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def definition def or abbrev high

methodReport

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The methodReport definition produces the fixed string confirming the standalone CPM method certificate by instantiating the empty certificate structure and invoking its verified predicate. Researchers auditing URC adapters would cite this for machine-readable consistency checks on the CPM assumptions. The body is a direct term construction that applies the verified_any lemma together with forced evaluation of the three toy-model positivity facts.

claimThe method report is the constant string ``CPM Method Report: OK'' obtained by constructing the empty CPMMethodCert instance, confirming its verified property via the any-witness lemma, and forcing evaluation of the toy-model statements that defect, energy, and $c_{min}$ are positive.

background

In the URCAdapters.CPMReports module the definition supplies a simple, #eval-friendly audit report for the standalone CPM method certificate. The CPMMethodCert structure (imported from URCGenerators) is an empty record whose verified field asserts consistency of the generic A/B/C method plus toy-model witness. Upstream structures supply the supporting foundations: J-cost minimization and local 8-tick dynamics from PhysicsComplexityStructure, spectral emergence of gauge content and three generations from SpectralEmergence, and ledger factorization from DAlembert.LedgerFactorization.

proof idea

The definition constructs an empty CPMMethodCert instance and applies the verified_any lemma from the certificate module to obtain the required proof. It then forces evaluation of the three toy-model facts (defect_pos, energy_pos, cmin_pos) before returning the literal string. This is a pure term-mode construction with no tactics or additional lemmas.

why it matters in Recognition Science

The definition feeds the one-line wrapper methodReport_ok in the same module, providing the machine-readable endpoint for the CPM audit path. It closes the standalone certificate check within the URC adapters layer, linking to the Recognition Science chain through the imported phi-forcing and complexity structures. No open questions or scaffolding are addressed.

scope and limits

Lean usage

#eval methodReport

formal statement (Lean)

  18noncomputable def methodReport : String :=

proof body

Definition body.

  19  let cert : URCGenerators.CPMMethodCert := {}
  20  have _ : URCGenerators.CPMMethodCert.verified cert :=
  21    URCGenerators.CPMMethodCert.verified_any cert
  22  -- Also force evaluation of the toy witness facts.
  23  let _ := URCGenerators.toyModel_defect_pos
  24  let _ := URCGenerators.toyModel_energy_pos
  25  let _ := URCGenerators.toyModel_cmin_pos
  26  "CPM Method Report: OK"
  27

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