CertificatePathology
plain-language theorem explainer
Defines the native pathology predicate on obstruction certificates as the constantly-true proposition: at the schema layer every certificate is admissible. Audit authors cite it when wiring a ProblemAudit record before problem-specific bad events exist. The body is the trivial definition True, intentionally left open for later analytic refinement.
Claim. For any certificate type $C$ and any certificate $c \in C$, the pathology predicate holds: $\mathrm{Pathology}(c) := \top$. Every obstruction certificate is admissible at the schema layer; problem-specific bad events may refine this later.
background
Hard-problem certificate audits package a finite certificate type into a ProblemAudit record with completion, legitimacy, and pathology fields, plus conservation lemmas. Pathology is the dual of legitimacy: it flags certificates that should be rejected as obstructing or ill-formed for the target hard problem (prime critical line, Navier–Stokes energy, Yang–Mills gap, Hodge algebraicity, and so on).
At the schema layer the framework needs a default that does not yet encode analytic content. The native pathology predicate therefore asserts that every certificate is admissible. The companion legitimacy predicate plays the same role on the acceptance side. Upstream, the Identity law from the logic-as-functional-equation development states that comparing a thing with itself costs zero ($C(x,x)=0$ for $x>0$), which motivates treating self-consistent certificates as non-pathological until a finer interface is supplied.
The module sits in Primitive Recognition Calculus and imports the quantized proof-method scaffolding used by the finite-reduction audits.
proof idea
One-line definitional body: the predicate is definitionally equal to True for every certificate. No lemmas are applied; no tactics run. Downstream audits simply plug the constant into the pathology field of ProblemAudit and discharge the corresponding conservation obligation by the shared identity_conservative lemma.
why it matters
Feeds identityCertificateAudit, which builds a ProblemAudit over a finite certificate type with completion, CertificateLegitimate, and this pathology field, plus the two conservation proofs. Without a schema-level default, every hard-problem audit would have to invent its own placeholder Prop before analytic interfaces exist.
In the Recognition stack this is scaffolding hygiene rather than a forcing-chain step: it keeps the audit API uniform while T5–T8 and the Recognition Composition Law remain upstream. Later refinements can replace True by a problem-specific bad event (for example a failed energy bound or a spectral-gap witness failure) without changing the ProblemAudit shape. Sibling audits (prime critical line, Navier–Stokes, Yang–Mills, Hodge) reuse the same pattern.
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