generateAuditSummary
This definition assembles the audit summary record for CPM constants verification in Recognition Science by aggregating the length of the verified constants list, two consistency checks for cone and eight-tick models, the count of example certificates, the precomputed coincidence probability bound, and the fixed status string. Researchers running machine audits of constant derivations from the Recognition Composition Law and forcing chain would cite this summary to export verification reports. The construction is a direct record literal that re
claimThe audit summary is the record with fields numConstants equal to the cardinality of the list of verified constants, consistencyChecks equal to 2, numExamples equal to the cardinality of the list of example certificates, coincidenceProb equal to the probability field of the CPM coincidence bound, and status equal to the string VERIFIED.
background
The CPM Constants Audit module supplies machine-checkable verification of constants derived from Recognition Science invariants, including the Recognition Composition Law and the forcing chain from T0 to T8. The central structure is AuditSummary, whose fields record the total number of verified constants, the number of consistency checks passed, the number of examples exercised, the coincidence probability bound, and the overall status string. Upstream results include the fundamental tick τ₀ defined as 1 in RS-native units, the status declaration confirming c = 1, ħ = φ^{-5}, and the φ-ladder, plus the list of all narrative geodesic plot families and the set of all 8 kinship systems.
proof idea
The definition is a direct record construction that references verifiedConstants.length for the constant count, hardcodes the value 2 for the two consistency checks, references exampleCertificates.length for the example count, pulls the probability from cpmCoincidenceBound, and sets the status literal to VERIFIED. It is a one-line wrapper that assembles the summary from sibling definitions without further reduction.
why it matters in Recognition Science
This definition supplies the concrete summary object consumed by the downstream audit_passes theorem, which proves that the status equals VERIFIED, the number of constants is positive, and the number of consistency checks is positive. It closes the audit infrastructure for CPM constants, ensuring machine verification of derivations grounded in the Recognition Science forcing chain and the eight-tick octave. It touches the open question of numerical coincidence bounds for constant agreement.
scope and limits
- Does not derive or recompute any physical constants.
- Does not execute the underlying consistency proofs for cone or eight-tick models.
- Does not update the lists of verified constants or certificates dynamically.
- Does not perform statistical analysis beyond the supplied coincidence bound.
Lean usage
theorem audit_passes : generateAuditSummary.status = formal statement (Lean)
182noncomputable def generateAuditSummary : AuditSummary := {
proof body
Definition body.
183 numConstants := verifiedConstants.length,
184 consistencyChecks := 2, -- cone and eight-tick
185 numExamples := exampleCertificates.length,
186 coincidenceProb := cpmCoincidenceBound.probability,
187 status := "VERIFIED"
188}
189
190/-- The audit passes all checks. -/