IndisputableMonolith.Verification.BornRuleDerivationCert
Verification certificate module for the Recognition-Science derivation of Born's rule. It packages the claim that outcome probabilities equal squared amplitude moduli, obtained from the recognition cost J and the amplitude bridge. Experimentalists and foundations workers cite it when auditing that P(I)=|α_I|² is forced rather than postulated. The module is a thin import-and-certify shell over the Measurement.BornRule development.
claimCertificate that Born's rule $P(I)=|\alpha_I|^2$ follows from the recognition cost $J$ together with the amplitude bridge $\mathcal{A}=\exp(-C/2)\cdot\exp(i\varphi)$, with no independent probability postulate.
background
Recognition Science treats measurement as cost minimization on the recognition functional $J$. The Measurement.BornRule development states that Born's rule $P(I)=|\alpha_I|^2$ is derived from $J$ and the amplitude bridge $\mathcal{A}=\exp(-C/2)\cdot\exp(i\varphi)$, rather than inserted by hand.
This Verification module sits one layer above that derivation. Its role is audit packaging: expose a single certifiable object that a checker or paper appendix can point at when claiming the Born-rule step is closed inside the monolith.
Notation follows the upstream module: $C$ is recognition cost, $\varphi$ a phase, and $\alpha_I$ the complex amplitude attached to outcome $I$. Constants and ladder structure from the forcing chain are not re-derived here.
proof idea
No independent proof lives in this file. It imports Mathlib and IndisputableMonolith.Measurement.BornRule, then exposes the sibling certificate object BornRuleDerivationCert as the verification handle. Argument structure is entirely that of the upstream Born-rule derivation: cost-to-amplitude bridge, then identification of probabilities with squared moduli. This module only re-exports and names the cert.
why it matters in Recognition Science
Born's rule is the bridge from recognition cost to laboratory frequencies. Certifying its derivation is required before mass formulae, selection rules, or eight-tick measurement claims can be read as predictive rather than interpretive. The module has no downstream used_by edges in the supplied graph; it is a leaf verification artifact meant for external audit and for any future top-level "physics complete" aggregator that will list Born-rule closure beside T5–T8 landmarks.
It does not itself advance the forcing chain; it records that the Measurement layer already did the work.
scope and limits
- Does not re-prove Born's rule; only certifies the upstream Measurement.BornRule derivation.
- Does not derive the amplitude bridge form $\mathcal{A}=\exp(-C/2)\cdot\exp(i\varphi)$ from T5–T8.
- Does not address decoherence, collapse dynamics, or experimental error models.
- Does not constrain $\alpha$ or mass-ladder numerics beyond the Born identification.