IndisputableMonolith.Verification.BornRuleDerivationCert
Verification certificate module packaging the derivation of Born's rule from the recognition cost. It re-exports and certifies that outcome probabilities equal squared amplitudes, via the cost functional J and the amplitude bridge. Physicists checking the RS measurement layer would cite it. The module is structural: it wires the Measurement.BornRule development into the verification surface rather than reproving the identity.
claimCertificate that Born's rule $P(I)=|\alpha_I|^2$ follows from the recognition cost $J$ and the amplitude bridge $\mathcal{A}=\exp(-C/2)\cdot\exp(i\varphi)$, as developed in the measurement layer.
background
Recognition Science obtains quantum measurement statistics from a single cost functional $J$, fixed uniquely in the forcing chain (T5) as $J(x)=(x+x^{-1})/2-1$. The measurement layer builds an amplitude bridge $\mathcal{A}=\exp(-C/2)\cdot\exp(i\varphi)$ that converts recognition cost $C$ into complex amplitudes.
The upstream module Measurement.BornRule states the goal explicitly: derive $P(I)=|\alpha_I|^2$ from $J$ and that bridge. This Verification module sits one level up: it does not redefine $J$ or the bridge; it packages that derivation as a named certificate for audit and export.
Local setting is the Verification domain of the monolith: thin certificate shells over substantive Measurement and Foundation results, so downstream checkers can point at a single import rather than the full proof graph.
proof idea
This is a certificate/aggregation module, not a fresh proof development. It imports Mathlib and Measurement.BornRule, then exposes a certificate object (BornRuleDerivationCert) that witnesses the Born-rule derivation already established upstream. No independent tactic script or algebraic reduction lives here; the logical content is the import edge and the certificate wrapper.
why it matters in Recognition Science
Born's rule is the empirical core of the quantum measurement story. In RS it is not postulated: it is forced from $J$ and the amplitude bridge. Placing that derivation behind a Verification certificate makes the claim auditable beside other certified identities (constants, mass ladder, dimensional forcing).
No downstream used_by edges are recorded yet; the module is a leaf in the current graph, intended as an export and review surface. It closes the measurement side of the recognition story against the same cost functional that drives T5–T8 and the Recognition Composition Law, so a referee can treat $P=|\alpha|^2$ as a certified consequence rather than an extra axiom.
scope and limits
- Does not reprove Born's rule; certifies the upstream Measurement.BornRule derivation.
- Does not derive the form of J or the amplitude bridge; those are assumed from Foundation/Measurement.
- Does not address decoherence, collapse dynamics, or experimental error models.
- Does not claim a unique measurement postulate beyond $P(I)=|\alpha_I|^2$.
- Does not feed recorded downstream theorems in the current graph.