navierStokesEnergy_finiteReduction
plain-language theorem explainer
The Navier–Stokes energy audit admits a finite-certificate reduction: every legitimate datum and every pathology is witnessed by some finite certificate. Anyone packaging the four hard-problem audit stubs cites this fact. The proof is a one-line wrapper around the generic problem-audit finite-reduction lemma.
Claim. Let $A$ be the identity certificate audit for the Navier–Stokes energy certificate type. Then $A$ has a finite reduction: for every legitimate datum $d$ there exists a certificate $c$ that certifies $d$, and for every pathology $d$ there likewise exists a certifying $c$.
background
In the quantized proof method, a continuum problem is packaged as a ProblemAudit with three type parameters (nominal objects, data, certificates) together with predicates for legitimate objects and pathologies, and a completion map that issues certificates. Finite reduction means both classes descend to the certificate layer: legitimate data and pathologies are each witnessed by some finite certificate under the completion.
The Navier–Stokes energy audit is the identity audit on the Navier–Stokes energy certificate type: nominal, data, and certificate types coincide, and the audit is built by the generic identity-certificate construction. The module collects four such hard-problem stubs (prime critical line, Navier–Stokes energy, Yang–Mills gap, Hodge algebraic) as audit schemas rather than continuum solutions.
Upstream, the generic lemma states that every problem audit has a finite reduction, by transferring certificates along the completion using the audit's conservative legitimacy and pathology maps.
proof idea
One-line wrapper. Apply the generic theorem that every ProblemAudit satisfies finite reduction, instantiated at the Navier–Stokes energy audit. That generic proof itself calls the finite-certificate transfer lemma on the audit's completion, legitimacy predicate, pathology predicate, and the two conservativity hypotheses built into the audit record. No Navier–Stokes-specific analysis appears.
why it matters
Feeds the hard-problem audit headline, which conjoins finite-reduction theorems for the four application stubs (prime critical line, Navier–Stokes energy, Yang–Mills gap, Hodge algebraic). The headline doc-comment is explicit: these are audit schemas with concrete finite certificate inventories, not solutions of the underlying continuum problems. In the Recognition Science foundation layer this sits inside the primitive recognition calculus, recording that the Navier–Stokes energy stub is certificate-ready in the same sense as the other three. It does not touch the forcing chain (T0–T8), RCL, or the phi-ladder mass formula; it is organizational scaffolding for hard-problem interfaces.
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