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Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor (m02) -- Reproducibility bundle

William Dwyer
Aug 2026 · Zenodo (CERN European Organization for Nuclear Research)

Abstract

Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor William J. Dwyer, MD, MPH, FAAP — Department of Mathematics and Statistics, University of Massachusetts Lowell. ORCID 0009-0004-0855-7222. Concept DOI (always resolves to the latest version): 10.5281/zenodo.21844797. Published v1.0.0:10.5281/zenodo.21844798. What this is The reproducibility deposit for a single combined manuscript on detecting sparse departures from independence in a two-way contingency table — the regime where dependence hides in a few cells rather than spreading across the table, so the omnibus chi-square is under-powered and a naive per-cell scan mis-calibrates. It is organized in three parts under one set of front/back matter, with a shared derivations supplement (D02): Part I — the heteroscedasticity profile and the detection boundary. The per-cell standardized deviations are heteroscedastic under the margin-conditional null; profiling that heteroscedasticity gives a closed-form detection boundary separating the sparsity/strength regimes where any test can succeed from those where none can. Part II — an adaptive higher-criticism gate. A higher-criticism statistic tuned to the margin-conditional cell law attains that boundary, with its exact null law and power characterized. Part III — an assumption-lean exact anchor and reporting apparatus. An exact margin-conditional calibration anchor and a routing rule, so a scan that mis-sizes under the asymptotic reference is replaced by one that holds its level: on a corpus of 5,543 real tables the asymptotic per-cell scan mis-sizes about two-thirds of them (mean realized size ≈ 0.33 against a 0.05 target) while the exact anchor holds near 0.01. What the deposit contains Combined manuscript (manuscripts/Dwyer_M02_Combined.{docx,pdf} + M02_Combined_Manuscript.md) and the three part-sources (manuscripts/parts/, provenance for the assembled combined text), plus the D02 derivations companion (derivations/). Verification and study code (code/) — the boundary, exact-anchor, and higher-criticism verification scripts and the power/size study drivers (numpy/scipy, fixed seeds); the docx builder (build_docx.py), the shared math-typography core (mseries_mathtype.py), the inline- and caption-math delimiters, the combined assembler (assemble_combined.py), and the audit gates (structure_audit.py, math_render_audit.py). Locked data (data/) — the study outputs (size/power, boundary, estimated-margins, efficiency) and the higher-replication "big box" runs, so every number regenerates. Figures (figures/), the novelty reviews (novelty_reviews/), the prior-art / adversarial / consistency audits (audits/), and the in-browser detector tools/honest_detection.html. All evaluation is simulation-based; the one empirical component is the public-corpus calibration scan, which uses only openly distributed contingency tables. Code is released under the MIT License; text, figures, and data under CC BY 4.0. How to cite Please cite this deposit if you use the package or the method. Citing the concept DOI references the work in general and always resolves to the latest version; cite a specific version DOI to point at an exact snapshot. Dwyer, W. J. (2026). Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor — reproducibility deposit [Software]. Zenodo. https://doi.org/10.5281/zenodo.21844797 BibTeX: bibtex @software{dwyer_m02_2026, author = {Dwyer, William J.}, title = {Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor --- reproducibility deposit}, year = {2026}, publisher = {Zenodo}, doi = {10.5281/zenodo.21844797}, url = {https://doi.org/10.5281/zenodo.21844797}, orcid = {0009-0004-0855-7222} } The DOI above is the concept DOI (resolves to the latest version); to cite a specific release use that version's DOI in place of it (e.g. 10.5281/zenodo.21844798 for v1.0.0). When the accompanying journal article appears, please cite it as the primary reference for the method and this deposit as the reproducibility archive. Version history v1.0.3 — deterministic recut (2026-08-30): the bundle is now cut with the shared mseries_deposit.write_deterministic_zip, so rebuilding the same content yields a byte-identical zip and a stable md5. Every manuscript, derivation, figure, dataset, code file, novelty review, and audit is byte-identical to v1.0.2 (all files SHA-256-matched except the three version-stamped ones). No number, theorem, table, figure, or dataset changed. Publishes as a New Version on concept 10.5281/zenodo.21844797 (build_m02_deposit.py; md5 8f2fa9f7e814ba807710480a7f60cb65, 112 files, 6,044,685 bytes). v1.0.2 — impact-first reframe (2026-08-23): the introduction and abstract reframed to lead with the applied motivation (sparse independence departures in genomics, network/text co-occurrence, pharmacovigilance, ecology, survey cross-tabulation) and the corpus calibration failure, before the detection-boundary theory. No number, theorem, figure, or dataset changed. v1.0.1 — published (2026-08-08): adds the Zenodo concept DOI to the manuscript Availability statement and CITATION.cff, and the widened Figure 8 top box. Content otherwise identical to v1.0.0. v1.0.0 ✅ 10.5281/zenodo.21844798 — first published deposit: the combined three-part manuscript, the D02 derivations, the verification and study code with fixed seeds and locked outputs, all figures, the in-browser detector, and the prior-art / adversarial / consistency audits. Provenance: every number traces to a named, deterministically-seeded script under code/; the combined manuscript is assembled by code/assemble_combined.py and built by code/build_docx.py. Related identifiers: T_root methodology 10.5281/zenodo.21522471; exact conditional engine 10.5281/zenodo.21831680.

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