IndisputableMonolith.Verification.KernelMatchCert
Packages the pointwise kernel identity J(r(θ))=2 cot θ as a verification certificate drawn from Measurement.KernelMatch. Anyone tracing the C=2A bridge (Local-Collapse Appendix D) cites this packaging layer. The module re-exports the constructive match; it adds no independent proof content.
claimCertificate packaging the pointwise identity $J(r(\vartheta))=2\cot\vartheta$ for the profile $r(\vartheta)=(1+2\cot\vartheta)+\sqrt{(1+2\cot\vartheta)^2-1}$, the kernel match that enables the integral bridge $C=2A$.
background
Recognition Science fixes the cost $J(x)=(x+x^{-1})/2-1$ (T5 J-uniqueness). Measurement.KernelMatch proves the constructive kernel match from Local-Collapse Appendix D: for the radial profile
$r(\vartheta)=(1+2\cot\vartheta)+\sqrt{(1+2\cot\vartheta)^2-1}$,
one has $J(r(\vartheta))=2\cot\vartheta$ pointwise. Integrating against the angular measure then yields the geometric identity $C=2A$ between cost and area.
This Verification module sits one layer above that proof. It imports only KernelMatch and exposes the identity as a named certificate object for downstream verification consumers.
proof idea
Definition and packaging module, not a proof module. It wraps the already-proved pointwise identity from Measurement.KernelMatch into a certificate form; no new lemmas or tactic scripts are introduced here.
why it matters in Recognition Science
Foundational ingredient for the $C=2A$ bridge proof, per the module doc-comment. It lifts the Appendix D kernel match out of the Measurement layer so verification paths can depend on a single certificate rather than the full constructive development. No recorded used_by edges yet; the intended parents are any bridge or audit theorems that quote the packaged identity.
scope and limits
- Does not reprove J(r(θ))=2 cot θ; that proof lives in Measurement.KernelMatch.
- Does not itself integrate to the global identity C=2A.
- Does not supply numerical or floating-point certificates.
- Does not invoke forcing-chain steps beyond the J-cost definition.