cert

Physics RS Module 9 targets the proton-electron mass ratio in the Recognition framework. The module notes that $\varphi^{12}\approx 321.9$, leaving a residual factor $\sim 5.7$ relative to the observed $\approx 1836$, so the present content is structural rather than a finished mass prediction.

The certificate type bundles three properties of a local domain cost (a real-valued cost on pairs of positive reals, built from the global $J$-cost $J(x)=(x+x^{-1})/2-1$). Upstream, nonnegativity of recognition-event cost is already known: any recognition event has $0\le e.\mathrm{cost}$ via $J$-cost nonnegativity. The siblings domainCost_at_eq, domainCost_nonneg, and canonicalThreshold_pos specialize that picture to the module-9 cost and threshold.

Status of the module is STRUCTURAL THEOREM (zero sorry, zero axiom).

Pure structure constructor. The three fields of the certificate are filled by the already-proved sibling facts: diagonal vanishing of the domain cost, nonnegativity of the domain cost on positive arguments, and positivity of the canonical threshold. No tactics, no new lemmas.

Gives a single named inhabitant of the Module-9 certificate type so downstream code can treat the three cost/threshold axioms as one discharged package. The module itself is the structural shell around the proton-electron mass-ratio discussion ($\varphi^{12}\approx 321.9$ versus observed $\approx 1836$). It does not yet close the residual gap factor; it only certifies that the local cost geometry is well-behaved (zero on equals, nonnegative, positive threshold), consistent with the global $J$-cost minimum at identity and the forcing-chain uniqueness of $J$. No downstream users are recorded in the graph yet; the companion cert_inhabited is the natural next consumer.