NavierStokesAnalyticPathology
plain-language theorem explainer
The Navier-Stokes analytic pathology predicate is the constantly-true proposition on any analytic display record for the energy bridge. Certificate auditors cite it as the pathology half of the Navier-Stokes problem-audit pair. The body is a one-line constant assignment to True, so every display satisfies pathology by definition.
Claim. For every Navier-Stokes analytic display record $d$ (carrying an energy certificate, cell resolution, energy depth, and display payload), the associated pathology predicate holds: it is the constantly true proposition.
background
The HardProblemCertificateAudits module packages audit interfaces for several Millennium-scale bridges (prime critical line, Navier-Stokes energy, Yang-Mills gap, Hodge). Each bridge supplies a domain-specific analytic display record and a pair of predicates: legitimate and pathology.
A Navier-Stokes analytic display bundles an energy certificate with discrete parameters (cell resolution, energy depth) and a display payload. The pathology predicate is the second half of the audit pair: it marks when a display is treated as pathologically certified under the completion map.
Local convention: audit records implement a ProblemAudit structure with completion, legitimate, pathology, and a conservativity witness. Pathology here is not a PDE blow-up criterion; it is a certificate-side flag inside that audit interface.
proof idea
Pure definition, not a proved theorem. The body ignores its display argument and returns the proposition True. No lemmas, tactics, or upstream equalities are invoked; the assignment is definitional.
why it matters
This predicate is wired into navierStokesAnalyticAudit as the pathology field of the ProblemAudit for Navier-Stokes energy certificates, and into navierStokesAnalytic_conservative, which asserts Conservativity of both the legitimate and pathology sides under the analytic completion map.
Because pathology is constantly True, the pathology half of conservativity is immediate: from any display one recovers its energy certificate by projection. That keeps the audit interface total and conservative while the legitimate side carries the real certificate content. In the broader Recognition certificate stack it is scaffolding for a hard-problem bridge, not a claim about Navier-Stokes regularity or the forcing chain (T0-T8).
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