CertifiedDisplay
plain-language theorem explainer
Pairs a finite certificate with a continuum-side payload so hard-problem displays carry native witnesses. Auditors of prime, Navier–Stokes, Yang–Mills, and Hodge certificate pipelines cite it as the display carrier. It is a two-field product structure with no proof obligations.
Claim. A certified display is a pair $(c, p)$ where $c$ is a finite certificate of type $\mathrm{Cert}$ and $p$ is a continuum/display payload of type $\mathrm{Payload}$. The certificate is the native witness that authorizes the display object.
background
In the Primitive Recognition Calculus, continuum statements are not taken as primitive. Native data live on the finite side; continuum objects appear only as displays of that data. The upstream completion interface packages this: a map from native $N$ to display $D$, together with a relation saying which certificates cover which displays.
This structure is the concrete display type used by the hard-problem certificate audits. The certificate field is the finite witness (prime critical line, energy bound, mass gap, Hodge algebraicity, etc.). The payload is an analytic tag on the continuum side. Authority flows only through the certificate, not through the payload.
The module sits in the foundation layer that audits Millennium-style claims by reducing them to finite certificates and conservative completions, rather than by open continuum arguments alone.
proof idea
No proof. Two-field structure declaration: a certificate component and a payload component, with automatic Repr. Downstream, the completion map sends a certificate $c$ to the pair $(c, \mathrm{default})$ and certifies a display $d$ exactly when $c = d.\mathrm{cert}$.
why it matters
This is the display carrier for the hard-problem audit stack. It feeds the certified-display completion, the trivial legitimacy/pathology predicates, and the generic certified-display audit, which specialize to prime, Navier–Stokes, Yang–Mills, and Hodge audits.
Those audits are the module’s bridge from finite certificates to continuum-facing claims under a conservative completion. The structure itself does not solve any hard problem; it standardizes how a finite witness is attached to a display object so conservativity and audit lemmas can be stated uniformly.
In the broader Recognition framework this matches the pattern that continuum geometry and analysis are displays of ledger-level finite structure (forcing chain, eight-tick octave, $D=3$), not independent primitives.
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