certified_display_audits_headline
plain-language theorem explainer
The four hard-problem display audits (prime critical line, Navier–Stokes energy, Yang–Mills gap, Hodge) each satisfy finite reduction: every admissible display carries an explicit finite certificate. Cite this for the Delta-native bridge shape on those stubs, not as a solution of the problems. The proof is a four-way conjunction applying the generic finite-reduction lemma to each certified display audit.
Claim. The certified display audits for the prime-critical-line, Navier–Stokes energy, Yang–Mills gap, and Hodge algebraic certificates each satisfy finite reduction: each problem audit of a certified display object reduces to a finite certificate check.
background
This module packages certificate audits for four classical hard problems inside the Primitive Recognition Calculus. Each problem is represented by a certificate type (prime critical line, Navier–Stokes energy, Yang–Mills gap, Hodge algebraic) together with a certified display: a non-identity display interface that pairs the certificate with a domain-specific payload and records an explicit finite witness.
Finite reduction is the Quantized Proof Method predicate that a problem audit collapses to a finite certificate check rather than an open-ended analytic obligation. The upstream lemma problemAudit_finiteReduction states that every audit built by the certified-display constructor inherits that property. Display itself, from Hilbert display completion, realizes an $F_{RS}$ amplitude as a finite Hilbert vector, so the certificate side stays finite-dimensional.
Local setting: these audits replace identity stubs with the correct Delta bridge shape. They do not yet encode solutions; they only guarantee that later analytic interfaces sit on a finite-reduction spine.
proof idea
Term-mode four-tuple. Each conjunct is obtained by applying the generic lemma that every certified-display problem audit has finite reduction, once to each of the four audits (prime, Navier–Stokes, Yang–Mills, Hodge). No case analysis or extra hypotheses: the constructor of those audits already matches the lemma’s input shape.
why it matters
This is the headline that the hard-problem stubs now carry non-identity certified displays with finite certificates. Downstream, the strong-closure certificate in Delta-native strong closure assembles the closed Delta-native theorem surface and consumes this conjunction among its certified-analytic and display entries.
In the Recognition framework it is scaffolding hygiene, not a forcing-chain step: it does not touch T5–T8, the RCL, or the mass ladder. It only locks the bridge shape so later domain-specific analytic interfaces (prime, fluids, gauge gap, Hodge) can attach without reopening the finite-reduction obligation. The doc-comment is explicit: still not a solution of the four problems; the correct Delta bridge for those interfaces.
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