A calibrated confidence region for sparse-table interaction: score re-studentization, a coverage law, and an exact-corner certificate (m01cd) — reproducibility deposit

Reproducibility deposit for the merged confidence-region paper M01cd, which combines the translation-invariant, score/Rao re-studentized region for the interaction of a sparse contingency table (formerly m01c) with its coverage law, analytic-refutation decomposition, and exact-conditional corner certificate, plus a standard-vs-new comparison heatmap (formerly m01d). The primary manuscript is the single merged build Dwyer_M01cd_Region (author and anonymized); the component m01c and m01d markdown sources are retained as drafting history. Also contains the shared region apparatus and every locked result CSV (coverage sweep, two-moment scores, skew-spectrum, exact-corner enumeration, refutation ladder, region comparison), the five figures, and the shared build/audit modules. PROVENANCE.md pins the seeds, grids, reps, and environment; the 2x2x2 corner numbers are exact by complete enumeration, the rest are deterministically seeded, so every reported number regenerates bit-for-bit. This is the single self-contained record for the confidence-region work; there is no separate m01c or m01d deposit.v1.0.2: Reproducibility deposit for the merged confidence-region paper M01cd, "A calibrated confidence region for sparse-table interaction: score re-studentization, a coverage law, and an exact-corner certificate." The paper combines the translation-invariant, score/Rao re-studentized confidence region for the interaction vector of a sparse contingency table (formerly m01c) with its two-moment coverage law, the analytic-refutation decomposition, and the exact-conditional corner certificate (formerly m01d).The naive "carried for free" region — the calibrated omnibus restated about the interaction with the covariance frozen at the independence margins — is not translation-invariant: its coverage is exactly 1 - alpha only at the null and degrades as the interaction grows, badly under sparsity and skew (falling to 0.18 at the 2x2x2 corner). The deposit reproduces the closed-form remedy (a tau-dependent score/Rao re-studentization at the hypothesized mean that restores near-nominal coverage with no extra simulation) and its trust certificate: a two-moment (Satterthwaite) coverage law accurate to a mean absolute error of about 0.01 for interaction dimension m >= 12, with an invertible effect budget; an honest refutation of the fully-analytic (Imhof) version of that law, decomposed as a second-moment error; a guaranteed-coverage region that floors coverage across the uncertified intermediate zone with a proved finite-sample bound at two operating points (a distribution-free Monte-Carlo cutoff and a simulation-free analytic cutoff); and an exact-conditional certificate at the 2x2x2 corner by complete enumeration of all 239,539 positive-margin tables, against which the Gaussian cutoff is wrong by up to threefold.The primary manuscript is the single merged build Dwyer_M01cd_Region (author and anonymized; docx + PDF). The component m01c and m01d markdown sources are retained as drafting history. The deposit also contains the shared region apparatus and every locked result CSV (coverage sweep, two-moment scores, skew-spectrum, exact-corner enumeration, refutation ladder, region comparison, and the Berger-Boos guaranteed-region run), the six figures, the figure generators, the deep dives, and the shared build/audit modules. PROVENANCE.md pins the seeds, grids, replications, and environment; the 2x2x2 corner numbers are exact by complete enumeration, the rest are deterministically seeded, so every reported number regenerates bit-for-bit. This is the single self-contained record for the confidence-region work; there is no separate m01c or m01d deposit.v1.0.3: Added a deployable, simulation-free cutoff built from the Section 6 two-moment coverage law — turning that law from a diagnostic into an operational tool.A two-moment (Satterthwaite) guard cutoff taken at the worst-case (maximal-association) dispersion at the plugged-in effect, which holds the coverage floor across the near-Gaussian envelope — no design below 0.94 at interaction dimension m ≥ 12 and skew ≤ 1, versus a 14% undercoverage rate for the fixed frozen cutoff. A tighter plug-in variant pulls over-covering cells back toward nominal to recover power; under skew it degrades and the region routes to the guaranteed Berger–Boos region (exactly where the analytic law is itself refuted).The new deposit-scale runner rc_m01cd_rho_interval.py (+ its result CSV) and the shared delta-method moment core mseries_moments.py (the m01cd instance of the series' dispersion toolkit, reproducing the effect-size engine bit-for-bit).One scoped sentence in the manuscript's Section 6 recording the guard; all prior content, numbers, and figures unchanged.v1.0.4: adds the proof-complete long-form Derivations Companion (D1–D9); retargets the submission package to the Journal of Statistical Computation and Simulation (off Computational Statistics). Manuscript body, figures, and results unchanged from v1.0.2; supersedes the unpublished v1.0.3. v1.0.5: folds the JSCS-submission refresh — manuscript variants rebuilt to the 149-word abstract, 10 keywords, and version-stamped AI declaration; the new anonymized long-form Derivations Companion (docx/pdf/md) for the single-anonymous review track; and the corrected single-anonymous step-by-step. Documents-only — no number, runner, or figure changed from v1.0.4. Code — the .py runners and modules under rerun_cochran/ — is released under the MIT License (LICENSE-MIT.txt), © 2026 William J. Dwyer. All non-software content — the manuscript, supplement, derivation companion, tables, and rendered figures — is released under the Creative Commons Attribution 4.0 International Public License (CC BY 4.0) (LICENSE-CC-BY-4.0.txt): "You are free to share and adapt the material for any purpose, including commercially, provided appropriate credit is given." Canonical URL: https://creativecommons.org/licenses/by/4.0/legalcode. Attribution: Dwyer, W. J. (2026). A confidence region for sparse-table interaction that carries its own trust certificate: closed-form, guaranteed, or exact by regime.