Mutation by Natural Dominance: finite-sample bounds for recovery-corrected route comparisons

Methods extension 0.5.0 adds finite-sample simultaneous confidence bounds for the recovery-corrected W/A/M route contrast in Mutation by Natural Dominance (TMD). It is a methods report with reproducible software and synthetic checks. It is distinct from archived software v2.6.5 and the earlier research-report version 0.1.0.

Main mathematical and computational result

The preceding 0.4.0 interior likelihood declined all-success and all-failure control tables. This update uses established Clopper-Pearson intervals and Bonferroni projection to retain observed boundary counts. For C prespecified contexts, twelve scalar intervals per context receive marginal two-sided error alpha/(12C). Projection onto the recovery-corrected finite log contrast gives an interval for each context. Rejecting a shared contrast only when their intersection is empty has false rejection probability at most alpha, conditional on valid marginal sampling laws, fixed prespecified analysis and route-relative control transport. Independence between components is unnecessary for the union bound; correct trial units and binomial/multinomial marginals remain essential.

Accepted numerical endpoints are conservative outer approximations certified with exact integer binomial tails. Exact rational bounds for J=exp(2theta) determine intersection; rounded logarithms do not decide rejection. The prototype admits at most 5,000 trials per scalar, 64 contexts and alpha from 1e-12 to below one. Observed zeros are retained; missing counts never become zeros. Structural true zero probabilities make the finite log target undefined. All-success controls can retain finite information; unbounded uncertainty is preserved. This is not a boundary maximum-likelihood fit, p-value, equivalence test, mechanism identification or externally novel statistical theorem.

Software review and synthetic evaluation

All 13 unit tests passed. Independent internal review checked the frozen source, endpoint certificates, exact binomial tails, rational-grid coverage, 4,096 projection corners and six deterministic fixtures. The repeated-sample diagnostic retains all 160 synthetic datasets: 40 exact reanalyses of earlier high-recovery stress counts and 120 new draws. The reused and new high-recovery shared-contrast scenarios each produced 0/40 rejections with finite compatible intervals; a deliberately strong departure produced 40/40 rejections; low-recovery stress produced 0/40 with unbounded compatible intervals. All true per-context J values were covered in these sampled checks. No dataset was replaced and no bootstrap was used. These are limited software diagnostics, not biological confirmation or certified power. Descriptive Wilson 95% intervals for rejection frequencies are 0-8.76% for 0/40 and 91.24-100% for 40/40.

In More Basic Terms

Recovering all 100 introduced control cells is useful evidence that recovery is high. It does not prove that recovery is perfect. We keep a range of possible rates and include uncertainty in the biological route counts. If corrected ranges across conditions have no value in common, that challenges the proposed common contrast under the stated assumptions. Overlap means the data have not settled the question. A control with no recovered units can leave a range unbounded; we leave that uncertainty visible. Exact arithmetic prevents rounding errors from deciding the comparison, but experimental records must still justify trial units, recovery transfer and independent outcomes within each binomial sample.

Scope, literature and provenance

A targeted primary-source review adds exact-binomial boundary-confidence work and recent whole-cell/DNA recovery and single-cell isolation studies. They inform measurement design; none supplies an authenticated matched TMD route-control panel. An archive audit also recovered a historical incorrect interval inversion. Original files remain preserved. No new laboratory experiment, matched biological validation, raw third-party dataset analysis, new physical law or external mathematical priority is claimed. Optional stopping, dependent culture descendants, misclassification, uncertain denominators and route-dependent transport failure require additional treatment.

Files and reuse

The new 0.5.0 PDF and reviewed ZIP contain the derivation, source audit, tests, count tables, seeds, exact rational targets, internal reviews, literature notes, checksums and In More Basic Terms explanation. The unchanged 0.2.0, 0.3.0 and 0.4.0 ZIPs preserve intervening methods releases in this research-report DOI family; they retain their own versions and notices. The earlier 0.1.0 report remains available as a preceding Zenodo version.

New report and documentation: CC BY 4.0. New software: MIT. Original publications and observations retain their attribution and rights. AI assistance was used in development, analysis and internal review. Neither EDISON grant 675419 nor MOSBRI grant 101004806 funded TMD. No research grant is claimed.

GitHub project: https://github.com/maldonado-research/TMD
Current methods overview: https://github.com/maldonado-research/TMD/blob/main/TMD_RESEARCH_EXTENSION_0_5_0.md
Previous Zenodo report: https://zenodo.org/records/23068056
Earlier archived software: https://zenodo.org/records/22398093