Mutation by Natural Dominance (TMD): analysis-only toolkit v2.4 — clean evidence & entropy atlas, exact Bayesian evidence, and time-to-first-winner extensions

Mutation by Natural Dominance (TMD) — v2.4 Status: testable framework (pre‑theory). When preregistered gates G1–G3 (and ideally G4) pass across real systems and independent labs, it becomes reasonable to use: “The Theory of Mutation by Natural Dominance (TMD)”. Until then, this remains a framework / hypothesis family rather than a finished Theory. Core idea Evolution often follows the “easiest” route. TMD quantifies “ease” via a hazard‑level model of first successful arrivals: Genetics: λᵢ ∝ μᵢ · Aᵢ · Fᵢ Origins chemistry: λₖ ∝ kₖ · aₖ · fₖ where λ is a successful‑arrival hazard (a “first‑arrival rate”), μ is mutation/variation supply, A is genome accessibility / context, and F is a fixation/persistence factor from population genetics. For chemistry, k is an effective reaction/network rate, a is accessibility (concentrations, surfaces, cycling, compartments), and f is persistence/continuation. First fixation is modeled as a Poisson race: P_first,i = λᵢ / Σⱼ λⱼ, giving a softmax/logistic law over competing routes. Two‑route dominance is parameterized by: δ = log₂(λ₁/λ₂), Δ = δ ln 2 P₁ = 1/(1+e^(−Δ)), P₂ = 1−P₁ Predictability is summarized by path entropy and an effective number of routes: H = −Σᵢ Pᵢ ln Pᵢ N_eff = eᴴ What’s new in v2.4 This release tightens the link between predictability (entropy) and strength of evidence, and ships a clean evidence/entropy “atlas snapshot” so the framework is easier to test on real systems. 1) Clean evidence & entropy atlas (real systems) Adds a compact “mini‑atlas” summary format across multiple literature systems, focused on: observed winner counts (G3), inferred dominance δ and predictability (H, N_eff), and transparent uncertainty / evidence summaries. 2) Exact Bayesian evidence (dominance vs null) Adds exact Bayes‑factor style evidence calculations for winner‑count data (beta‑binomial / Dirichlet‑multinomial logic). This avoids relying only on large‑n normal approximations and supports small‑n literature datasets. 3) Entropy–evidence identity (key result) For K routes with observed winner fractions p̂, the log‑likelihood ratio (MLE vs uniform‑null) is: log Λ = n · (ln K − H(p̂)), so evidence for non‑uniform dominance scales directly with the entropy deficit (how far the system is from maximum unpredictability). 4) Time‑to‑first‑winner extension (competing‑risks) Adds a “time‑to‑first‑fixation” / competing‑risks layer so that, when available, arrival times (not just winner counts) can be incorporated into hazard inference. 5) Test‑readiness: prereg + design helpers Includes prereg/design templates so independent labs can pre‑commit routes, measurements (μ/A/F), replicate number, and pass/fail criteria. What this release is NOT This record is analysis‑only: no lab protocols, no new biological experiments, no claim of experimental validation. It provides an open mathematical framework + templates + literature/synthetic demonstrations designed to be tested and potentially falsified by independent labs.