ExampleCertificate
plain-language theorem explainer
ExampleCertificate packages an example identifier, real-valued K_net and C_proj, and a reference string to document instances where CPM constants are exercised. It is referenced by the exampleCertificates list and the VerifiedConstant structure inside the CPM audit module. The declaration is a plain structure definition with four fields and no computational content or lemmas.
Claim. A record consisting of a string identifier, real numbers $K_{net}$ and $C_{proj}$, and a reference string.
background
The CPM Constants Audit module supplies machine-checkable verification that constants satisfy required properties derived from Recognition Science invariants, including consistency checks between constant sets and probability bounds for coincidental agreement. ExampleCertificate serves as a container for concrete instances exercising these constants. Upstream dependencies include structure definitions such as LedgerFactorization.of for the calibration of J and PhiForcingDerived.of for J-cost, which supply the underlying invariants used in constant derivations.
proof idea
This is a structure definition that introduces four fields: example as String, Knet and Cproj as ℝ, and reference as String. No lemmas or tactics are applied; the declaration functions purely as a data container.
why it matters
The structure supports the export infrastructure for audit reports by supplying example data that populates the exampleCertificates list. It feeds the VerifiedConstant structure and contributes to the module's goal of machine-checkable verification of CPM constants against Recognition Science forcing-chain results such as the eight-tick octave and phi-ladder mass formulas. It touches the open question of how numerical coincidence bounds translate into formal probability statements.
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