IndisputableMonolith.Verification.MetricCurvatureCert
Verification module packaging the metric-side curvature certificate that sits on the π⁵ configuration-space derivation. It records that the curvature correction enters the Recognition metric with the fixed rational prefactor over π⁵. Anyone checking the geometric constants chain cites it. The module is thin: it imports the curvature-space certificate and exposes a single named certificate object.
claimThe metric curvature certificate asserts that the curvature correction is $\delta_\kappa = -103/(102\pi^5)$, with the $\pi^5$ factor forced by integration over a five-dimensional configuration space rather than by an ad hoc choice of units.
background
Recognition Science fixes geometric correction terms from counting and integration on the configuration space of the recognition ledger, not from free phenomenological fits. The upstream curvature-space certificate states that the curvature correction $\delta_\kappa = -103/(102\pi^5)$ uses $\pi^5$ because the integration is over a five-dimensional configuration space, and lists as a key result that the configuration-space dimension equals 5.
This module lives in the Verification domain. It imports that curvature-space certificate and Mathlib, and exposes the sibling object MetricCurvatureCert as the metric-facing packaging of the same claim. The local setting is certificate assembly: pin the constant, pin the dimensional origin of $\pi^5$, and make the result available to downstream metric or constant-audit developments.
proof idea
This is a thin verification module, not a long tactic development. It imports the curvature-space certificate (the $\pi^5$ derivation and the dimension-5 configuration-space result) and re-exports or wraps that content as the metric curvature certificate. No independent analytic derivation is performed here; the logical work is upstream, and the module structure is import-plus-named-certificate.
why it matters in Recognition Science
The module earns its place by giving the metric layer a stable handle on $\delta_\kappa$ with an explicit dimensional justification for $\pi^5$. That constant is part of the Recognition geometric-correction package used when matching ledger-derived curvature to continuum metric structure. Upstream, CurvatureSpaceCert supplies the $\pi^5$ and dimension-5 facts; this module is the metric-side certificate surface. No downstream used-by edges are recorded in the graph snapshot, so its immediate consumers are external constant audits and metric-verification developments rather than a named parent theorem in-repo.
scope and limits
- Does not re-derive $\delta_\kappa$ from scratch; it packages the upstream curvature-space result.
- Does not prove spatial dimension $D=3$; that is a separate forcing-chain claim (T8).
- Does not fix $G$, $\alpha$, or mass-ladder constants; only the curvature correction term.
- Does not supply numerical floating-point bounds beyond the exact rational-over-$\pi^5$ form.
- Does not claim independent experimental validation inside this module.