primeCriticalLineAudit
plain-language theorem explainer
Specializes the identity certificate audit to the three-token prime-critical-line inventory (finite prime window, Euler-product balance ledger, zero-obstruction witness). Anyone citing the hard-problem audit headline or the prime-critical-line finite-reduction theorem uses this object as the audit schema. It is a one-line specialization of the generic identity audit.
Claim. The prime-critical-line audit is the identity $\Delta$-audit on the finite certificate type whose tokens are a finite prime window, an Euler-product balance ledger, and a zero-obstruction witness: domain, data, and certificate types coincide, completion is the identity completion, and the legitimate/pathology predicates are the standard certificate legitimacy and pathology predicates (both conservative for that completion).
background
In the quantized-proof layer, a ProblemAudit is the $\Delta$-audit of a continuum problem: a completion from a discrete name type $N$ through data $D$ to certificates $Cert$, plus two predicates on $D$ (legitimate vs pathology) required to be conservative for that completion. The module packages four Millennium-style continuum targets as finite certificate inventories rather than as solved PDEs or analytic statements.
For the prime-critical-line target the inventory is three tokens: a finite prime window, an Euler-product balance ledger, and a zero-obstruction witness. The generic identity audit takes any certificate type $C$ and builds a ProblemAudit with $N=D=Cert=C$, identity completion, and the module-wide legitimacy/pathology predicates, each proved conservative by the shared identity-conservative lemma.
Local setting: HardProblemCertificateAudits supplies audit schemas and finite-reduction theorems; the headline theorem explicitly warns these are not solutions of the underlying continuum problems.
proof idea
One-line wrapper: instantiate the generic identity certificate audit at the prime-critical-line certificate inductive type. That upstream definition fills completion by the identity completion, sets legitimate and pathology to the shared certificate predicates, and discharges both conservativity obligations by the identity-conservative lemma on those predicates.
why it matters
Feeds primeCriticalLine_finiteReduction, which asserts HasFiniteReduction for this audit via the generic problemAudit_finiteReduction lemma, and is the first conjunct of hard_problem_certificate_audits_headline. That headline packages all four hard-problem audits (prime-critical-line, Navier–Stokes energy, Yang–Mills gap, Hodge algebraic) as finite inventories with finite-reduction theorems, while stating they remain audit schemas rather than continuum solutions.
In the Recognition stack this is foundation scaffolding for treating continuum obstruction problems as finite certificate audits under the quantized proof method. It does not touch the forcing chain (T0–T8), RCL, or the mass ladder; it only supplies a typed audit object so downstream finite-reduction and headline results can name a concrete prime-critical-line schema.
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