coincidence_negligible
plain-language theorem explainer
The probability that four independent CPM constants match Recognition Science predictions to three decimal places by chance is bounded below 10^{-10}. Auditors of constant derivations in the CPM framework cite this bound when quantifying the unlikelihood of accidental agreement in audit reports. The proof is a one-line term simplification that unfolds the precomputed coincidence bound and reduces the numerical comparison via exponent negation and normalization.
Claim. The probability of coincidental agreement among four independent constants matching Recognition Science predictions to three decimal places satisfies $p < 10^{-10}$.
background
The CPM Constants Audit module supplies machine-checkable verification that constants satisfy properties derived from Recognition Science invariants, along with consistency checks and probability bounds on coincidental agreement. The central upstream definition supplies a coincidence bound stating that four independent constants each matching to three decimal places yield a probability of coincidental agreement at most $10^{-12}$. This sits inside the Recognition Science setting where constants appear in native units ($c=1$, $G=phi^5/pi$, $alpha^{-1}$ inside (137.030, 137.039)) and physical quantities occupy discrete phi-tiers.
proof idea
The proof is a term-mode one-liner that applies simp only on the coincidence bound definition together with zpow_neg, then invokes norm_num to discharge the resulting numerical inequality.
why it matters
The result closes the negligible-coincidence claim inside the CPM audit pipeline and is invoked by the probability-printing routine and the JSON report generator. It reinforces the framework's assertion that constant matches arise from the forcing chain (T0-T8) and Recognition Composition Law rather than chance, while leaving open the precise identification of which four constants enter the bound.
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