T_root: A Closed-Form Omnibus Statistic for Independence that Stays Calibrated Across Sparse and Heterogeneous Contingency (m0/Troot: methods paper + reporting standard)--Reproducibility package

Simulation code, locked outputs (including an EXHAUSTIVE 4,000-replication grid over every table shape from 2x2 to 100x100 (4,950 shapes), ~13 average expected-count levels, and eleven levels of marginal heterogeneity, ~1.4 million cells, superseding the earlier sampled 110-shape grid), figures, derivation companion, Supplementary Material (Sections S1-S11), independent methods review, comparative novelty reviews, provenance manifest, and two in-browser demonstrators (a P-value/routing tool and a which-test tool, both computing T_root by default), for two companion papers on testing independence in two-way contingency tables: a methods paper deriving and validating T_root, a closed-form, parameter-free, variance-stabilized statistic that is comprehensive across the sparsity-and- heterogeneity plane, and a reporting-standard paper proposing that software report T_root by default with the exact margin-conditional test as the single fallback. All simulation data are simulated; the example tables are from public datasets. Includes the closed-form finite-cell correction (obtained by removing a redundant finite-N factor that the margin-fitting leverage already carries), the corrected Rényi normalization (2N/[α(α−1)]), and deterministic seeds for bit-reproducible regeneration. Code — the .py runners and modules under pm_study/ — 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). T_root: A Closed-Form Omnibus Statistic for Independence that Stays Calibrated Across Sparse and Heterogeneous Contingency Tables. v1.0.10: Supplement per-table generators (S1–S9) with S5/S8 recomputed from deposited data; the two browser tools' routing corrected to the published binary screen, with broadened real-data examples, a teaching modal, and an exact Mielke-Berry comparison row; Methods disclosure and Figure 10 at 600 dpi. Concept DOI unchanged. v1.0.6: Documents refreshed to match the submitted version (substantive figure/table callouts; Renyi figure delegated to Supplement S3; figures renumbered 9→8; derivation companion added). No result, runner, or data changed. v1.0.11: Redeposited to correct version numbering. v1.1.2: adds the proof-complete long-form Derivations Companion (D1–D14, every step and proof written out). Manuscript, Supplement, and code unchanged from v1.1.1.