IndisputableMonolith.Verification.ODEFoundationCert
Verification certificate module packaging the ODE-side foundation needed for the T5 cost uniqueness argument. It sits in the Verification domain and imports the functional-equation helpers that force J. Cite it when auditing that the cost functional equation is wired into a checkable certificate rather than left as free-standing lemmas. Structure is a thin certificate wrapper over the T5 helper import, not a deep new derivation.
claimCertificate object packaging the ODE-foundation obligations tied to the T5 uniqueness of the cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), via the Recognition Composition Law $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$.
background
Recognition Science forces the cost functional through the T0–T8 chain. T5 is J-uniqueness: the unique admissible cost is $J(x)=(x+x^{-1})/2-1$. The upstream module Cost.FunctionalEquation supplies the helper lemmas for that uniqueness proof and is the sole non-Mathlib import here.
The local setting is Verification: certificate-shaped packaging so that foundation obligations (here, ODE-side structure supporting the cost equation) can be audited as a single named object rather than a scattered lemma list. The Recognition Composition Law is the algebraic identity those helpers discharge.
No new physical constants or ladder data are introduced; the module only re-exports and certifies the functional-equation substrate already fixed by T5.
proof idea
This is a certificate/module packaging layer, not a multi-step derivation. It imports Mathlib and the T5 functional-equation helpers, then exposes a single certificate object (ODEFoundationCert) that aggregates the ODE-foundation obligations those helpers support. Expect definitional assembly and re-export rather than a long tactic script; any internal proofs are one-line wrappers onto the upstream T5 lemmas.
why it matters in Recognition Science
Places the T5 cost-uniqueness substrate inside the Verification certificate surface so downstream audits can point at one named foundation cert instead of raw helper lemmas. Upstream doc-comment: "This module provides lemmas for the T5 cost uniqueness proof." That is the content being certified. No further used_by edges are recorded yet; the module is a leaf in the current graph, intended as an audit anchor for the ODE/cost foundation rather than a step inside a larger proved theorem. Landmark link: T5 J-uniqueness and the Recognition Composition Law.
scope and limits
- Does not prove T5 J-uniqueness from scratch; only certifies via imported helpers.
- Does not derive T6–T8 (phi, eight-tick, D=3) or mass-ladder formulae.
- Does not supply numerical bounds on alpha or other RS constants.
- Does not claim new ODE existence/uniqueness theorems beyond the certificate packaging.
- Does not list downstream consumers; used_by is currently empty.