W3 R93/R93-A — exact original and independent observable-law evidence¶

Scope: exact rational binary-outcome counterexample conditional on one originally missing target stratum. This is neither a fitted continuous gaze model nor a frequentist validation study. The ledger retains original source/provenance and the independent mandatory artifact replay.

Original exact proof and full source-artifact archive¶

The original archive includes exact_rational_evidence.json and SHA256SUMS, and preserves each of the 27 exact rational models and all four observable event probabilities. The original GitHub workflow run binds artifact provenance to the original checkout. The artifact does not include a separately embedded source-commit.txt; no such file is claimed.

Failure-inclusive CI note: The original first attempt had three failing pytest jobs before the mathematics ran, because its minimal workflow installed only pytest while the repository's test conftest.py imports matplotlib. The research workflow was amended to install full repository development dependencies, without altering the proof equations, and the corrected 4/4 run above passed. Both CI records should be retained.

Independent source algebra, SHA256 and exact likelihood audit¶

The independently coded R93-A script does not import the original R93 proof module or public eyetrajectoriespy methods. It independently reconstructs the outcome probabilities by assigning the invited nonreturn mass to the \(Z=0\) group, to both equally, or to the \(Z=1\) group. It verifies exact \(p\), \(c_0\), \(c_1\), returned successes \(q_0\), \(q_1\), invited nonresponse, all source-likelihood probabilities, complete nine-cell/27-world keys and original SHA256 integrity. Three Python-version tests plus a separate actual immutable source-artifact download and replay passed. The audit tests equal product likelihood for observed event sequences, while the unconditional finite-length implication follows from equality of one-record distributions under the stated independent-record submodel.

Exact sharp sets and interpretation¶

The sharp population region \(p\in[q_1,1-q_0]\) is identified from the observed distribution and the assumed binary support, not a realized finite-sample confidence interval. With \(g=0.50\) and 99% invited completion, all three latent worlds yield observed probabilities \((0.5, 0.2475, 0.2475, 0.005)\) in the order not invited, returned zero, returned one, invited nonresponse. Even \(g=1\) leaves ambiguity if some assigned outcomes do not complete.

The tiny 0.001 gap at 99.9% completion is part of the result: high actual return narrows what remains unknown, but does not generally point-identify it. No statement about practical effect magnitude, superpopulation sampling uncertainty, correlated time-series trajectories or nominal functional confidence-band coverage follows from this existence counterexample.

Website publication/release gates¶

The article, methods, sharp-set figure and exact observable-law figure are documentation-only candidates. They require a strict documentation CI build and all 25 exact-head PR workflows, followed by a separately verified protected-main GitHub Pages docs-build and deploy success. Original research and audit PR #456/#457 remain draft/unmerged.

Unrestricted actual outcome-dependent return is not identified by randomized invitations alone. R93 does not claim identification for real missing gaze, arbitrarily correlated functional data, source-specific slope models or validated 90% simultaneous bands. Blockers #296 and #289 stay open. Public 1.1.0 unchanged, v1.2/GitHub Release/PyPI HOLD.