IndisputableMonolith.Verification.ODEFoundationCert
Verification module that packages an ODE-foundation certificate on top of the T5 cost-uniqueness helpers. Auditors cite it when checking that continuous dynamics sit on the unique J-cost rather than an ad-hoc Lagrangian. The module is import-thin: Mathlib plus FunctionalEquation; it exposes the certificate object rather than a long proof development.
claimModule-level certificate that the ODE foundation used by Recognition Science is compatible with the unique cost $J(x)=(x+x^{-1})/2-1$ forced by the T5 functional equation (Recognition Composition Law).
background
Recognition Science derives dynamics from a single cost functional fixed by T5: $J$ is the unique (normalized) solution of the Recognition Composition Law $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$, equivalently $J(x)=\cosh(\log x)-1$. The upstream module Cost.FunctionalEquation supplies the helper lemmas for that uniqueness proof.
This verification module lives in the Verification domain and imports only Mathlib and those T5 helpers. Its role is to expose a named certificate object tying the continuous (ODE) side of the framework to that unique $J$, so downstream audits do not re-open the functional-equation argument.
proof idea
No standalone theorem development: the module is a thin certification wrapper. It imports the T5 functional-equation helpers and assembles the ODE-foundation certificate from those lemmas plus Mathlib. Argument structure is packaging and re-export, not a new tactic script.
why it matters in Recognition Science
Places an auditable certificate at the ODE/continuous-dynamics boundary of the forcing chain, anchored on T5 J-uniqueness. Downstream used-by edges are empty in the current graph, so the module presently serves as a verification leaf rather than a lemma feeder. It keeps the continuous side honest to the same $J$ that forces $\phi$, the eight-tick octave, and $D=3$ later in the chain.
scope and limits
- Does not reprove T5 J-uniqueness; relies on Cost.FunctionalEquation.
- Does not derive mass formulae, alpha bounds, or discrete eight-tick results.
- Does not supply a numerical ODE solver or existence/uniqueness theorem for a concrete IVP.
- Does not claim downstream consumers; used_by is currently empty.