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W3 R81: independently audited skew-contaminated Student-t5 source and original figure ledger

Source/plot provenance · 20 October 2026 · research-only

Numerical reproducibility is not general inference calibration

All original data are fully observed synthetic heavy-tailed Gaussian-conditional sources with a known centered rare asymmetric Bernoulli shock; no real eye tracker or actual MNAR loss is tested. W3 #289/#296 remain open and version 1.2/PyPI release stays on hold.

Figure 1 — new generating asymmetric contamination law

Prespecified centered rare unit-level contamination shock and analytic covariance contribution

The original source model adds an independent unit-specific Bernoulli centered event with p=.08, amplitude A=.16, signed functional profile (.75+.25t)[1,-.65], to the Student-t5 radial × nonseparable Gaussian unit innovations. The contamination shock is constant across the 31×2 trajectory and all three trials of a participant. It increases the source-known variance by A²p(1−p)H² and also creates cross-time/cross-coordinate covariance. The R81 source-known reference is therefore Student-t5 plus asymmetric Bernoulli, not R80's Student-t5-only oracle.

Figure 2 — whole 31×2 generating slope truth inclusion

R81 full-grid truth inclusion for original and regularized methods and known Student-t5 plus skew benchmark

Predictor-dependent variance Curves: 2 extreme units Curves: 16 extreme units Participants: 2 extreme units Participants: 16 extreme units
Original W3 wild-HC1 1/32 14/32 5/32 26/32
Baseline estimated HC3 Gaussian 10/32 26/32 16/32 27/32
Frozen λ=.25 estimated Gaussian 21/32 29/32 20/32 31/32
Frozen λ=.50 estimated Gaussian 24/32 30/32 24/32 32/32
Simulation-known Student-t5 plus skew source 29/32 31/32 29/32 30/32

Each entry uses the actual independent source-denominator n=32 newly generated primitive blocks per cell, NOT 256 factorial-case replications and NOT 999 conditional reference draws. The successful event is entire 31×2 known generating slope contained simultaneously. In the primary two-anchor heteroskedastic cell, frozen λ=.50 includes 24/32 (75%) of curves and participants; this is not generally nominal 90% calibrated inference.

Two-anchor constant-variance controls: baseline HC3 / λ=.25 / λ=.50 / source-known non-Gaussian law = 23/32, 26/32, 26/32, 28/32 curves and 24/32, 28/32, 30/32, 30/32 participants; wild-HC1 16/32 curves and 18/32 participants. The original immutable source report preserves all other cells and failed-source accounting.

Figure 3 — source-specific lower-tail SE ratios and joint criticals

R81 mean source-specific estimated marginal to true SE lower-tail and estimated Gaussian 90% criticals

Two-anchor heteroskedastic source mean Baseline HC3 Fixed λ=.25 Fixed λ=.50
Curves estimated/true SE 10th percentile 0.505329 0.604494 0.656213
Participants estimated/true SE 10th percentile 0.454295 0.478274 0.497540
Curves Gaussian max-statistic critical 2.625530 2.924467 3.042587
Participants Gaussian max-statistic critical 2.227093 2.788894 2.992941

The known Student-t5 plus skew simulation law maximum critical averages 3.179659 for curves and 2.431226 for repeated participants in the adverse cell. Different critical values must not be compared without their accompanying SE scales or joint maximum-statistic distributions. The true SE is known only in synthetic generating-law source evidence.

Exact scientific source identities and numerical verification

Evidence item Independently verified source
Preregistered original generating specification Research draft R81 PR #417, including a completed pre-result protocol
Original scientific source run Workflow #39490888383: 12/12 dedicated scientific jobs successful
Original complete SHA256 evidence Artifact #12295607688
Pinned actual original scientific checkout 698bf1eb80a9e856bfc2e0b5bdc362f425a75dc1
Independent real original-source reconstruction Research draft R81-A PR #418
Independent mandatory original archive audit Workflow #39491187099: 4/4 dedicated audit jobs successful
Independent reconstructed source report Artifact #12296301870
Complete/attempted original source cases 256/256 complete, zero refusals
True independent primitive source denominator 32 per design / support / variance cell
Original independently re-created reference values 256 sources × five references × 999 draws = 1,278,720 numerical maxima
Data-estimated candidates (all unchanged) Original wild-HC1, original HC3 Gaussian, fixed λ=.25 and fixed λ=.50 HC3 regularized Gaussian references
Source-known comparison Unit-specific Student-t5 chi-square radial and centered asymmetric Bernoulli mixture; only simulator knows probability/amplitude/covariance
True unit variance R80 Gaussian-conditional unit variance + A²p(1−p)H²
Research qualification Numerically audited only; no general nominal-90% inference, no genuine observation-process loss
Public release decision No inference method merge, stable 1.1.0 unchanged, version 1.2/PyPI HOLD, issues #289/#296 OPEN

The original and independent implementations each reconstruct source X/Y and all five reference arrays; this tests source identities, RNG ordering, covariance formulas, conditional skewed Student-t5 sampling, reference quantiles and numerical correspondence. It does not provide new independent field validation. R80 and R81 source blocks were newly and separately generated, so between-study differences are not source-paired causal effects.

Read R81 research article · Read rare unit-shock methods companion · Previous R80 heavy-tail evidence