domain_specific_analytic_audits_headline
plain-language theorem explainer
The four Millennium-style analytic audits (prime critical line, Navier–Stokes energy, Yang–Mills gap, Hodge algebraic) each admit a finite-certificate reduction: every legitimate display and every pathology is witnessed by some finite certificate. Anyone assembling the Delta-native strong-closure surface cites this headline. The proof is a four-fold application of the generic finite-reduction transfer for problem audits.
Claim. Each of the four domain-specific analytic audits (prime critical line, Navier–Stokes energy, Yang–Mills mass gap, Hodge algebraic cycles) satisfies the finite-reduction property: for every legitimate display $d$ there exists a finite certificate $c$ that certifies $d$, and likewise for every pathology display.
background
In the quantized proof method, a ProblemAudit packages a continuum display type, a finite certificate type, a completion map, and two predicates (legitimate vs pathology) that are conservative with respect to certification. HasFiniteReduction asserts that both predicates descend to finite certificates: every legitimate object and every pathology is witnessed by some certificate under the completion map.
The four audits named here are the domain-specific analytic display records for the hard-problem stubs: prime critical line, Navier–Stokes energy, Yang–Mills gap, and Hodge algebraic cycles. Each record carries completion, legitimacy, pathology, and the two conservatism witnesses required by the audit interface.
The module sits in Primitive Recognition Calculus and only records display interfaces. As the doc-comment states, the reductions still do not solve the problems; they fix the exact interface that future analytic proofs must refine.
proof idea
One-line term proof. For each of the four audits, apply problemAudit_finiteReduction, which itself is the generic transfer: given a problem audit whose legitimacy and pathology predicates are conservative with respect to the completion map, finite_certificate_transfer yields HasFiniteReduction. The headline is just the four-fold conjunction of those instances.
why it matters
This headline is the analytic half of the hard-problem certificate surface. Downstream, strongClosureCertificate in Delta-native strong closure assembles the closed theorem surface and pulls certified analytic entries; the finite-reduction status of these four audits is part of what that certificate packages.
Within Recognition Science foundation work, the point is bookkeeping rather than a solution of RH, NS regularity, YM gap, or Hodge: the stubs now have named analytic display records with certificate fields and domain-specific parameters, so later genuine analytic arguments have a fixed Lean interface to refine. It does not touch the forcing chain (T0–T8), RCL, or the phi-ladder mass formula; it is scaffolding closure for the hard-problem audit layer.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.