends that responsibility to algorithms, tools, and workflows,
while software-citation guidance emphasizes identifying the exact software object and version used [ Wilkinson et al. , 2016, Lamprecht
et al. , 2020, Smith et al. , 2016]. DuckRabbit applies these principles narrowly: it makes the construction pipeline and its generated
artifacts citable and inspectable, but it does not treat metadata quality as evidence of a perceptual effect.
The package is organized around three falsifiable engineering hypotheses:
1. Identical typed requests produce identical canonical arrays and canonical digests.
2. Encoders and decoders preserve declared media facts within an explicit format-specific tolerance, or verification fails.
3. Parameter manipulations change measurable physical stimulus properties; any observer-level interpretation remains a preregis-
tered hypothesis until data exist.
This boundary has a nineteenth-century scientific lineage. Fechner’s Elemente der Psychophysik formalized the problem of relating
controlled stimulus differences to measured sensation, while Wheatstone’s binocular-vision experiments made the distinction between
the physical images delivered to two eyes and the resulting depth interpretation experimentally explicit [ Fechner, 1860, Wheatstone,
1838]. Helmholtz’s physiological optics then integrated measurement of the eye, visual geometry, and theories of perceptual inference
[Helmholtz, 1867]. DuckRabbit does not reproduce those historical experiments; it inherits their methodological lesson that stimulus
conditions and observer inferences must be represented as distinct objects.
That lineage has deeper and less geographically narrow roots. Ptolemy’s ancient Optics, Ibn al-Haytham’s medieval Arabic optics,
and the Mohist Canon’s early Chinese discussions of optics and mechanics show that questions about image formation, geometry,
knowledge, and evidence were developed across multiple intellectual traditions [ Ptolemy, 1996, al Haytham , 1989, Schemmel and
Boltz, 2022, Dai, 2015]. Early-modern discussions sharpened the distinction between a physical presentation and an inferred percept:
Kircher documented optical display, Berkeley analyzed learned spatial inference, and the Molyneux–Cheselden record made cross-
sensory transfer and observer testimony explicit problems [ Kircher, 1646, Berkeley, 1709, Degenaar and Lokhorst , 2020, Cheselden,
1728]. DuckRabbit cites these sources as historical and methodological precedents, not as evidence that its generated files reproduce
ancient, early-modern, or clinical observations.
The present catalog contains 18 entries, of which 17 are implemented, 0 are planned, and 1 require external fixtures. This status
vocabulary makes breadth visible without claiming that a finite package covers all known phenomena.
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3 Methodology
3.1 Request and canonical artifact
DuckRabbit starts from a typed request
𝑞 = (𝑖, 𝜃, 𝑠, 𝑒) (1)
where 𝑖 is an illusion identifier, 𝜃 is an immutable parameter object, 𝑠 is a deterministic seed, and 𝑒 is an optional encoding request.
A registered generator maps the request to a canonical artifact:
𝐴 = 𝐺𝑖(𝜃; 𝑠), 𝐴 ∈ {𝐼, 𝑋, 𝑉 , 𝐴𝑉 } (2)
The four artifact types are an image frame 𝐼, audio buffer 𝑋, video sequence 𝑉 , and audiovisual timeline 𝐴𝑉. The generator core is
independent of Pillow, W A V containers, GIF, MP4, and ffmpeg. Each artifact retains its shape, dtype, units, clock, channels, and
timing offsets.
3.2 Typed parameter domains
Value objects validate finite ranges at construction time. Image parameters include dimensions, color mode, luminance bounds,
grayscale levels, and quantization levels. Audio parameters include frequency, phase, amplitude, duration, envelope, sample rate,
channel count, and PCM depth. Video parameters include dimensions, rational frame rate, frame count, and temporal offsets.
Audiovisual parameters compose audio and video clocks with declared synchronization and spatial discrepancies.
The canonical sample count and frame timestamps are explicit. For audio duration 𝑇 and sample rate 𝑓𝑠, 𝑁 is rounded once at
construction. For a video with frame rate 𝑓𝑟, frame index 𝑘 is timestamped on the presentation clock. The audio-minus-video sign
convention is explicit:
𝑁 = round(𝑓𝑠𝑇 ), 𝑡 𝑘 = 𝑘/𝑓𝑟, Δ 𝐴𝑉 = 𝑡 audio − 𝑡video (3)
The package rejects non-finite values, invalid shapes, out-of-range samples, aliasing frequencies, incompatible channel layouts, impos-
sible frame rates, and contradictory encoding requests.
3.3 Canonical serialization and provenance
Canonical arrays are contiguous little-endian float32 buffers with explicit metadata. Serialization includes the array values, shape,
clock, and units; metadata are part of the identity rather than an informal annotation:
𝑐(𝐴) =SerializeLE,float32(𝐴,shape, clock, units), ℎ 𝑐(𝐴) = 𝐻(𝑐(𝐴)) (4)
The canonical digest is independent of PNG, W A V, GIF, MP4, and NPZ delivery choices. The v2 manifest records the parameter
schema, serialized parameters, taxonomy, evidence boundary, canonical facts, objective metrics, encoding profile, backend identity,
decoded inspection, and verification status. A v1 reader remains available and marks upconverted records unverified until the encoded
file is re-inspected.
This separation follows a reproducibility principle from computational research: a result is not made reproducible merely by publishing
a final file; the executable inputs, transformation steps, versioned software, and provenance must remain identifiable [ Sandve et al. ,
2013, Wilson et al. , 2014]. The manifest therefore records the construction identity and delivery identity separately. A downstream
user can cite the software version and regenerate the canonical object, or cite a particular encoded artifact when the delivery file itself
is the relevant research object [ Smith et al. , 2016].
The distinction also follows the older psychophysical problem of relating a controlled physical increment to a measured sensation.
Fechner’s 1860 treatise made measurement, stimulus control, and response comparison explicit parts of the scientific object [ Fechner,
1860]. DuckRabbit adopts the stimulus-control and provenance aspects of that tradition, but it does not pretend that a canonical
digest or media metric is a sensation measurement: observer data still require a task, presentation conditions, and a registered
analysis.
3.4 Encoding and verification
For an encoding request 𝑒, the delivered file 𝐹 and decoded inspection 𝐼 are:
𝐹 = 𝐸 𝑒(𝐴), 𝐼 = 𝐷(𝐹 ), 𝑉 (𝐹 , 𝑀 ) ∈ { pass, fail} (5)
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The manifest 𝑀 binds 𝐴, 𝐹 , and 𝐼 through hashes, typed summaries, and format-specific tolerances. PNG, GIF, W A V, and NPZ use
local deterministic adapters. MP4 and muxed audiovisual output use an optional ffmpeg backend. Missing backends are reported as
capability errors. Writes are atomic, parent directories are created, overwrite behavior is explicit, and a conflicting format argument
is rejected.
3.5 Objective metric definitions
MetricRecord and MetricSuite carry a metric name, value, unit, computation version, source artifact, tolerance, and claim level.
Luminance statistics, quantization levels, RMS and peak amplitude, spectral summaries, frame deltas, stream durations, and syn-
chronization offsets are physical or decoded-media facts. They are not observer responses and cannot by themselves establish an
illusion effect. For canonical image samples 𝑦1, … , 𝑦𝑛, audio samples 𝑥1, … , 𝑥𝑛, and adjacent video frames 𝑌𝑘, 𝑌𝑘+1, the principal
metrics are:
𝜇𝑌 = 1
𝑛
𝑛
∑
𝑗=1
𝑦𝑗, 𝜎 𝑌 =
√√√
⎷
1
𝑛
𝑛
∑
𝑗=1
(𝑦𝑗 − 𝜇𝑌 )2, 𝑅𝑀 𝑆 𝑋 =
√√√
⎷
1
𝑛
𝑛
∑
𝑗=1
𝑥2
𝑗 (6)
𝐷𝑘 = 1
|𝑌 | ∑
𝑝
|𝑌𝑘+1(𝑝) − 𝑌𝑘(𝑝)|, centroid(𝑋) =
∑𝑓 𝑓 𝑃𝑋(𝑓)
∑𝑓 𝑃𝑋(𝑓) (7)
The level count is the cardinality of the finite-value set after canonical quantization; an empty or non-finite artifact is invalid rather
than assigned a default statistic. Every metric record carries units and a deterministic computation version. Observer interpretations
are represented separately by the typed observer protocol and claim levels.
For a future observer study, the estimand is defined by the protocol rather than by the generator itself:
𝜓 = 𝔼[𝑌 ∣ condition, protocol] (8)
This symbol names a planned analysis target only. DuckRabbit ships no human responses, fitted coefficients, or validated observer-
level estimate.
3.5.1 Synthetic psychophysics boundary
DuckRabbit v0.5.0 adds a transparent synthetic-psychophysics diagnostic for method orchestration. It is a hand-specified feature
observer, not a pretrained vision model and not an empirical psychophysics substitute. Let 𝜙(𝐴)be the bounded feature vector
extracted from a canonical artifact, 𝑤 the code-owned feature weights, and 𝜏 > 0 the declared temperature:
𝑝𝑀 (𝑐 ∣ 𝐴𝑟, 𝐴𝑐) = 𝜎 (𝑤T𝜙(𝐴𝑐) − 𝑤T𝜙(𝐴𝑟)
𝜏 ) (9)
The model identity, version, preprocessing features, weights, temperature, seed, calibration statement, and the human_data=false
flag are serialized with each prediction. The diagnostic is useful for checking that typed parameter sweeps produce deterministic,
inspectable model outputs and for exercising analysis orchestration end to end. It does not estimate a human psychometric func-
tion, establish a sensitivity threshold, or support an observer-level claim. Human psychophysics remains future work requiring a
preregistered task, calibrated display/playback, participant data, and an analysis contract.
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4 Results
4.1 Generated catalog, metrics, and outputs
The live registry reports 17 implemented generators, 18 catalog entries, 18 evidence records, and 36 source records in the checked-in
scholarship audit snapshot. The complete catalog is generated in Appendix A rather than copied into prose. The companion figure
keeps the categorical registry, source namespace, and implementation statuses visible at a glance.
Figure 1: A matrix lists all catalog entries with modality, mechanism, signature, input requirement, and implementation status.
What this figure shows: A matrix lists all catalog entries with modality, mechanism, signature, input requirement, and implementation
status. The live catalog matrix contains 18 entries and keeps modality, mechanism, perceptual signature, input requirement, evidence
status, and implementation status as separate facets. Source data output/data/catalog_matrix.json preserve the exact taxonomy
snapshot and its source-reference namespace; status is not a proxy for perceptual validation. Controls: live taxonomy registry; evidence
matrix snapshot; seed not applicable to the catalog diagram. Objective facts: 18 catalog rows; categorical facets and statuses; no
observer-level quantity is applicable. Claim level: source_supported. Source data: output/data/catalog_matrix.json (SHA-256
digest recorded in the figure registry). Evidence lineage: gregory1997visual, hirst2020sound, bruns2019ventriloquist. Limitations:
Taxonomy facets are engineering classifications and remain provisional where the literature supports competing accounts. Boundary:
Catalog coverage is bounded to this registered package and does not enumerate all known illusions.
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The complete catalog matrix fig. 1 is tabulated in the standalone Appendix A sec. 10, tbl. 10. The corresponding machine-readable
evidence matrix records the source role, exact supported claim, engineering departure, and limitation for every entry. Keeping the
table in an appendix gives the main results narrative room to explain the contract without turning a mutable registry snapshot into
a prose claim.
4.2 Typed domains and delivery profiles
Table 1: Typed parameter domains and units.
Type Unit Validated domain Role
PixelDimension pixels 8–4096 image/video width and height
GrayscaleLevels levels 2–256 representable grayscale levels
QuantizationLevels levels 2–256 output quantization buckets
FrequencyHz Hz > 0 and finite oscillator and harmonic
frequencies
SampleRate samples/s 1,000–384,000 audio sampling clock
FrameRate frames/s 1–240 video presentation clock
SyncOffsetMs ms −10,000–10,000 audio relative to video
SpatialOffset normalized −1–1 declared crossmodal spatial
discrepancy
The parameter contracts are summarized in tbl. 1. They constrain physical construction and serialization; they are not psychophysical
scales.
Table 2: Encoding profiles and backend capabilities.
Format Backend Artifact Profile Status
PNG Pillow image lossless uint8 raster available
W A V python wave audio PCM 8/16/24/32-bit available
GIF Pillow video palette animation with
declared duration
available
NPZ NumPy canonical artifact exact little-endian
float32 archive
available
MP4 ffmpeg video/audiovisual H.264 or muxed MP4;
decode inspected
available
The delivery profiles are summarized in tbl. 2. Backend availability is environment-dependent and is recorded at generation time.
The catalog distinguishes a physical construction from an observer claim. For example, the sound-induced-flash generator establishes
one flash and one or two beep events on a shared clock; it does not establish a reported flash count. Similarly, the temporal-
ventriloquism generator exposes a declared timing offset, while the literature reports observer-dependent temporal judgments under
specific tasks and timing conditions [ Vroomen and de Gelder , 2004].
4.3 Pipeline and provenance
What this figure shows: Five labeled stages connect a typed request to a deterministic canonical artifact, encoded media, decoded
inspection, and a verification manifest. This schematic separates a typed request from the canonical artifact it generates, the optional
delivery encoder, decoded inspection, and the manifest-level verification decision. Arrows indicate data and provenance dependencies
rather than a causal model of perception; the seed is 0 and the complete stage record is in source data output/data/architecture.json.
Controls: typed request q=(i, 𝜃,s,e) with seed s=0; default generator and delivery-independent canonicalization. Objective facts: no
unit-bearing objective quantity is applicable to this architecture diagram; stage identities and provenance fields are recorded in the
sidecar. Claim level: canonical_stimulus. Source data: output/data/architecture.json (SHA-256 digest recorded in the figure registry).
Evidence lineage: formalism:eq:typed_request, formalism:eq:canonical_generation, formalism:eq:encoding_verification. Limitations:
The schematic abstracts implementation boundaries and does not represent an observer study or a causal theory of perception.
Boundary: The pipeline verifies reproducible media facts, not what a person experiences.
The generated architecture figure fig. 2 shows the separation between request, canonical artifact, delivery adapter, decoded inspection,
and manifest. The canonical digest is the identity of the in-memory stimulus; an encoded hash is the identity of the delivered file.
The difference is intentional.
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Figure 2: Five labeled stages connect a typed request to a deterministic canonical artifact, encoded media, decoded inspection, and
a verification manifest.
4.4 Visual constructions and parameter sweeps
What this figure shows: A 9-panel gallery shows every currently implemented visual catalog entry, with stable IDs and physical
raster summaries: Duck-rabbit ambiguous figure, Simultaneous contrast stimulus, Apparent-motion frame sequence, Müller-Lyer
geometric illusion, Poggendorff geometric illusion, Ponzo perspective illusion, Kanizsa illusory-contour triangle, Ebbinghaus
context-size illusion, Zöllner orientation illusion. This complete gallery presents one deterministic representative from each of the
9 currently implemented visual catalog entries: Duck-rabbit ambiguous figure, Simultaneous contrast stimulus, Apparent-motion
frame sequence, Müller-Lyer geometric illusion, Poggendorff geometric illusion, Ponzo perspective illusion, Kanizsa illusory-contour
triangle, Ebbinghaus context-size illusion, Zöllner orientation illusion. The panel therefore covers the package’s available visual
families—ambiguous figure, contrast, apparent motion, geometric context, illusory contour, contextual size, and orientation-related
constructions—using typed defaults at seed 0. For the temporally expressed apparent-motion entry, the displayed tile is its first
frame and the source data preserve the full sequence. The source data sidecar output/data/visual_panel.json records the stable
ID, generator parameters, canonical SHA-256 digest, Rec. 709 or grayscale luminance statistics, raster-level counts, and parameter
boundary for every tile. Controls: one default typed parameter object per implemented visual entry; seed s=0; dimensions, luminance
bounds, grayscale, and quantization controls remain in each generator schema; temporal entries display their first frame but retain
sequence metrics. Objective facts: per tile: mean and standard-deviation relative luminance, unique raster levels, and canonical
SHA-256 digest; temporal entries additionally retain frame count, frame rate, and frame deltas; definitions and units are in the source
data JSON. Claim level: canonical_stimulus. Source data: output/data/visual_panel.json (SHA-256 digest recorded in the figure
registry). Evidence lineage: gregory1997visual, brugger1999duckrabbit, howe2005muller, morgan1999poggendorff, fisher1967ponzo,
yildiz2022ponzo, kanizsa1976contours, mruczek2015ebbinghaus, earle1995zollner, wertheimer1912motion, sekuler1996wertheimer.
Limitations: The gallery is complete for implemented visual entries in this package, not a complete survey of visual illusions; literature
families, historical displays, and DuckRabbit rasters are not pixel-identical by default. Viewing scale, display calibration, viewing
distance, and observer conditions can change the relevance of a construction; the gallery does not measure an observer’s perceptual
report. Boundary: The figure establishes coverage of the package’s implemented visual constructions and their deterministic raster
facts. It does not establish that any viewer will perceive the named signature, nor that the set is exhaustive of the visual-illusion
literature.
The visual panel fig. 3 is deliberately a coverage figure: it contains one deterministic representative for every currently implemented
visual entry, including apparent motion and Zöllner in addition to the static ambiguous-figure, contrast, geometric-context, illusory-
contour, and contextual- size families. Equalities, masks, line geometry, luminance bounds, and temporal positions are properties of
the typed rasters or sequences. They are not observer scores, and the gallery is not an exhaustive ontology of visual illusions.
What this figure shows: A labeled grid crosses five duck–rabbit blend weights with five grayscale and quantization settings, with
physical metrics recorded for each cell. This 5 ×5 sweep varies duck–rabbit blend weight across rows and jointly varies grayscale
and quantization levels across columns. Each cell is regenerated from an immutable typed parameter object at seed 0; source
data output/data/visual_sweep.json records canonical digests, unique-level counts, normalized luminance, and effective dynamic
range for every condition. Controls: duck_weight ∈ {0,.25,.5,.75,1}; grayscale=quantization ∈ {2,4,8,16,32}; seed s=0. Objective
facts: 25 canonical rasters; unique levels, normalized mean luminance, and effective dynamic range per cell. Claim level: physi-
cal_metric. Source data: output/data/visual_sweep.json (SHA-256 digest recorded in the figure registry). Evidence lineage: brug-
ger1999duckrabbit, gregory1997visual. Limitations: The grid is a sensitivity of the construction parameters, not a psychophysical
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Figure 3: A 9-panel gallery shows every currently implemented visual catalog entry, with stable IDs and physical raster summaries:
Duck-rabbit ambiguous figure, Simultaneous contrast stimulus, Apparent-motion frame sequence, Müller-Lyer geometric illusion,
Poggendorff geometric illusion, Ponzo perspective illusion, Kanizsa illusory-contour triangle, Ebbinghaus context-size illusion, Zöllner
orientation illusion.
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Figure 4: A labeled grid crosses five duck–rabbit blend weights with five grayscale and quantization settings, with physical metrics
recorded for each cell.
sensitivity curve or a validated observer effect. Boundary: The chosen grid is an engineering sampling of the parameter domain and
does not imply an optimal or perceptually uniform spacing.
The sweep fig. 4 varies duck-weight from 0 to 1 and jointly varies representable grayscale and quantization levels. The source data
preserve canonical digests and unique-value counts; no perceptual score is assigned to a sweep cell.
4.5 Temporal and auditory constructions
What this figure shows: Six ordered frames are labeled with timestamps and paired with a line plot of adjacent-frame normalized
pixel differences. The frame strip exposes the order and timestamps of the apparent-motion construction, while the lower trace
reports adjacent-frame mean absolute pixel differences. Source data output/data/temporal_sequence.json preserve frame count,
frame rate, reduced rational timebase, timestamps in seconds, and the nonzero transition series; seed 0 identifies the generated
sequence. Controls: visual.apparent_motion default typed parameters; frame rate and frame count from the canonical sequence; seed
s=0. Objective facts: timestamps in seconds, frame rate in frames/s, frame count, rational timebase, and adjacent-frame normalized
pixel difference. Claim level: physical_metric. Source data: output/data/temporal_sequence.json (SHA-256 digest recorded in the
figure registry). Evidence lineage: wertheimer1912motion, sekuler1996wertheimer. Limitations: Frame succession and frame deltas
are physical file properties; playback timing, display persistence, and motion reports require a controlled observer task. Boundary:
The figure documents temporal structure rather than the presence, direction, or strength of perceived motion.
The temporal figure fig. 5 reports frame succession, rational frame rate, and frame-to-frame mean absolute differences. These facts
establish temporal structure in the file, not the presence or strength of perceived motion.
What this figure shows: Five labeled rows show canonical audio waveforms, relative one-sided spectral bars, RMS and peak in nor-
malized amplitude, and spectral summaries in hertz. Five implemented auditory constructions—Shepard tone, missing fundamental,
tritone paradox, octave illusion, and auditory continuity—are shown as canonical waveforms with compact one-sided FFT summaries.
Source data output/data/audio_signals.json records sample rate, channel layout, RMS, peak, spectral centroid, bandwidth, crest
factor, canonical digest, and the declared display-bin convention; no pitch or stream report is inferred. Controls: default typed
audio parameters; per-generator channel layout and sample rate; seed s=0; one-sided FFT display with 48 sampled bins. Objec-
tive facts: RMS and peak in normalized amplitude; spectral centroid and bandwidth in Hz; sample rate in samples/s; channel
layout and canonical SHA-256 digest. Claim level: physical_metric. Source data: output/data/audio_signals.json (SHA-256 di-
gest recorded in the figure registry). Evidence lineage: shepard1984scale, zatorre2005missing, deutsch1986tritone, repp1997tritone,
deutsch1974octave, warren1970continuity, riecke2011continuity. Limitations: Playback level, transducer response, dichotic separa-
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Figure 5: Six ordered frames are labeled with timestamps and paired with a line plot of adjacent-frame normalized pixel differences.
tion, masker design, and listener judgments are external to the canonical buffer. Boundary: The figure compares generated signal
properties and literature-linked families; it does not establish pitch, continuity, or stream organization for a listener.
The auditory figure fig. 6 shows canonical waveforms and spectral summaries for Shepard, missing-fundamental, tritone, octave, and
continuity constructions. RMS, peak, spectral centroid, bandwidth, and channel layout are calculated from the canonical buffer with
explicit units and windowing rules. Pitch direction, pitch height, continuity, and stream organization remain observer-level outcomes
that depend on playback and task conditions.
4.6 Audiovisual timing and encoding
What this figure shows: Two labeled traces share a normalized time axis: video mean luminance and audio absolute amplitude, with
signed synchronization and spatial offsets printed below. Video mean luminance and rectified audio amplitude are placed on a common
normalized time axis for the sound-induced-flash construction. Source data output/data/audiovisual_timeline.json records the video
frame clock, audio sampling clock, event traces, signed audio-minus-video synchronization offset in milliseconds, and normalized spatial
discrepancy; alignment is declared by the generator, not estimated from perception. Controls: audiovisual.sound_induced_flash
default shared timeline; declared sync offset ΔA V and spatial offset; seed s=0. Objective facts: video luminance and audio envelope
on normalized shared time; ΔA V in ms; spatial discrepancy in normalized units; frame and sample clocks in the sidecar. Claim level:
physical_metric. Source data: output/data/audiovisual_timeline.json (SHA-256 digest recorded in the figure registry). Evidence
lineage: shams2000sifi, hirst2020sound, vroomen2004temporal, hartcherobrien2011temporal. Limitations: Display refresh, audio
hardware, event latency, and observer temporal binding are not measured by this figure. Boundary: A shared-clock construction is
not evidence that observers bind the events at the declared or any other perceptual time.
The audiovisual timeline fig. 7 displays video luminance and audio amplitude against the shared clock, alongside declared synchro-
nization and spatial offsets. Ventriloquist stimuli require stereo playback and spatially resolved display; temporal binding requires
controlled timing and an observer task [ Bruns, 2019, Vroomen and de Gelder , 2004].
What this figure shows: A five-row comparison lists format, backend, preserved canonical facts, and the corresponding decoded
verification checks. The comparison separates the canonical artifact from delivery containers: PNG, W A V, GIF, NPZ, and op-
tional MP4/muxed MP4. Source data output/data/encoding_verification.json records backend identity, preserved canonical facts,
decoded inspection targets, and capability status as observed in the generation environment; the table therefore describes an adapter
contract rather than a claim about codec quality. Controls: typed encoding profile selected per artifact; overwrite and back-
end capability checks; seed inherited from the stimulus request. Objective facts: format availability and verification scope are
environment observations; NPZ is exact while other formats are decoded and tolerance-checked. Claim level: encoded_media.
Source data: output/data/encoding_verification.json (SHA-256 digest recorded in the figure registry). Evidence lineage: engi-
neering:typed_media_adapters. Limitations: Backend availability, codec versions, container metadata, and lossy tolerances are
environment-dependent; playback software can expose additional behavior. Boundary: A successful encode or decode does not
validate an observer effect or guarantee cross-device perceptual equivalence.
The encoding matrix fig. 8 makes backend capability and verification scope visible. NPZ is the exact canonical archive; PNG, W A V,
GIF, and MP4 are delivery containers whose decoded facts are checked against the manifest.
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Figure 6: Five labeled rows show canonical audio waveforms, relative one-sided spectral bars, RMS and peak in normalized amplitude,
and spectral summaries in hertz.
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Figure 7: Two labeled traces share a normalized time axis: video mean luminance and audio absolute amplitude, with signed
synchronization and spatial offsets printed below.
Figure 8: A five-row comparison lists format, backend, preserved canonical facts, and the corresponding decoded verification checks.
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4.7 Objective metric results
Table 3: Objective metric definitions and epistemic boundary.
Metric Unit Definition Tolerance Claim level
mean_luminance normalized_luminance mean Rec. 709 relative
luminance (grayscale is
identity)
exact canonical physical_metric
unique_values levels count of distinct
canonical image values
exact integer physical_metric
rms normalized_amplitude root-mean-square audio
amplitude
finite scalar physical_metric
peak normalized_amplitude maximum absolute
audio amplitude
finite scalar physical_metric
spectral_centroid_hz Hz energy-weighted
one-sided spectral
centroid
finite scalar physical_metric
spectral_bandwidth_hz Hz spectral standard
deviation around the
one-sided centroid
finite scalar physical_metric
crest_factor ratio audio peak divided by
RMS with zero-RMS
guard
finite scalar physical_metric
mean_temporal_delta normalized_pixel_difference mean adjacent-frame
absolute difference
finite scalar physical_metric
sync_offset ms declared
audio-minus-video offset
typed value physical_metric
The metric definitions in tbl. 3 are computed from canonical or decoded artifacts and do not encode observer interpretations.
The default duck-rabbit artifact contains 3 unique raster levels and has mean normalized luminance 0.7770. These values are live
generated facts, not perceptual effect sizes.
4.8 Observer estimands and verification controls
Table 4: Data-free observer outcomes and preregistered estimands.
Estimand Response and model Reference and contrast Uncertainty
sifi flash count contrast event count; poisson or ordinal sifi one beep; two-beep minus
one-beep event-count response
95% confidence interval
temporal binding offset
contrast
continuous magnitude; linear
mixed
temporal sync; reported timing
shift per declared sync offset
95% confidence interval
The analysis contract in tbl. 4 specifies estimands and uncertainty procedures without asserting any result.
Table 5: Verification failure modes and negative controls.
Failure mode Control Expected result
altered encoded file recompute encoded SHA-256 fail
stale canonical digest recompute canonical little-endian float32
digest
fail
incorrect decoded dimensions compare inspection facts with manifest
summary
fail
stream timing mismatch compare duration/timebase and declared
sync offset
fail
unsupported backend capability probe before encoding explicit capability error
conflicting format requests reject format_name/output_spec
disagreement
parameter error
The negative controls in tbl. 5 test package integrity and media contracts; they are not null findings about perception.
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4.9 Synthetic psychophysics model diagnostic
Figure 9: A narrow-range line plot shows deterministic model probability across duck_weight values beside the model identity,
temperature, no-training-data statement, and human-data boundary.
What this figure shows: A narrow-range line plot shows deterministic model probability across duck_weight values beside
the model identity, temperature, no-training-data statement, and human-data boundary. The hand-specified feature observer
compares duck_weight variants with a fixed canonical reference. Its probability trace is computed analytically from serialized
features, weights, and temperature; source data output/data/synthetic_psychophysics.json records model ID/version, reference
and comparison digests, seed, calibration, training_data=none , and human_data=false . The y-axis is deliberately a narrow
model-output range rather than a human psychometric scale. Controls: duck_weight comparison against fixed reference;
serialized feature weights and temperature; seed s=0. Objective facts: model probability and score delta on the displayed
model-output scale; canonical stimulus digests; human_data=false; training_data=none. Claim level: synthetic_model_output.
Source data: output/data/synthetic_psychophysics.json (SHA-256 digest recorded in the figure registry). Evidence lineage:
observer:preregistered_estimands. Limitations: The model is hand-specified, has no training data, has not been calibrated against
observers, and does not estimate a human threshold or effect size. Its probabilities are model outputs, not participant responses or
a psychometric function. Boundary: This diagnostic tests deterministic orchestration and metamorphic input-output behavior only;
empirical psychophysics remains future work.
The diagnostic fig. 9 evaluates a fully serialized, hand-specified feature observer against a fixed canonical reference while varying
duck_weight. Its logistic probabilities are model outputs generated from explicit features, weights, temperature, and seed; they are
not a pretrained vision-model score, a human psychometric function, an assumed human effect size, or participant data. A future
human study would require a preregistered task, calibrated display and playback, consented participants, exclusion and missingness
rules, and an analysis contract before any observer claim could be made.
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5 Experimental and Computational Setup
Core generation uses Python, NumPy, Pillow, and the standard library. The default seed is 0 and generation is offline. PNG,
GIF, W A V, and NPZ are available without ffmpeg; MP4 and muxed audiovisual output require both ffmpeg and ffprobe. Optional
capabilities fail explicitly rather than silently changing the requested artifact.
The deterministic validation suite executes real NumPy synthesis and real temporary-file media round trips. It checks finite normalized
arrays, typed parameter boundaries, canonical hashes, dimensions, channel layouts, sample rates, frame counts, timebases, duration
agreement, synchronization offsets, decoded stream facts, and registry/evidence consistency.
This is a software-validation protocol, not a psychophysical experiment. The tests establish repeatability under the declared software
and dependency conditions; they do not establish replicability of an observer effect under a new display, playback chain, population,
or task. That distinction is why the release reports both the exact environment contract and the missing observer evidence.
The publication workflow writes 15 scientific PNG figures plus a separately provenance-recorded editorial cover, machine-readable
source-data sidecars, a typed figure registry, 10 markdown tables, and a publication report. Each generated figure records its source
function, seed, caption, alt text, claim level, and SHA-256 digest. Generated files are disposable; the tracked source is the generator
and its tests.
The registry and cover report are independently revalidated after generation. The registry validator rechecks code-owned captions,
evidence namespaces, source-data hashes, and figure hashes. The cover validator rechecks the editorial source digest, portrait
dimensions, variant set, and delivery hashes. These checks prevent a successfully rendered image from becoming an unexamined
publication claim.
The observer harness is a data-free design layer. It creates reproducibly randomized trial records, exports typed study plans, generates
synthetic responses for contract tests, and exposes model templates. It does not collect or ship participant data. The publication
atlas additionally runs duckrabbit.synthetic.feature_observer , an explicitly hand-specified feature model with no training corpus.
Its canonical pairwise probabilities are serialized as model output and are useful for end-to-end orchestration tests; they are not a
real vision-model estimate, a psychometric function, or an observer result. Human sensitivity is deferred until a calibrated, consented,
preregistered study supplies response data and an analysis contract.
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6 Reproducibility and Provenance
The reproducibility contract is:
1. construct the same frozen parameter dataclass;
2. use the same generator ID and the same deterministic seed;
3. compare the canonical artifact digest;
4. record the parameter schema, typed parameters, taxonomy, evidence boundary, canonical byte serialization, objective metrics,
and encoding request;
5. if a file is written, inspect the decoded media and compare dimensions, channels, rates, frame counts, durations, timing offsets,
and encoded hash;
6. retain the v2 manifest and source-data sidecars with the generated figure or table.
The contract is deliberately stronger than “the file can be downloaded. ” Research-software guidance treats versioned code, executable
procedures, dependencies, and retained inputs as part of the reproducible object [ Sandve et al. , 2013, Wilson et al. , 2014]. F AIR
guidance further asks that digital research objects be findable, accessible, interoperable, and reusable, while noting that software has
lifecycle and maintenance constraints that are not identical to those of static data [ Wilkinson et al. , 2016, Lamprecht et al. , 2020].
DuckRabbit operationalizes those principles with typed metadata, deterministic hashes, source-data sidecars, explicit licenses, and
release gates rather than by implying that a generated media file is a complete scientific replication.
The package reports implemented, planned, input_required as its catalog status vocabulary and currently covers audio_visual,
auditory, visual. The evidence layer contains 18 entry records backed by 36 source records. The publication workflow produces 15
figures and 10 tables from the live registry.
The intended public software record is the DuckRabbit public GitHub repository , with Daniel Ari Friedman of the Active Inference
Institute as author. Until that public repository and a DOI are created, the private sidecar remains the release source and the DOI
field correctly remains forthcoming.
The canonical buffer is the primary identity of a stimulus. Encoded files are delivery artifacts with format-specific tolerances. The
observer protocol is a separate evidence layer: a manifest can prove what was presented without proving what an observer experienced.
Synthetic psychophysics is a third, deliberately bounded object. The model identity, version, feature schema, weights, temperature,
seed, calibration statement, canonical reference/comparison digests, and human_data=false flag are retained in output/data/syntheti
c_psychophysics.json. Re-running this diagnostic checks deterministic model orchestration and stimulus-feature sensitivity; it does
not estimate a human observer or replace empirical psychophysics.
The v2 verifier is a relational check rather than a field-presence check. It rejects summaries whose dimensions, dtype, byte count, rates,
duration, signal range, frame deltas, or signed audiovisual offset disagree. Public manifest and inspection mappings are recursively
frozen after validation, and rational frame rates are reduced before entering the clock contract. The read-only capability probe records
whether Pillow, NumPy, ffmpeg, or ffprobe are available in the current environment; unavailable delivery paths remain explicit rather
than being silently downgraded.
The minimal regeneration commands are:
uv run pytest -q --cov=src/duckrabbit --cov-fail-under=90
uv run python scripts/generate_publication_outputs.py
uv run python scripts/z_generate_manuscript_variables.py
6.1 Data availability and software citation
No participant records, fitted observer coefficients, or human psychophysics are bundled. The synthetic diagnostic is explicitly
model output with human_data=false and training_data=none . Reuse should cite Daniel Ari Friedman and the release metadata
in CITATION.cff, together with the source-specific scholarship in references.bib. Software-citation principles recommend citing the
software object itself, with enough version and identity information to distinguish one release from another [ Smith et al. , 2016]. The
DOI field remains empty with status forthcoming until a real DOI is minted; the release must not manufacture a resolver URL before
that identifier exists.
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7 Scope, Related Work, and Limitations
7.1 Scope and epistemic boundary
DuckRabbit is a typed, reproducible stimulus-construction platform. Its unit of work is an immutable request that yields a canonical
image, audio buffer, video sequence, or audiovisual timeline, together with objective measurements and provenance. It is not an
exhaustive ontology of all illusions, a perceptual theory, a participant database, or a substitute for a controlled psychophysics
experiment. The live registry is therefore a deliberately bounded catalog: it enumerates the families for which this release has both
a generator contract and a stated evidence boundary. Appendix A gives the complete current matrix; the absence of a family from
that matrix is not a claim that the family is unimportant or unsupported in the wider literature.
The central distinction is between a construction and an observation. A DuckRabbit generator can establish the dimensions, pixel
values, sample values, frequency components, frame clock, declared synchronization offset, encoded hash, and decoded media facts of
its output. It cannot, from those facts alone, establish what a person sees, hears, counts, localizes, groups, or reports. Every figure
caption, evidence record, and claim-ledger entry preserves this boundary. In particular, a literature citation establishes a source-
supported statement about a stimulus family or result under that source’s conditions; it does not certify pixel- or task-identical
replication by a DuckRabbit artifact.
The historical foundation is intentionally worldwide and layered. The package does not present a single invention narrative: it places
ancient Greek, medieval Arabic, classical Chinese, and early-modern European sources beside nineteenth-century psychophysics and
modern experimental work. This is a scholarly orientation for separating physical construction, interpretation, and observer evidence;
it is not a claim that the current source set exhausts the visual, auditory, or perceptual traditions of any region.
7.2 Visual families
The modern label “visual illusion” sits on a longer experimental history than the package’s contemporary review sources alone suggest.
Oppel’s mid-century catalogue of geometrical-optical illusions is now accessible with translation and commentary [ Wade et al. , 2017],
and the primary nineteenth-century records include Zöllner’s account of crossing-line distortions and Müller-Lyer’s report of the
arrow-wing configuration [ Zöllner, 1860, Müller-Lyer, 1889]. These sources are treated as historical anchors, not as evidence that a
present-day raster is identical to an original plate or that its observer effect is invariant across conditions.
Gregory’s classification is useful as a historical and conceptual orientation, but it is not a universally agreed ontology. DuckRabbit
consequently stores visual modality, mechanism, perceptual signature, stimulus requirements, and evidence status as separate facets
rather than treating a single label as an explanation [ Gregory, 1997]. The visual atlas covers the implemented families currently
registered in the package: ambiguous figure, contrast, apparent motion, Müller-Lyer, Poggendorff, Ponzo, Kanizsa-type subjective
contour, Ebbinghaus contextual size, and Zöllner/Judd orientation-related geometry. “Coverage” here means one deterministic
representative per live entry, not a claim that one raster captures the historical stimulus space.
The duck/rabbit construction is an explicit example of why that distinction matters. Brugger’s historical analysis discusses variation
among figure variants and observers; DuckRabbit therefore exposes a blend parameter and labels its output as a construction rather
than promising a fixed alternation rate or universal bistability [ Brugger, 1999]. The Müller-Lyer entry uses typed arrow geometry. Its
engineering form is compatible with a family whose image statistics have been analyzed as potentially informative about image-source
relationships, but the implementation does not adjudicate that account or infer a perceived-length report [ Müller-Lyer, 1889, Howe
and Purves , 2005].
The Poggendorff generator makes the occluding geometry and virtual-line orientation explicit. This is appropriate to a literature
in which orientation estimation and filtering accounts are theoretically relevant, while avoiding the stronger claim that a particular
raster reproduces a published bias without the same observers, viewing conditions, and response task [ Morgan, 1999]. The Ponzo
construction is similarly bounded: the converging context and test bars are deterministic, whereas the literature contains multiple
explanations of Ponzo-like effects rather than one settled mechanism [ Fisher, 1967, Yildiz et al. , 2022].
Kanizsa-style subjective contours are represented as an illusory-contour construction with explicit inducer geometry. The historical
account motivates the family label, while modern reviews place contour completion within a wider literature on grouping, figure-
ground organization, attention, and neural mechanisms [ Kanizsa, 1976, Wagemans et al. , 2012]. Neither source licenses a claim
that the generated mask produces a uniform contour percept across observers. The Ebbinghaus entry controls target and surround
geometry; classic work demonstrates that judged size depends on context, contour, and comparison conditions, while later work shows
that motion and other parameters can alter the effect [ Weintraub, 1979, Mruczek et al. , 2015]. DuckRabbit’s static default is therefore
an engineering baseline rather than a task-identical replication. Zöllner/Judd geometry is likewise retained as a source-linked line
arrangement. Zöllner’s 1860 report supplies the historical primary anchor, while later work supplies a modern analysis of spatial
filtering [ Zöllner, 1860, Earle and Maskell , 1995]. Its typed line lengths and orientations make the spatial stimulus auditable, while
orientation judgments remain outside the package contract.
Finally, apparent motion is included in the visual coverage panel because its defining engineering object is temporal succession, not
merely a static pattern. The package verifies frame order, frame rate, timestamps, and frame-to-frame differences. Wertheimer’s
foundational work and Sekuler’s later analysis motivate the family distinction; neither source turns a generated frame strip into a
universal report of motion [ Wertheimer, 1912, Sekuler, 1996].
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7.3 Auditory families
The auditory catalog separates harmonic construction, spectral completion, pitch-class context, dichotic channel assignment, and
continuity/masking. A Shepard-like signal is represented through additive partials and explicit envelopes, following a historical
literature of tone psychology and later work on assimilation to an internalized musical scale [ Stumpf, 1883, Shepard and Jordan ,
1984]. The canonical buffer exposes sample rate, amplitude bounds, channel count, partial frequencies, and envelope parameters. It
does not determine a listener’s perceived pitch height or direction.
The missing-fundamental construction removes a low component while retaining harmonically related partials. This makes the
spectral condition reproducible; the associated pitch interpretation remains a listener-level question [ Zatorre, 2005]. Tritone and
octave entries preserve channel structure, phase, frequency relationships, and timing in typed parameters. Deutsch’s foundational
accounts and Repp’s analysis of spectral-envelope and context effects motivate the evidence records, while also making listener and
context dependence central limitations [ Deutsch, 1986, Repp, 1997, Deutsch, 1974].
Auditory continuity is represented as an interrupted target with a typed masker and gap. Warren’s classic perceptual-restoration
result and Riecke and colleagues’ separation of sensory and decisional contributions justify the family’s inclusion, but a generated
masker is not evidence that a listener will report an uninterrupted sound [ Warren, 1970, Riecke et al., 2011]. The audio atlas therefore
reports RMS, peak, spectral centroid, bandwidth, channel layout, and exact sample-level provenance—not continuity, pitch, or stream
judgments.
7.4 Audiovisual and temporal binding families
Audiovisual constructions require a shared clock and an explicit sign convention for offsets. The sound-induced-flash entry creates
a typed visual event and one or more audio events; the evidence record links it to the primary demonstration and to a review of
the broader literature [ Shams et al. , 2000, Hirst et al. , 2020]. The package can verify event timestamps, sample/frame clocks, and
declared offsets. It does not infer a reported flash count, and it does not assume that the same temporal window applies across
displays, headphones, latencies, or observers.
The spatial ventriloquist construction treats spatial discrepancy as a parameter and records the channel and display requirements.
Reviews describe the ventriloquist illusion as a tool for studying multisensory processing, but the review’s scope is not a license
to claim spatial capture from a file alone [ Bruns, 2019]. More general audiovisual accounts describe integration and segregation
as a causal-inference problem shaped by temporal regularities and signal reliability [ Noppeney and Lee , 2018]. That framework
clarifies why a declared offset is an experimental input, not an observer-level outcome. Temporal ventriloquism receives a separate
temporal-binding signature rather than being collapsed into spatial capture. Vroomen and de Gelder manipulated sound–flash timing
in a flash-lag task and reported timing-dependent changes under those experimental conditions; Hartcher-O’Brien and Alais studied
temporal ventriloquism in a purely temporal context [ Vroomen and de Gelder , 2004, Hartcher-O’Brien and Alais , 2011]. DuckRabbit
implements the stimulus-side timing contract and leaves the observer-side temporal-recalibration estimate to a future study.
McGurk remains input_required. The classic speech study motivates the family, but a lawful and reproducible implementation
requires checksummed speech and video fixtures, licensing or consent records, a precise preprocessing contract, and an ethical
validation protocol [ McGurk and MacDonald , 1976]. Cataloguing the gap is more informative than silently substituting an unrelated
synthetic voice or claiming that a generic audiovisual mismatch is a McGurk replication.
7.5 From literature to engineering contract
For each entry, the evidence matrix records a source role, exact source-supported claim, engineering basis, limitation, and audit status.
The roles distinguish primary demonstration, review or synthesis, theoretical account, engineering basis, limitation, and input gap.
This prevents three common category errors: treating a theory as settled mechanism, treating a review as validation of new code,
and treating a generator’s deterministic output as a participant result.
The package’s literature fidelity is therefore best described as “family-linked, parameterized engineering construction. ” Some defaults
are historically motivated; none should be read as a claim of pixel identity unless that identity is separately established. The checked-in
scholarship snapshot provides offline structural validation, including citation-key and DOI/URL format checks. The explicit network
audit adds resolver observations and metadata matching; reachability alone is not treated as bibliographic verification. This is a
reproducible evidence boundary, not a claim that every source is equally accessible or that theoretical disputes have been resolved.
7.6 Limitations and future observer work
The package does not claim clinical validity, universal effect sizes, cross-cultural invariance, perceptual equivalence across displays or
headphones, or observer-level truth from objective media metrics. Playback level, gamma and display calibration, viewing distance,
refresh rate, stereo separation, room acoustics, audio transducer response, attention, expectation, language, expertise, and task can
all matter. Codec behavior and device latency can introduce additional differences even when decoded media facts match within the
declared tolerance.
The synthetic observer diagnostic is intentionally not a substitute for a real vision model or human data. It is a serialized, hand-
specified feature function with training_data=none, calibration = analytic , and human_data=false; its metamorphic and sensitivity
checks test orchestration, not visual consciousness or human discrimination. A future observer study must pre-register the response
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scale, reference condition, estimand, exclusions, missing-data rule, randomization seed, display and playback controls, and uncertainty
procedure. It must also report the participant and item sampling frame rather than importing a model-output probability as an
assumed effect size. The observer harness is consequently study-ready scaffolding, not a result set.
No participant data are bundled with DuckRabbit. The data-availability boundary is intentional: canonical artifacts, encoded
fixtures where lawful, source-data sidecars, and deterministic synthetic diagnostics are software outputs; observer outcomes require
separately governed data collection. The package is authored by Daniel Ari Friedman and is DOI-forthcoming; release metadata and
software-citation guidance are generated from the same identity contract as the manuscript.
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8 Publication Atlas, Caption Contract, and Scholarship Audit
The publication layer is generated from the same typed package state as the stimuli. It contains 15 scientific figures, 10 machine-
readable tables, and a separately provenance-recorded editorial cover. The cover is an illustration of the project’s subject and methods
aesthetic; it is not a stimulus, a participant result, or evidence of a perceptual effect.
8.1 Claim-level visualization
Figure 10: Four numbered boxes separate canonical stimulus, physical metric, encoded media, and observer hypothesis, with a
boundary rule stating that observer effects require a separate study.
What this figure shows: Four numbered boxes separate canonical stimulus, physical metric, encoded media, and observer hypothesis,
with a boundary rule stating that observer effects require a separate study. The four-stage boundary distinguishes what DuckRab-
bit can establish directly—canonical stimulus identity, physical/media metrics, and decoded encoded-media facts—from a future
observer hypothesis. Source data output/data/claim_boundary.json records the stage definitions and boundary rule; the arrows
describe increasing evidential requirements, not an inference that one stage establishes the next. Controls: claim levels in the
taxonomy and manifest; seed not applicable to the explanatory diagram. Objective facts: no unit-bearing objective quantity is
applicable; stage definitions and evidence boundaries are preserved in the sidecar. Claim level: source_supported. Source data: out-
put/data/claim_boundary.json (SHA-256 digest recorded in the figure registry). Evidence lineage: formalism:eq:observer_estimand,
formalism:eq:canonical_digest. Limitations: The diagram is a documentation contract and does not replace a preregistered observer
study or empirical data. Boundary: A deterministic artifact can support a future hypothesis but cannot supply the observer data
required to test it.
The claim boundary in fig. 10 is a typed epistemic interface. A canonical digest identifies a deterministic buffer; objective metrics
identify properties of that buffer; encoded-media verification identifies facts of the delivered file. A future observer hypothesis is a
different object with its own protocol, estimand, and uncertainty interval.
8.2 Scholarship map and lineage
What this figure shows: Rows map catalog entries to source tiers, exact supported claims, engineering bases, limitations, and
implementation status. The map links every catalog entry to its primary, review, and theory records, then preserves the exact source-
supported claim, engineering departure, limitation, and implementation status. Source data output/data/scholarship_map.json are
generated from the checked-in evidence matrix; a source record supports only the statement written in that record and does not
certify pixel- or task-identical replication. Controls: checked-in evidence matrix; source roles and entry statuses; audit date recorded
in data/evidence_matrix.json. Objective facts: one evidence row per catalog entry (18 entries); source-tier counts, exact claim
text, engineering basis, limitation, and gap status. Claim level: source_supported. Source data: output/data/scholarship_map.json
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Figure 11: Rows map catalog entries to source tiers, exact supported claims, engineering bases, limitations, and implementation
status.
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(SHA-256 digest recorded in the figure registry). Evidence lineage: gregory1997visual, brugger1999duckrabbit, yildiz2022ponzo,
hirst2020sound, bruns2019ventriloquist. Limitations: The offline snapshot validates citation and lineage structure; live resolver
status is a separate audit, and classifications can remain contested. Boundary: Scholarship coverage bounds the package’s evidence
record and does not establish that any generated stimulus produces a universal percept.
The source map fig. 11 and tbl. 7 make five distinctions explicit: a primary demonstration, a review, a theoretical account, DuckRab-
bit’s engineering basis, and an evidence limitation. Brugger’s duck/rabbit study documents variation across figure variants and
observers; this supports a careful ambiguity-family record, not a universal bistability claim [ Brugger, 1999]. Yildiz et al. review
competing explanations of Ponzo-like illusions, so the catalog retains both a geometric construction and an unresolved theoretical
boundary [ Yildiz et al. , 2022]. Repp’s tritone analysis likewise motivates listener- and context-sensitive limitations [ Repp, 1997].
The audit also treats software and its metadata as part of the scholarly record. F AIR guidance emphasizes machine-actionable
provenance and reuse, and software-citation principles emphasize crediting an identifiable version rather than citing an undifferentiated
project name [ Wilkinson et al. , 2016, Smith et al. , 2016]. Accordingly, the release includes CITATION.cff, CodeMeta, Zenodo metadata,
versioned manifests, source-data sidecars, and resolver-linked bibliography entries. These improve discoverability and attribution; they
do not increase the evidential level of any perceptual claim.
The intended public software identity is explicit: DuckRabbit will be released at the DuckRabbit public GitHub repository under the
authorship of Daniel Ari Friedman, Active Inference Institute. The repository URL identifies the future citable software object; it is
not a claim that the private sidecar has already been publicly mirrored.
8.3 Formal traceability and objective metrics
What this figure shows: Rows connect equation labels to their mathematical definition, implementation paths, tests, figure
labels, and claim levels. The traceability registry connects the nine numbered equations to symbols, implementation modules,
tests, and registered figures. Source data output/data/formalism_traceability.json is the machine-readable crosswalk used by
the manuscript; it demonstrates contract coverage and test linkage without converting formal notation into empirical evidence.
Controls: formalism registry version; seed not applicable to the traceability diagram. Objective facts: nine equation records
with implementation, test, figure, and claim-level fields; no unit-bearing measurement is plotted. Claim level: physical_metric.
Source data: output/data/formalism_traceability.json (SHA-256 digest recorded in the figure registry). Evidence lineage: for-
malism:eq:canonical_digest, formalism:eq:clock_definition, formalism:eq:objective_statistics. Limitations: Traceability records
documentation and verification scope; it does not establish the truth of an observer-level theory. Boundary: A linked equation and
test can show an implemented contract, not a validated perceptual law.
The formalism registry fig. 12 links equations eqns. 1, 2, 4, 5, 3, 6, 7, 8, 9 to implementation modules, tests, and figures. The
contract is intentionally auditable: equation labels point to code-owned records, while empirical claims remain outside the generator’s
authority.
What this figure shows: Four artifact cards list image, audio, video, and audiovisual metrics with units, computation provenance,
and claim level. The dashboard presents representative measurements from image, audio, video, and audiovisual canonical
artifacts. Source data output/data/metrics_dashboard.json retains metric name, value, unit, computation version, tolerance,
claim level, and canonical digest; luminance is normalized, amplitude is normalized, spectra are in hertz, frame differences
are normalized pixel differences, and synchronization is in milliseconds. Controls: default canonical artifacts; metric compu-
tation version and tolerance recorded in the source-data sidecar; seed s=0. Objective facts: finite objective values with units:
normalized luminance/amplitude, Hz, normalized pixel difference, ms, counts, and durations. Claim level: physical_metric.
Source data: output/data/metrics_dashboard.json (SHA-256 digest recorded in the figure registry). Evidence lineage: formal-
ism:eq:objective_statistics, formalism:eq:temporal_spectral_metrics. Limitations: Metrics are media properties and do not encode
pitch, size, motion, localization, binding, or other observer interpretations. Boundary: Metric reproducibility is a package property;
interpretation as perception requires a separate observer design and data.
The metrics dashboard fig. 13 reports units, computation version, and canonical digests. Luminance statistics are normalized raster
properties; RMS and peak are normalized-amplitude properties; spectral values are in Hz; frame deltas are normalized pixel differences;
and synchronization offsets are in milliseconds. None is a psychophysical score.
What this figure shows: Horizontal interval markers show typed domains for dimensions, luminance, levels, frequency, sampling,
frame rate, synchronization, and spatial discrepancy. The domain map shows the validated ranges for dimensions, luminance,
grayscale and quantization levels, frequency, sampling rate, frame rate, synchronization offset, and spatial discrepancy. Source data
output/data/parameter_domains.json records the type name, unit, interval, and engineering role; intervals prevent malformed media
and are not proposed as sensitivity thresholds. Controls: parameter schema version and validated scalar domains; seed not applicable
to the domain diagram. Objective facts: dimensionless, pixel, level, Hz, samples/s, frames/s, ms, and normalized spatial units as listed
per parameter. Claim level: canonical_stimulus. Source data: output/data/parameter_domains.json (SHA-256 digest recorded in
the figure registry). Evidence lineage: formalism:eq:typed_request. Limitations: The intervals are software validation bounds and
do not encode safe listening levels, display limits, or psychophysical thresholds. Boundary: A valid parameter is a reproducible
construction request, not evidence that the requested value is perceptually effective.
The domain map fig. 14 is a validation visualization. Bounds are chosen to prevent malformed media and unsafe encodings, not to
predict a viewer, listener, or participant’s sensitivity.
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Figure 12: Rows connect equation labels to their mathematical definition, implementation paths, tests, figure labels, and claim levels.
24

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Figure 13: Four artifact cards list image, audio, video, and audiovisual metrics with units, computation provenance, and claim level.
25

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Figure 14: Horizontal interval markers show typed domains for dimensions, luminance, levels, frequency, sampling, frame rate,
synchronization, and spatial discrepancy.
26

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8.4 Observer-design boundary
Figure 15: A flow diagram connects trial identity, randomization, stimulus manifest, response, aggregate estimand, and analysis-model
templates, with a synthetic-only boundary.
What this figure shows: A flow diagram connects trial identity, randomization, stimulus manifest, response, aggregate estimand,
and analysis-model templates, with a synthetic-only boundary. The study-ready scaffold moves from pseudonymous trial iden-
tity and deterministic randomization to a stimulus manifest and encoded-file hash, typed response or missingness, and a pre-
registered estimand. Source data output/data/observer_protocol.json records the study design, randomization seed, model tem-
plates, and synthetic-only status; no participant record is included. Controls: study design and deterministic randomization
seed recorded in the sidecar; synthetic response generation is separate from human data. Objective facts: trial counts, condi-
tion structure, estimand templates, response schemas, and model families; participant outcomes are not applicable. Claim level:
observer_hypothesis. Source data: output/data/observer_protocol.json (SHA-256 digest recorded in the figure registry). Evidence
lineage: observer:preregistered_estimands. Limitations: The scaffold specifies future data collection and analysis but supplies no
participant responses, fitted coefficients, power claim, or validated observer effect. Boundary: The protocol is ready for ethical and
preregistered extension, not evidence that the proposed effect exists.
The observer scaffold fig. 15 starts with a pseudonymous trial identity and deterministic randomization, binds the stimulus manifest
and encoded hash, records a typed response or missingness state, and ends at a preregistered estimand. The companion diagnostic
fig. 9 is a deterministic, hand-specified feature observer with training_data=none and human_data=false; it is not a pretrained vision
model, psychometric function, or participant result. Human psychophysics remains a future evidence layer requiring calibrated
playback, consent, preregistration, and observed responses.
8.5 Generated audit tables
27

## Page 29

Table 6: Code-owned caption, source-data, and accessibility audit.
Figure / claim level Source and evidence Controls and objective facts
Limitations, boundary, and
accessibility
fig:architecture; canonical
stimulus
output/data/architecture.json;
formalism:eq:typed request,
formalism:eq:canonical
generation,
formalism:eq:encoding
verification
Controls: typed request
q=(i,𝜃,s,e) with seed s=0;
default generator and
delivery-independent
canonicalization Objective: no
unit-bearing objective quantity
is applicable to this
architecture diagram; stage
identities and provenance
fields are recorded in the
sidecar
Limitations: The schematic
abstracts implementation
boundaries and does not
represent an observer study or
a causal theory of perception.
Boundary: The pipeline
verifies reproducible media
facts, not what a person
experiences. Accessibility:
Stage names, mathematical
symbols, and arrow direction
are printed directly; color is
redundant.
fig:catalog matrix; source
supported
output/data/catalog
matrix.json; gregory1997visual,
hirst2020sound,
bruns2019ventriloquist
Controls: live taxonomy
registry; evidence matrix
snapshot; seed not applicable
to the catalog diagram
Objective: 18 catalog rows;
categorical facets and statuses;
no observer-level quantity is
applicable
Limitations: Taxonomy facets
are engineering classifications
and remain provisional where
the literature supports
competing accounts.
Boundary: Catalog coverage is
bounded to this registered
package and does not
enumerate all known illusions.
Accessibility: Every status and
facet is written as text; color
only reinforces the printed
status.
fig:visual panel; canonical
stimulus
output/data/visual panel.json;
gregory1997visual,
brugger1999duckrabbit,
howe2005muller,
morgan1999poggendorff,
fisher1967ponzo,
yildiz2022ponzo,
kanizsa1976contours,
mruczek2015ebbinghaus,
earle1995zollner,
wertheimer1912motion,
sekuler1996wertheimer
Controls: one default typed
parameter object per
implemented visual entry; seed
s=0; dimensions, luminance
bounds, grayscale, and
quantization controls remain
in each generator schema;
temporal entries display their
first frame but retain sequence
metrics Objective: per tile:
mean and standard-deviation
relative luminance, unique
raster levels, and canonical
SHA-256 digest; temporal
entries additionally retain
frame count, frame rate, and
frame deltas; definitions and
units are in the source data
JSON
Limitations: The gallery is
complete for implemented
visual entries in this package,
not a complete survey of
visual illusions; literature
families, historical displays,
and DuckRabbit rasters are
not pixel-identical by default.
Viewing scale, display
calibration, viewing distance,
and observer conditions can
change the relevance of a
construction; the gallery does
not measure an observer’s
perceptual report. Boundary:
The figure establishes coverage
of the package’s implemented
visual constructions and their
deterministic raster facts. It
does not establish that any
viewer will perceive the named
signature, nor that the set is
exhaustive of the
visual-illusion literature.
Accessibility: Each tile is
labeled by stable illusion ID
and accompanied by printed
luminance, level-count, and
digest fields; color only
reinforces grouping and is not
required to identify a stimulus.
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Figure / claim level Source and evidence Controls and objective facts
Limitations, boundary, and
accessibility
fig:visual sweep; physical
metric
output/data/visual sweep.json;
brugger1999duckrabbit,
gregory1997visual
Controls: duck weight ∈
{0,.25,.5,.75,1};
grayscale=quantization ∈
{2,4,8,16,32}; seed s=0
Objective: 25 canonical
rasters; unique levels,
normalized mean luminance,
and effective dynamic range
per cell
Limitations: The grid is a
sensitivity of the construction
parameters, not a
psychophysical sensitivity
curve or a validated observer
effect. Boundary: The chosen
grid is an engineering sampling
of the parameter domain and
does not imply an optimal or
perceptually uniform spacing.
Accessibility: Row and column
labels state the parameter
values; numerical metrics and
units are available in the
sidecar.
fig:temporal sequence; physical
metric
output/data/temporal
sequence.json;
wertheimer1912motion,
sekuler1996wertheimer
Controls: visual.apparent
motion default typed
parameters; frame rate and
frame count from the
canonical sequence; seed s=0
Objective: timestamps in
seconds, frame rate in
frames/s, frame count, rational
timebase, and adjacent-frame
normalized pixel difference
Limitations: Frame succession
and frame deltas are physical
file properties; playback
timing, display persistence,
and motion reports require a
controlled observer task.
Boundary: The figure
documents temporal structure
rather than the presence,
direction, or strength of
perceived motion.
Accessibility: Frame index,
seconds, frames per second,
and normalized-difference
labels remain interpretable
without color.
fig:audio signals; physical
metric
output/data/audio
signals.json; shepard1984scale,
zatorre2005missing,
deutsch1986tritone,
repp1997tritone,
deutsch1974octave,
warren1970continuity,
riecke2011continuity
Controls: default typed audio
parameters; per-generator
channel layout and sample
rate; seed s=0; one-sided FFT
display with 48 sampled bins
Objective: RMS and peak in
normalized amplitude; spectral
centroid and bandwidth in Hz;
sample rate in samples/s;
channel layout and canonical
SHA-256 digest
Limitations: Playback level,
transducer response, dichotic
separation, masker design, and
listener judgments are external
to the canonical buffer.
Boundary: The figure
compares generated signal
properties and
literature-linked families; it
does not establish pitch,
continuity, or stream
organization for a listener.
Accessibility: Waveform,
spectral, amplitude, and
frequency labels are printed;
bar color is not the sole
encoding.
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Figure / claim level Source and evidence Controls and objective facts
Limitations, boundary, and
accessibility
fig:audiovisual timeline;
physical metric
output/data/audiovisual
timeline.json; shams2000sifi,
hirst2020sound,
vroomen2004temporal,
hartcherobrien2011temporal
Controls: audiovisual.sound
induced flash default shared
timeline; declared sync offset
ΔA V and spatial offset; seed
s=0 Objective: video
luminance and audio envelope
on normalized shared time;
ΔA V in ms; spatial
discrepancy in normalized
units; frame and sample clocks
in the sidecar
Limitations: Display refresh,
audio hardware, event latency,
and observer temporal binding
are not measured by this
figure. Boundary: A
shared-clock construction is
not evidence that observers
bind the events at the declared
or any other perceptual time.
Accessibility: The two
channels, time axis, signed
offset convention, and
normalized spatial discrepancy
are labeled in text.
fig:encoding verification;
encoded media
output/data/encoding
verification.json;
engineering:typed media
adapters
Controls: typed encoding
profile selected per artifact;
overwrite and backend
capability checks; seed
inherited from the stimulus
request Objective: format
availability and verification
scope are environment
observations; NPZ is exact
while other formats are
decoded and tolerance-checked
Limitations: Backend
availability, codec versions,
container metadata, and lossy
tolerances are
environment-dependent;
playback software can expose
additional behavior.
Boundary: A successful
encode or decode does not
validate an observer effect or
guarantee cross-device
perceptual equivalence.
Accessibility: Format, backend,
preserved fact, and verification
columns are textual and
remain usable without color.
fig:synthetic psychophysics;
synthetic model output
output/data/synthetic
psychophysics.json;
observer:preregistered
estimands
Controls: duck weight
comparison against fixed
reference; serialized feature
weights and temperature; seed
s=0 Objective: model
probability and score delta on
the displayed model-output
scale; canonical stimulus
digests; human data=false;
training data=none
Limitations: The model is
hand-specified, has no training
data, has not been calibrated
against observers, and does not
estimate a human threshold or
effect size. Its probabilities are
model outputs, not participant
responses or a psychometric
function. Boundary: This
diagnostic tests deterministic
orchestration and
metamorphic input-output
behavior only; empirical
psychophysics remains future
work. Accessibility: Model
scale, reference line, model
identity, and human data=false
are printed; color is not
needed to interpret the curve.
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Figure / claim level Source and evidence Controls and objective facts
Limitations, boundary, and
accessibility
fig:claim boundary; source
supported
output/data/claim
boundary.json;
formalism:eq:observer
estimand,
formalism:eq:canonical digest
Controls: claim levels in the
taxonomy and manifest; seed
not applicable to the
explanatory diagram
Objective: no unit-bearing
objective quantity is
applicable; stage definitions
and evidence boundaries are
preserved in the sidecar
Limitations: The diagram is a
documentation contract and
does not replace a
preregistered observer study or
empirical data. Boundary: A
deterministic artifact can
support a future hypothesis
but cannot supply the
observer data required to test
it. Accessibility: Each stage is
named, numbered, and
described in text; the
boundary rule is readable
without color.
fig:scholarship map; source
supported
output/data/scholarship
map.json; gregory1997visual,
brugger1999duckrabbit,
yildiz2022ponzo,
hirst2020sound,
bruns2019ventriloquist
Controls: checked-in evidence
matrix; source roles and entry
statuses; audit date recorded
in data/evidence matrix.json
Objective: one evidence row
per catalog entry (18 entries);
source-tier counts, exact claim
text, engineering basis,
limitation, and gap status
Limitations: The offline
snapshot validates citation and
lineage structure; live resolver
status is a separate audit, and
classifications can remain
contested. Boundary:
Scholarship coverage bounds
the package’s evidence record
and does not establish that
any generated stimulus
produces a universal percept.
Accessibility: Source roles,
claims, limitations, and
statuses are printed or
available in the sidecar; no
category is encoded by color
alone.
fig:formalism traceability;
physical metric
output/data/formalism
traceability.json;
formalism:eq:canonical digest,
formalism:eq:clock definition,
formalism:eq:objective
statistics
Controls: formalism registry
version; seed not applicable to
the traceability diagram
Objective: nine equation
records with implementation,
test, figure, and claim-level
fields; no unit-bearing
measurement is plotted
Limitations: Traceability
records documentation and
verification scope; it does not
establish the truth of an
observer-level theory.
Boundary: A linked equation
and test can show an
implemented contract, not a
validated perceptual law.
Accessibility: Equation labels,
code paths, tests, and figure
labels are written as text.
fig:metrics dashboard; physical
metric
output/data/metrics
dashboard.json;
formalism:eq:objective
statistics,
formalism:eq:temporal spectral
metrics
Controls: default canonical
artifacts; metric computation
version and tolerance recorded
in the source-data sidecar; seed
s=0 Objective: finite objective
values with units: normalized
luminance/amplitude, Hz,
normalized pixel difference,
ms, counts, and durations
Limitations: Metrics are
media properties and do not
encode pitch, size, motion,
localization, binding, or other
observer interpretations.
Boundary: Metric
reproducibility is a package
property; interpretation as
perception requires a separate
observer design and data.
Accessibility: Every numerical
value is paired with a printed
unit or an explicit
dimensionless definition.
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Figure / claim level Source and evidence Controls and objective facts
Limitations, boundary, and
accessibility
fig:parameter domains;
canonical stimulus
output/data/parameter
domains.json;
formalism:eq:typed request
Controls: parameter schema
version and validated scalar
domains; seed not applicable
to the domain diagram
Objective: dimensionless,
pixel, level, Hz, samples/s,
frames/s, ms, and normalized
spatial units as listed per
parameter
Limitations: The intervals are
software validation bounds
and do not encode safe
listening levels, display limits,
or psychophysical thresholds.
Boundary: A valid parameter
is a reproducible construction
request, not evidence that the
requested value is perceptually
effective. Accessibility: Type
names, endpoints, units, and
roles are printed; interval color
is redundant.
fig:observer protocol; observer
hypothesis
output/data/observer
protocol.json;
observer:preregistered
estimands
Controls: study design and
deterministic randomization
seed recorded in the sidecar;
synthetic response generation
is separate from human data
Objective: trial counts,
condition structure, estimand
templates, response schemas,
and model families; participant
outcomes are not applicable
Limitations: The scaffold
specifies future data collection
and analysis but supplies no
participant responses, fitted
coefficients, power claim, or
validated observer effect.
Boundary: The protocol is
ready for ethical and
preregistered extension, not
evidence that the proposed
effect exists. Accessibility:
Every protocol step and the
no-participant-data boundary
is stated in text; arrows and
labels remain legible without
color.
Table 7: Source-tiered evidence, DOI/URL verification, exact supported claims, engineering departures, limitations, and explicit
planned/input-required gaps.
Key Record and citations DOI and URL Verification
Supported claim /
engineering / limitation
gregory 1997 visual review; gregory 1997
visual
DOI: recorded; URL
host/path:
pubmed.ncbi.nlm.nih.gov
snapshot validated;
offline snapshot
A non-exhaustive
classification of visual
illusion families.
hirst 2020 sound review; hirst 2020 sound DOI: recorded; URL
host/path:
www.sciencedirect.com
snapshot validated;
offline snapshot
A review of
sound-induced flash
paradigms and
multisensory temporal
inference.
howe 2005 muller theory; howe 2005
muller
DOI: recorded; URL
host/path: doi.org
snapshot validated;
offline snapshot
A statistical
image-source account of
Müller-Lyer geometry.
morgan 1999
poggendorff
theory; morgan 1999
poggendorff
DOI: recorded; URL
host/path: doi.org
snapshot validated;
offline snapshot
A mechanistic account
of Poggendorff
orientation estimation.
fisher 1967 ponzo primary; fisher 1967
ponzo
DOI: recorded; URL
host/path:
www.nature.com
snapshot validated;
offline snapshot
A primary investigation
of identical targets
embedded in an angular
context.
kanizsa 1976 contours primary; kanizsa 1976
contours
DOI: recorded; URL
host/path:
pubmed.ncbi.nlm.nih.gov
snapshot validated;
offline snapshot
Canonical
illusory-contour inducer
arrangements.
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Key Record and citations DOI and URL Verification
Supported claim /
engineering / limitation
mruczek 2015
ebbinghaus
primary; mruczek 2015
ebbinghaus
DOI: recorded; URL
host/path:
pmc.ncbi.nlm.nih.gov
snapshot validated;
offline snapshot
Context-dependent size
judgments in
Ebbinghaus-family
stimuli.
wertheimer 1912 motion primary; wertheimer
1912 motion
DOI: not recorded;
URL host/path:
bibbase.org
snapshot validated;
offline snapshot
Foundational
apparent-motion
experiments using
successive spatial
events.
sekuler 1996 wertheimer review; sekuler 1996
wertheimer
DOI: recorded; URL
host/path:
journals.sagepub.com
snapshot validated;
offline snapshot
A review connecting
Wertheimer’s
successive-event
findings to later
apparent-motion
research and clarifying
their historical scope.
shepard 1984 scale primary; shepard 1984
scale
DOI: recorded; URL
host/path: doi.org
snapshot validated;
offline snapshot
Auditory scale and
pitch-class organization
in Shepard-like tones.
zatorre 2005 missing review; zatorre 2005
missing
DOI: recorded; URL
host/path: doi.org
snapshot validated;
offline snapshot
The
missing-fundamental
problem as a
pitch-inference
phenomenon.
deutsch 1986 tritone primary; deutsch 1986
tritone
DOI: recorded; URL
host/path:
online.ucpress.edu
snapshot validated;
offline snapshot
The tritone paradox
and dependence on
pitch-class context and
listener.
deutsch 1974 octave primary; deutsch 1974
octave
DOI: recorded; URL
host/path: doi.org
snapshot validated;
offline snapshot
Dichotic alternating
high/low tone
construction underlying
the octave illusion.
shams 2000 sifi primary; shams 2000 sifi DOI: recorded; URL
host/path: doi.org
snapshot validated;
offline snapshot
The one-flash/two-beep
sound-induced flash
contrast.
bruns 2019 ventriloquist review; bruns 2019
ventriloquist
DOI: recorded; URL
host/path:
pmc.ncbi.nlm.nih.gov
snapshot validated;
offline snapshot
Spatial audiovisual
capture and
multisensory integration
constraints.
vroomen 2004 temporal primary; vroomen 2004
temporal
DOI: recorded; URL
host/path:
pubmed.ncbi.nlm.nih.gov
snapshot validated;
offline snapshot
Sound timing can alter
the apparent temporal
structure of a visual
event.
mcgurk 1976 speech primary; mcgurk 1976
speech
DOI: recorded; URL
host/path: doi.org
snapshot validated;
offline snapshot
Speech-dependent
audiovisual categorical
integration, requiring
validated fixtures.
warren 1970 continuity primary; warren 1970
continuity
DOI: recorded; URL
host/path: doi.org
snapshot validated;
offline snapshot
Auditory
continuity/restoration
as a future calibrated
masker family.
brugger 1999
duckrabbit
primary; brugger 1999
duckrabbit
DOI: recorded; URL
host/path:
pubmed.ncbi.nlm.nih.gov
snapshot validated;
offline snapshot
Variation in
duck/rabbit ambiguity
across figure variants
and observers.
yildiz 2022 ponzo review; yildiz 2022
ponzo
DOI: recorded; URL
host/path:
pubmed.ncbi.nlm.nih.gov
snapshot validated;
offline snapshot
Competing depth-based
and non-depth-based
explanations of
Ponzo-like illusions.
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Key Record and citations DOI and URL Verification
Supported claim /
engineering / limitation
repp 1997 tritone primary; repp 1997
tritone
DOI: recorded; URL
host/path:
pubmed.ncbi.nlm.nih.gov
snapshot validated;
offline snapshot
Listener- and
context-dependent
effects of spectral
envelope and pitch-class
structure in tritone
judgments.
hartcherobrien 2011
temporal
primary; hartcherobrien
2011 temporal
DOI: recorded; URL
host/path:
pubmed.ncbi.nlm.nih.gov
snapshot validated;
offline snapshot
Audiovisual timing can
shift temporal
judgments in a purely
temporal context
without spatial
grounding.
earle 1995 zollner primary; earle 1995
zollner
DOI: recorded; URL
host/path:
journals.sagepub.com
snapshot validated;
offline snapshot
Crossing oblique and
long-line geometry used
to measure orientation
interactions in the
Zöllner family.
zoellner 1860
pseudoscopy
primary; zoellner 1860
pseudoscopy
DOI: recorded; URL
host/path:
onlinelibrary.wiley.com
snapshot validated;
offline snapshot
The nineteenth-century
primary description of
the crossing-line
orientation family later
known as the Zöllner
illusion.
riecke 2011 continuity primary; riecke 2011
continuity
DOI: recorded; URL
host/path: doi.org
snapshot validated;
offline snapshot
Interrupted sounds with
masking context and
the separation of
sensory and decisional
contributions.
wagemans 2012 gestalt review; wagemans 2012
gestalt
DOI: recorded; URL
host/path:
pubmed.ncbi.nlm.nih.gov
snapshot validated;
offline snapshot
Contemporary
perceptual-grouping,
contour-completion,
and figure-ground
accounts relevant to
Kanizsa-type
constructions.
weintraub 1979
ebbinghaus
primary; weintraub
1979 ebbinghaus
DOI: recorded; URL
host/path:
pubmed.ncbi.nlm.nih.gov
snapshot validated;
offline snapshot
A classic contextual-size
experiment varying
surround geometry and
comparison conditions
in Ebbinghaus-family
displays.
noppeney 2018 causal review; noppeney 2018
causal
DOI: recorded; URL
host/path: doi.org
snapshot validated;
offline snapshot
Causal-inference and
temporal-prediction
accounts of audiovisual
integration and
segregation.
alhazen 1989 optics primary; alhazen 1989
optics
DOI: not recorded;
URL host/path:
www.cca.qc.ca
snapshot validated;
offline snapshot
The English translation
and commentary
preserves Ibn
al-Haytham’s
eleventh-century Arabic
optics as a historical
source on direct vision
and geometrical image
formation.
34

## Page 36

Key Record and citations DOI and URL Verification
Supported claim /
engineering / limitation
mozi 2023 canons review; mozi 2023
canons
DOI: recorded; URL
host/path:
link.springer.com
snapshot validated;
offline snapshot
A modern translation
and commentary
documents Mohist
Canon sections on
knowledge, optics, and
mechanics, providing a
Chinese Warring
States-period context
for early technical
reasoning about vision.
ptolemy 1996 optics primary; ptolemy 1996
optics
DOI: not recorded;
URL host/path:
sites.dlib.nyu.edu
snapshot validated;
offline snapshot
The scholarly
translation makes
Ptolemy’s
second-century Optics
available as an early
work on visual
perception and
mathematical visual
theory.
berkeley 1709 vision primary; berkeley 1709
vision
DOI: not recorded;
URL host/path:
www.maths.tcd.ie
snapshot validated;
offline snapshot
Berkeley’s 1709 essay
treats visual distance
and space as mediated
by learned associations
rather than as a simple
direct readout of visual
geometry.
kircher 1646 light primary; kircher 1646
light
DOI: not recorded;
URL host/path:
collections.st-
andrews.ac.uk
snapshot validated;
offline snapshot
The digitized record
anchors Kircher’s 1646
Ars magna lucis et
umbrae as an
early-modern work on
light, shadow, and
optical display.
molyneux 2020 problem review; molyneux 2020
problem
DOI: not recorded;
URL host/path:
plato.stanford.edu
snapshot validated;
offline snapshot
The historical account
documents Molyneux’s
1688 question
separating tactile
learning from visual
recognition and its long
cross-sensory afterlife.
cheselden 1728 sight primary; cheselden 1728
sight
DOI: not recorded;
URL host/path:
archive.org
snapshot validated;
offline snapshot
The digitized
Philosophical
Transactions record
preserves Cheselden’s
1728 case report as a
historical observation
relevant to visual access
and the separation of
observer evidence from
stimulus description.
dai 2015 chinesescience review; dai 2015
chinesescience
DOI: recorded; URL
host/path:
link.springer.com
snapshot validated;
offline snapshot
A history of Chinese
science and technology
surveys ancient Chinese
physics and records
optical phenomena as
part of a non-European
history of visual science.
35

## Page 37

Key Record and citations DOI and URL Verification
Supported claim /
engineering / limitation
entry / visual.duck
rabbit
engineering / limitation
/ gap; brugger 1999
duckrabbit; gregory
1997 visual
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The entry instantiates a
controllable
ambiguous-figure
stimulus family.
Engineering basis:
Parameterized
ambiguous silhouette;
not a pixel-identical
reproduction of a
historical plate.
Limitation: The
generator verifies
geometry and
luminance, not bistable
reports. Missing
contract: none
entry /
visual.simultaneous
contrast
engineering / limitation
/ gap; gregory 1997
visual
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The physical center
patches are matched
while surround
luminance differs.
Engineering basis:
Equal central patches
on unequal luminance
surrounds. Limitation:
Display calibration and
observer adaptation are
not modeled. Missing
contract: none
entry / visual.apparent
motion
engineering / limitation
/ gap; wertheimer 1912
motion; sekuler 1996
wertheimer
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The sequence contains
controlled successive
spatial events.
Engineering basis:
Alternating rectangular
masks at a fixed
rational frame rate.
Limitation: The artifact
establishes temporal
succession, not
perceived motion.
Missing contract: none
entry / audio.shepard
tone
engineering / limitation
/ gap; shepard 1984
scale
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The audio contains
octave-related partials
with controlled sweep
parameters.
Engineering basis:
Additive octave-spaced
partials with a
deterministic envelope.
Limitation: Playback
transducers and listener
pitch judgments are
external. Missing
contract: none
36

## Page 38

Key Record and citations DOI and URL Verification
Supported claim /
engineering / limitation
entry / audio.missing
fundamental
engineering / limitation
/ gap; zatorre 2005
missing
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The nominal
fundamental component
is absent from the
canonical spectrum.
Engineering basis:
Harmonic components
are synthesized while
the nominal
fundamental is omitted.
Limitation: Pitch
completion is an
observer-level inference.
Missing contract: none
entry /
audiovisual.sound
induced flash
engineering / limitation
/ gap; shams 2000 sifi;
hirst 2020 sound
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The declared beep/flash
event counts and offsets
are physically encoded.
Engineering basis: One
flash paired with one or
two timed beeps on a
shared clock.
Limitation: The
stimulus does not
establish a reported
flash count. Missing
contract: none
entry / audiovi-
sual.ventriloquist
engineering / limitation
/ gap; bruns 2019
ventriloquist; noppeney
2018 causal
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The audio and visual
channels carry a
declared spatial
discrepancy.
Engineering basis:
Stereo panning and
visual displacement
encode a spatial
discrepancy. Limitation:
Perceived localization
depends on room,
headphones, display,
and observer. Missing
contract: none
entry / visual.muller
lyer
engineering / limitation
/ gap; gregory 1997
visual; howe 2005 muller
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The two bar lengths are
equal in the canonical
raster while wing
geometry varies.
Engineering basis:
Equal bars with
controlled arrow-wing
geometry. Limitation:
The chosen normalized
geometry is one
engineering variant.
Missing contract: none
37

## Page 39

Key Record and citations DOI and URL Verification
Supported claim /
engineering / limitation
entry /
visual.poggendorff
engineering / limitation
/ gap; gregory 1997
visual; morgan 1999
poggendorff
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The occluder and
diagonal continuation
are generated from
explicit geometry.
Engineering basis: A
diagonal continuation is
separated by a
rectangular occluder.
Limitation: Alignment
judgments and
orientation filters are
not measured. Missing
contract: none
entry / visual.ponzo engineering / limitation
/ gap; fisher 1967 ponzo;
yildiz 2022 ponzo
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
Target bars are
physically equal and
rails converge toward a
vanishing region.
Engineering basis:
Equal target bars are
placed inside converging
rails. Limitation:
Perspective
interpretation is
observer- and
display-dependent.
Missing contract: none
entry / visual.kanizsa
triangle
engineering / limitation
/ gap; kanizsa 1976
contours; wagemans
2012 gestalt
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The image contains
incomplete inducers
with no explicitly
drawn triangle edge.
Engineering basis:
Three incomplete
circular inducers are
rasterized around a
triangular gap.
Limitation: Illusory
contour completion is
not directly measured.
Missing contract: none
entry /
visual.ebbinghaus
engineering / limitation
/ gap; mruczek 2015
ebbinghaus; weintraub
1979 ebbinghaus
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
Central target geometry
is held equal while
contextual circle
geometry differs.
Engineering basis:
Equal central targets
are surrounded by
different context-circle
sizes. Limitation:
Perceived size depends
on viewing scale and
context. Missing
contract: none
38

## Page 40

Key Record and citations DOI and URL Verification
Supported claim /
engineering / limitation
entry / visual.zollner engineering / limitation
/ gap; zoellner 1860
pseudoscopy; earle 1995
zollner; gregory 1997
visual
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The entry instantiates a
controlled crossing-line
orientation stimulus
family. Engineering
basis: Vertical long lines
crossed by short oblique
inducers with explicit
normalized spacing and
angle. Limitation: The
raster verifies line
geometry, not
orientation judgments
or a pixel-identical
historical reproduction.
Missing contract: none
entry / audio.tritone
paradox
engineering / limitation
/ gap; deutsch 1986
tritone; repp 1997
tritone
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The canonical pair has
an explicit half-octave
frequency relation.
Engineering basis: Two
octave-complex tones
are separated by a
half-octave interval.
Limitation:
Ascending/descending
reports vary across
listeners and contexts.
Missing contract: none
entry / audio.octave
illusion
engineering / limitation
/ gap; deutsch 1974
octave
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The two channels
receive alternating
octave-related tones.
Engineering basis:
Alternating high and
low tones are assigned
to opposite stereo
channels. Limitation:
The auditory percept
depends on dichotic
presentation and
listener. Missing
contract: none
entry / audio.auditory
continuity
engineering / limitation
/ gap; warren 1970
continuity; riecke 2011
continuity
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The canonical audio
contains a reproducible
interruption interval
and masker family.
Engineering basis: An
interrupted sinusoidal
carrier is replaced
during a declared gap
by a deterministic tone
or white-noise masker
with typed amplitude.
Limitation: The
generator reports the
physical interruption
and masker, not a
listener’s continuity
judgment or sensory-
versus-decisional effect.
Missing contract: none
39

## Page 41

Key Record and citations DOI and URL Verification
Supported claim /
engineering / limitation
entry /
audiovisual.temporal
ventriloquism
engineering / limitation
/ gap; vroomen 2004
temporal;
hartcherobrien 2011
temporal; hirst 2020
sound; noppeney 2018
causal
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
Audio and video event
timing and declared
offset are deterministic
and inspectable.
Engineering basis: A
visual flash and audio
click share a clock with
explicit offset.
Limitation: The
generated single-event
pair is a simplified
engineering stimulus.
Missing contract: none
entry /
audiovisual.mcgurk
engineering / limitation
/ gap; mcgurk 1976
speech
DOI: n/a; URL
host/path:
data/evidence_matrix.json
snapshot validated;
offline snapshot
The catalog identifies a
speech-dependent
audiovisual family
without claiming
implementation.
Engineering basis:
Requires validated
speech audio/video
fixtures and licensing
records. Limitation: No
fixture, consent record,
or perceptual validation
contract is bundled.
Missing contract: A
licensed or consented
checksummed speech
audio/video fixture,
synchronization
contract, and
preregistered perceptual
validation protocol are
required.
Table 8: Formal equation-to-code traceability.
Label Definition and symbols Implementation and tests Figures and claim level
eq:typed request q = (i, 𝜃, s, e) Symbols: i, 𝜃, s,
e
Code: registry.py, schema.py;
Tests: test generators.py
Figures: fig:architecture,
fig:formalism traceability;
Level: canonical stimulus
eq:canonical generation A = G i(𝜃; s) Symbols: A, G i,
𝜃, s
Code: registry.py,
generators.py; Tests: test
generators.py, test v03
contracts.py
Figures: fig:architecture,
fig:visual panel; Level:
canonical stimulus
eq:canonical digest c(A) = Serialize_LE,float32(A,
shape, clock, units); h_c(A) =
H(c(A)) Symbols: c(A), h_c,
H
Code: canonical.py,
manifest.py; Tests: test v03
contracts.py
Figures: fig:architecture,
fig:encoding verification; Level:
physical metric
eq:encoding verification F = E e(A), I = D(F), V(F, M)
∈ {pass, fail} Symbols: F, E e,
D, I, V, M
Code: render.py, inspection.py,
manifest.py; Tests: test media
and render.py, test v03
contracts.py
Figures: fig:encoding
verification; Level: encoded
media
eq:clock definition N = round(f_s T), t_k =
k/f_r, Δ_A V = t_audio −
t_video Symbols: N, f_s, T,
t_k, f_r, Δ_A V
Code: parameters.py,
artifacts.py; Tests: test
parameters.py, test media and
render.py
Figures: fig:temporal sequence,
fig:audiovisual timeline; Level:
physical metric
40

## Page 42

Label Definition and symbols Implementation and tests Figures and claim level
eq:objective statistics 𝜇_Y, 𝜎_Y, RMS_X = M(A;
units, tolerance, version)
Symbols: 𝜇_Y, 𝜎_Y,
RMS_X, M
Code: metrics.py,
publication.py; Tests: test v04
scholarly.py
Figures: fig:metrics dashboard,
fig:audio signals; Level:
physical metric
eq:temporal spectral metrics D_k = mean absolute
difference of adjacent frames;
centroid(X) = Σ
fP_X(f)/ΣP_X(f) Symbols:
D_k, P_X, f
Code: metrics.py, artifacts.py;
Tests: test v04 scholarly.py
Figures: fig:temporal sequence,
fig:metrics dashboard; Level:
physical metric
eq:observer estimand 𝜓 = E[Y conditional on
condition and protocol]
Symbols: 𝜓, Y, condition,
protocol
Code: observer analysis.py,
observer.py; Tests: test v04
scholarly.py
Figures: fig:synthetic
psychophysics, fig:observer
protocol; Level: observer
hypothesis
eq:synthetic observer p_M(c given A_r,A_c) =
𝜎((w⋅𝜑(A_c) − w⋅𝜑(A_r))/𝜏 )
Symbols: p_M, c, A_r, A_c,
w, 𝜑, 𝜏
Code: synthetic
psychophysics.py, metrics.py;
Tests: test synthetic
psychophysics.py
Figures: fig:synthetic
psychophysics; Level:
synthetic model output
Table 9: Claim ledger separating code-derived facts, scholarship, engineering departures, limitations, scope, and observer hypotheses.
Claim ID Claim and level Basis Lineage and limitation
catalog:count The catalog contains 18 entries.
Level: canonical_stimulus
derived_from_code Lineage: taxonomy entries()
Limitation: Catalog
membership is not a
completeness claim about all
known illusions. Manuscript:
manuscript/09 appendix
catalog.md
evidence:source count The checked-in evidence
matrix contains 36 source
records. Level:
source_supported
checked_in_scholarship Lineage: data/evidence
matrix.json::sources
Limitation: The offline
snapshot does not imply that
every URL is currently
reachable or that a source
supports more than its exact
record. Manuscript:
manuscript/06 scope and
related work.md
scope:no participant data No participant data are
bundled with the package.
Level: observer_hypothesis
derived_from_code Lineage: experiments/observer
protocol.md;
output/data/synthetic
psychophysics.json Limitation:
Future observer studies require
preregistration, consent,
calibrated presentation, and
separate data governance.
Manuscript: manuscript/07
publication audit.md
synthetic:diagnostic boundary The synthetic observer is a
deterministic model-output
diagnostic, not human
psychophysics. Level:
synthetic_model_output
synthetic_model_output Lineage:
src/duckrabbit/synthetic
psychophysics.py;
output/data/synthetic
psychophysics.json Limitation:
The hand-specified model has
no training data and has not
been calibrated against
observers. Manuscript:
manuscript/02
methodology.md
41

## Page 43

Claim ID Claim and level Basis Lineage and limitation
cover:editorial boundary The cover is a publication
illustration, not an
experimental stimulus or
observer result. Level:
publication_illustration
publication_illustration Lineage: output/reports/cover
visualization.json Limitation:
The editorial asset is not part
of the deterministic scientific
stimulus registry. Manuscript:
manuscript/07 publication
audit.md
evidence:visual.duck rabbit The entry instantiates a
controllable ambiguous-figure
stimulus family. Level:
source_supported
checked_in_scholarship Lineage:
sources=brugger1999duckrabbit;
gregory1997visual;
data/evidence matrix.json;
engineering=Parameterized
ambiguous silhouette; not a
pixel-identical reproduction of
a historical plate.;
limitation=The generator
verifies geometry and
luminance, not bistable
reports.; missing
contract=none Limitation:
The generator verifies
geometry and luminance, not
bistable reports. Manuscript:
manuscript/06 scope and
related work.md
evidence:visual.simultaneous
contrast
The physical center patches
are matched while surround
luminance differs. Level:
source_supported
checked_in_scholarship Lineage:
sources=gregory1997visual;
data/evidence matrix.json;
engineering=Equal central
patches on unequal luminance
surrounds.; limitation=Display
calibration and observer
adaptation are not modeled.;
missing contract=none
Limitation: Display
calibration and observer
adaptation are not modeled.
Manuscript: manuscript/06
scope and related work.md
evidence:visual.apparent
motion
The sequence contains
controlled successive spatial
events. Level:
source_supported
checked_in_scholarship Lineage:
sources=wertheimer1912motion;
sekuler1996wertheimer;
data/evidence matrix.json;
engineering=Alternating
rectangular masks at a fixed
rational frame rate.;
limitation=The artifact
establishes temporal
succession, not perceived
motion.; missing
contract=none Limitation:
The artifact establishes
temporal succession, not
perceived motion. Manuscript:
manuscript/06 scope and
related work.md
42

## Page 44

Claim ID Claim and level Basis Lineage and limitation
evidence:audio.shepard tone The audio contains
octave-related partials with
controlled sweep parameters.
Level: source_supported
checked_in_scholarship Lineage:
sources=shepard1984scale;
data/evidence matrix.json;
engineering=Additive
octave-spaced partials with a
deterministic envelope.;
limitation=Playback
transducers and listener pitch
judgments are external.;
missing contract=none
Limitation: Playback
transducers and listener pitch
judgments are external.
Manuscript: manuscript/06
scope and related work.md
evidence:audio.missing
fundamental
The nominal fundamental
component is absent from the
canonical spectrum. Level:
source_supported
checked_in_scholarship Lineage:
sources=zatorre2005missing;
data/evidence matrix.json;
engineering=Harmonic
components are synthesized
while the nominal fundamental
is omitted.; limitation=Pitch
completion is an observer-level
inference.; missing
contract=none Limitation:
Pitch completion is an
observer-level inference.
Manuscript: manuscript/06
scope and related work.md
evidence:audiovisual.sound
induced flash
The declared beep/flash event
counts and offsets are
physically encoded. Level:
source_supported
checked_in_scholarship Lineage:
sources=shams2000sifi;
hirst2020sound; data/evidence
matrix.json; engineering=One
flash paired with one or two
timed beeps on a shared clock.;
limitation=The stimulus does
not establish a reported flash
count.; missing contract=none
Limitation: The stimulus does
not establish a reported flash
count. Manuscript:
manuscript/06 scope and
related work.md
evidence:audiovisual.ventriloquist The audio and visual channels
carry a declared spatial
discrepancy. Level:
source_supported
checked_in_scholarship Lineage:
sources=bruns2019ventriloquist;
noppeney2018causal;
data/evidence matrix.json;
engineering=Stereo panning
and visual displacement
encode a spatial discrepancy.;
limitation=Perceived
localization depends on room,
headphones, display, and
observer.; missing
contract=none Limitation:
Perceived localization depends
on room, headphones, display,
and observer. Manuscript:
manuscript/06 scope and
related work.md
43

## Page 45

Claim ID Claim and level Basis Lineage and limitation
evidence:visual.muller lyer The two bar lengths are equal
in the canonical raster while
wing geometry varies. Level:
source_supported
checked_in_scholarship Lineage:
sources=gregory1997visual;
howe2005muller;
data/evidence matrix.json;
engineering=Equal bars with
controlled arrow-wing
geometry.; limitation=The
chosen normalized geometry is
one engineering variant.;
missing contract=none
Limitation: The chosen
normalized geometry is one
engineering variant.
Manuscript: manuscript/06
scope and related work.md
evidence:visual.poggendorff The occluder and diagonal
continuation are generated
from explicit geometry. Level:
source_supported
checked_in_scholarship Lineage:
sources=gregory1997visual;
morgan1999poggendorff;
data/evidence matrix.json;
engineering=A diagonal
continuation is separated by a
rectangular occluder.;
limitation=Alignment
judgments and orientation
filters are not measured.;
missing contract=none
Limitation: Alignment
judgments and orientation
filters are not measured.
Manuscript: manuscript/06
scope and related work.md
evidence:visual.ponzo Target bars are physically
equal and rails converge
toward a vanishing region.
Level: source_supported
checked_in_scholarship Lineage:
sources=fisher1967ponzo;
yildiz2022ponzo;
data/evidence matrix.json;
engineering=Equal target bars
are placed inside converging
rails.; limitation=Perspective
interpretation is observer- and
display-dependent.; missing
contract=none Limitation:
Perspective interpretation is
observer- and
display-dependent.
Manuscript: manuscript/06
scope and related work.md
evidence:visual.kanizsa
triangle
The image contains incomplete
inducers with no explicitly
drawn triangle edge. Level:
source_supported
checked_in_scholarship Lineage:
sources=kanizsa1976contours;
wagemans2012gestalt;
data/evidence matrix.json;
engineering=Three incomplete
circular inducers are rasterized
around a triangular gap.;
limitation=Illusory contour
completion is not directly
measured.; missing
contract=none Limitation:
Illusory contour completion is
not directly measured.
Manuscript: manuscript/06
scope and related work.md
44

## Page 46

Claim ID Claim and level Basis Lineage and limitation
evidence:visual.ebbinghaus Central target geometry is
held equal while contextual
circle geometry differs. Level:
source_supported
checked_in_scholarship Lineage:
sources=mruczek2015ebbinghaus;
weintraub1979ebbinghaus;
data/evidence matrix.json;
engineering=Equal central
targets are surrounded by
different context-circle sizes.;
limitation=Perceived size
depends on viewing scale and
context.; missing
contract=none Limitation:
Perceived size depends on
viewing scale and context.
Manuscript: manuscript/06
scope and related work.md
evidence:visual.zollner The entry instantiates a
controlled crossing-line
orientation stimulus family.
Level: source_supported
checked_in_scholarship Lineage:
sources=zoellner1860pseudoscopy;
earle1995zollner;
gregory1997visual;
data/evidence matrix.json;
engineering=Vertical long lines
crossed by short oblique
inducers with explicit
normalized spacing and angle.;
limitation=The raster verifies
line geometry, not orientation
judgments or a pixel-identical
historical reproduction.;
missing contract=none
Limitation: The raster verifies
line geometry, not orientation
judgments or a pixel-identical
historical reproduction.
Manuscript: manuscript/06
scope and related work.md
evidence:audio.tritone paradox The canonical pair has an
explicit half-octave frequency
relation. Level:
source_supported
checked_in_scholarship Lineage:
sources=deutsch1986tritone;
repp1997tritone;
data/evidence matrix.json;
engineering=Two
octave-complex tones are
separated by a half-octave
interval.; limita-
tion=Ascending/descending
reports vary across listeners
and contexts.; missing
contract=none Limitation:
Ascending/descending reports
vary across listeners and
contexts. Manuscript:
manuscript/06 scope and
related work.md
45

## Page 47

Claim ID Claim and level Basis Lineage and limitation
evidence:audio.octave illusion The two channels receive
alternating octave-related
tones. Level:
source_supported
checked_in_scholarship Lineage:
sources=deutsch1974octave;
data/evidence matrix.json;
engineering=Alternating high
and low tones are assigned to
opposite stereo channels.;
limitation=The auditory
percept depends on dichotic
presentation and listener.;
missing contract=none
Limitation: The auditory
percept depends on dichotic
presentation and listener.
Manuscript: manuscript/06
scope and related work.md
evidence:audio.auditory
continuity
The canonical audio contains a
reproducible interruption
interval and masker family.
Level: source_supported
checked_in_scholarship Lineage:
sources=warren1970continuity;
riecke2011continuity;
data/evidence matrix.json;
engineering=An interrupted
sinusoidal carrier is replaced
during a declared gap by a
deterministic tone or
white-noise masker with typed
amplitude.; limitation=The
generator reports the physical
interruption and masker, not a
listener’s continuity judgment
or sensory-versus-decisional
effect.; missing contract=none
Limitation: The generator
reports the physical
interruption and masker, not a
listener’s continuity judgment
or sensory-versus-decisional
effect. Manuscript:
manuscript/06 scope and
related work.md
evidence:audiovisual.temporal
ventriloquism
Audio and video event timing
and declared offset are
deterministic and inspectable.
Level: source_supported
checked_in_scholarship Lineage:
sources=vroomen2004temporal;
hartcherobrien2011temporal;
hirst2020sound;
noppeney2018causal;
data/evidence matrix.json;
engineering=A visual flash
and audio click share a clock
with explicit offset.;
limitation=The generated
single-event pair is a simplified
engineering stimulus.; missing
contract=none Limitation:
The generated single-event
pair is a simplified engineering
stimulus. Manuscript:
manuscript/06 scope and
related work.md
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## Page 48

Claim ID Claim and level Basis Lineage and limitation
evidence:audiovisual.mcgurk The catalog identifies a
speech-dependent audiovisual
family without claiming
implementation. Level:
source_supported
checked_in_scholarship Lineage:
sources=mcgurk1976speech;
data/evidence matrix.json;
engineering=Requires
validated speech audio/video
fixtures and licensing records.;
limitation=No fixture, consent
record, or perceptual
validation contract is bundled.;
missing contract=A licensed
or consented checksummed
speech audio/video fixture,
synchronization contract, and
preregistered perceptual
validation protocol are
required. Limitation: No
fixture, consent record, or
perceptual validation contract
is bundled. Manuscript:
manuscript/06 scope and
related work.md
publication:figure count The publication atlas contains
15 registered scientific figures.
Level: physical_metric
derived_from_code Lineage: publication caption
specs() Limitation: The count
is a package-state fact, not
evidence of empirical validity.
Manuscript: manuscript/07
publication audit.md
publication:table count The publication appendix
contains the generated table
set defined by the publication
table payload registry. Level:
physical_metric
derived_from_code Lineage: publication table
payloads() Limitation:
Generated tables summarize
package state and do not
replace source or observer
evidence. Manuscript:
manuscript/07 publication
audit.md
The source-tiered evidence table tbl. 7, caption audit tbl. 6, formalism registry tbl. 8, and claim ledger tbl. 9 are generated sidecars.
They provide a publication appendix without duplicating mutable counts or silently converting literature statements into package
results.
The publication artifacts have two distinct provenance boundaries. Scientific figures are deterministic PNG renders whose source-data
JSON and SHA-256 digests are checked against the code-owned registry. The cover is an editorial charcoal illustration: its selected
candidate, prompt fingerprint, source asset digest, dimensions, variants, and provenance boundary are recorded in output/reports/c
over_visualization.json. Neither boundary is an observer result, and neither substitutes for display calibration or behavioral data.
The publication audit additionally resolves every formalism edge to a real package module, test file, manuscript equation label, and
registered figure. Figure source-data sidecars use a versioned schema with figure identity, generator, seed, and nested data payload;
the registry verifies this identity and hash independently of the renderer. This makes a visually plausible but stale or relabeled figure
fail the same provenance gate as a tampered stimulus.
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## Page 49

9 Discussion and Conclusion
DuckRabbit’s principal result is a reproducibility boundary rather than a new psychophysical finding. The same typed request can
be regenerated, hashed, encoded, decoded, and audited, while the evidence graph and observer layer remain explicit about what the
package cannot infer. This makes the atlas useful for stimulus construction, source comparison, and preregistration without treating
a rendered image or sound as behavioral evidence.
The scholarly contribution is correspondingly modest but operational. Rather than flattening visual, auditory, temporal, and mul-
tisensory families into a single “illusion” label, the package keeps mechanism, perceptual signature, requirements, evidence role,
engineering basis, and implementation status separate. A primary demonstration, a review, a theoretical account, and a source de-
scribing the DuckRabbit implementation answer different questions. The appendix and source-data sidecars make those distinctions
inspectable at the same time as the generated media.
The work is best understood as a research-software artifact with a bounded methods contribution. Its novelty claim is not that it
discovers a new illusion or resolves a disputed mechanism; it is that a heterogeneous stimulus catalog can be represented as typed,
reproducible, source-linked, and release-audited objects. This framing is consistent with software-citation and F AIR guidance, which
treats versioned software, metadata, provenance, and reuse conditions as part of the research record [ Smith et al. , 2016, Wilkinson
et al. , 2016, Lamprecht et al. , 2020].
The release is authored by Daniel Ari Friedman of the Active Inference Institute, and its intended public home is the DuckRabbit
public GitHub repository . That repository statement is part of the software’s citation identity; until the external handoff occurs, the
private sidecar and its generated bundle are the authoritative release candidate.
9.1 Conclusion
DuckRabbit v0.5.0 turns multimodal illusion generation into an auditable typed pipeline. A request produces a canonical artifact,
objective metrics, optional delivery files, decoded inspection, and a versioned evidence-bounded manifest. The catalog now records
not only what is implemented, but also what the literature supports and what remains unvalidated.
The main scientific contribution is a boundary: deterministic stimulus facts are reproducible software outputs, while perceptual effects
are hypotheses that require observer conditions and data. This boundary permits broad generator coverage without overclaiming.
Future additions should contribute a typed parameter contract, a literature record, an engineering-fidelity statement, objective
invariants, generated documentation, and tests before entering the implemented registry. Promotion is a release decision about
software readiness, not a verdict on whether a perceptual phenomenon is real.
The synthetic-psychophysics layer extends this boundary without crossing it. A transparent feature observer makes model inputs,
weights, calibration, and output hashes inspectable, so the full orchestration can be tested today. Its small curve is a diagnostic
of that specified model, not evidence that humans share its feature map or response function. Empirical observer work remains a
separate, ethically and methodologically governed stage.
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## Page 50

10 Appendix A. Complete catalog, source tiers, and evidence/implementation
boundaries
This appendix is the authoritative rendered snapshot of DuckRabbit’s live catalog. It is generated from the taxonomy registry and
evidence matrix during the publication build; the table is not hand-maintained. The snapshot records the package’s current scope,
not a claim to enumerate every illusion described in the literature.
10.1 How to read the matrix
Each row identifies a registered illusion family and separates five questions that are often collapsed in informal catalogs:
1. What modality, mechanism, and signature does the package assign to the construction?
2. What evidence and implementation status does the checked-in record support?
3. Which sources support the exact statement written in the row?
4. What physical claim is supported by the row?
5. What full source role, resolver, DOI status, and claim level are retained in the machine-readable record?
implemented means that DuckRabbit has a deterministic generator and a validated canonical artifact contract. It does not mean that
the generated stimulus is a pixel-identical reproduction of a historical experiment or that an observer effect has been re-established.
input_required means that the family remains catalogued but lacks a lawful, checksummed input fixture and/or the validation
contract required for deterministic generation. Evidence status and implementation status are deliberately independent.
The source column is a compact citation-key view. The full source role, resolver or DOI status, exact supported claim, engineering
departure, and limitation are retained in the machine-readable evidence matrix and in the generated evidence audit tbl. 7. A source
supports only the narrow claim recorded for it; a review or theory record is not evidence that a DuckRabbit rendering produces a
universal perceptual effect.
Table 10: DuckRabbit catalog entries, source tiers, and evidence/implementation boundaries.
ID Construction Evidence / status Sources Supported claim
visual.duck rabbit visual; ambiguity;
bistability
literature backed
engineering entry;
implemented
brugger 1999
duckrabbit; gregory
1997 visual
The entry instantiates a
controllable
ambiguous-figure
stimulus family.
visual.simultaneous
contrast
visual; contrast and
context; contrast
distortion
literature backed
engineering entry;
implemented
gregory 1997 visual The physical center
patches are matched
while surround
luminance differs.
visual.apparent motion visual; temporal motion;
illusory motion
literature backed
engineering entry;
implemented
wertheimer 1912
motion; sekuler 1996
wertheimer
The sequence contains
controlled successive
spatial events.
audio.shepard tone auditory; spectral
harmonic; continuity
literature backed
engineering entry;
implemented
shepard 1984 scale The audio contains
octave-related partials
with controlled sweep
parameters.
audio.missing
fundamental
auditory; spectral
harmonic; filling in
literature backed
engineering entry;
implemented
zatorre 2005 missing The nominal
fundamental component
is absent from the
canonical spectrum.
audiovisual.sound
induced flash
audio_visual;
crossmodal temporal;
fusion or fission
review backed
engineering entry;
implemented
shams 2000 sifi; hirst
2020 sound
The declared beep/flash
event counts and offsets
are physically encoded.
audiovisual.ventriloquist audio_visual;
crossmodal spatial;
spatial capture
review backed
engineering entry;
implemented
bruns 2019
ventriloquist; noppeney
2018 causal
The audio and visual
channels carry a
declared spatial
discrepancy.
visual.muller lyer visual; geometric
alignment; geometric
distortion
literature backed
engineering entry;
implemented
gregory 1997 visual;
howe 2005 muller
The two bar lengths are
equal in the canonical
raster while wing
geometry varies.
visual.poggendorff visual; geometric
alignment; geometric
distortion
literature backed
engineering entry;
implemented
gregory 1997 visual;
morgan 1999
poggendorff
The occluder and
diagonal continuation
are generated from
explicit geometry.
49

## Page 51

ID Construction Evidence / status Sources Supported claim
visual.ponzo visual; geometric
alignment; geometric
distortion
literature backed
engineering entry;
implemented
fisher 1967 ponzo; yildiz
2022 ponzo
Target bars are
physically equal and
rails converge toward a
vanishing region.
visual.kanizsa triangle visual; contrast and
context, geometric
alignment; filling in
literature backed
engineering entry;
implemented
kanizsa 1976 contours;
wagemans 2012 gestalt
The image contains
incomplete inducers
with no explicitly
drawn triangle edge.
visual.ebbinghaus visual; contrast and
context, geometric
alignment; geometric
distortion
literature backed
engineering entry;
implemented
mruczek 2015
ebbinghaus; weintraub
1979 ebbinghaus
Central target geometry
is held equal while
contextual circle
geometry differs.
visual.zollner visual; geometric
alignment; geometric
distortion
literature backed
engineering entry;
implemented
zoellner 1860
pseudoscopy; earle 1995
zollner; gregory 1997
visual
The entry instantiates a
controlled crossing-line
orientation stimulus
family.
audio.tritone paradox auditory; spectral
harmonic; categorical
recoding
literature backed
engineering entry;
implemented
deutsch 1986 tritone;
repp 1997 tritone
The canonical pair has
an explicit half-octave
frequency relation.
audio.octave illusion auditory; stream
segregation; fusion or
fission
literature backed
engineering entry;
implemented
deutsch 1974 octave The two channels
receive alternating
octave-related tones.
audio.auditory
continuity
auditory; stream
segregation; continuity
literature backed
engineering entry;
implemented
warren 1970 continuity;
riecke 2011 continuity
The canonical audio
contains a reproducible
interruption interval
and masker family.
audiovisual.temporal
ventriloquism
audio_visual;
crossmodal temporal;
temporal binding or
recalibration
review backed
engineering entry;
implemented
vroomen 2004 temporal;
hartcherobrien 2011
temporal; hirst 2020
sound; noppeney 2018
causal
Audio and video event
timing and declared
offset are deterministic
and inspectable.
audiovisual.mcgurk audio_visual; speech
categorization;
categorical recoding
literature backed input
dependent entry; input
required
mcgurk 1976 speech The catalog identifies a
speech-dependent
audiovisual family
without claiming
implementation.
10.2 Evidence boundary and future expansion
The matrix is intentionally a living registry snapshot. New families may be added when the package can state a typed parameter
contract, deterministic canonicalization rule, validation invariant, and evidence boundary. Planned or input-dependent families are
not silently promoted because a source exists: promotion requires an implementable contract, reproducible fixtures where needed,
and an explicit statement of what remains unvalidated. McGurk therefore remains input_required pending a consented or licensed,
checksummed speech/ video fixture and a study-ready validation protocol. The candidate-future catalog is documented separately
from this live matrix so that absence is not misread as a claim that a phenomenon is unknown or unimportant.
50

## Page 52

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53


---
*Extraction method: pypdf*