CertifiedDisplayPathology
plain-language theorem explainer
The pathology predicate on certified displays is the constantly true proposition: every continuum-facing display that carries a finite certificate satisfies it. Audit and conservativity lemmas for the certified-display completion cite this as the pathology slot. The body is the one-line constant True, so there is nothing to prove.
Claim. For certificate and payload types $C$ and $P$, and for any certified display $d$ (a pair of a finite certificate in $C$ and a continuum payload in $P$), the pathology predicate on $d$ holds identically: it is $\top$.
background
In this module, hard-problem claims are audited by pairing a finite native certificate with a continuum-facing display object. A certified display is exactly that pair: a structure with fields cert (the finite witness) and payload (the analytic/display-side tag). The certificate gives the display its authority; the payload is only a tag for the continuum side.
Audits are packaged as a completion map from certificates to certified displays, together with two predicates on the display side: a legitimacy predicate and a pathology predicate. Conservativity then asks that those predicates pull back correctly along the completion. The CKM-style Cert structure upstream is one example of a finite certificate type that can fill the certificate slot, but the pathology definition here is parametric in any certificate and payload types.
Local setting: Primitive Recognition Calculus certificate audits for continuum hard problems, with finite witnesses controlling display objects.
proof idea
Definitional, not a proof. The predicate ignores its certified-display argument and returns the constant proposition True. No lemmas are applied; unfolding the definition is the entire content.
why it matters
Fills the pathology slot of the certified-display audit bundle. Downstream, certifiedDisplayAudit wires this predicate in as pathology, alongside the completion map and the legitimacy predicate, so the audit record is complete. The companion theorem certifiedDisplay_conservative then shows conservativity of both legitimacy and pathology along the certified-display completion; the pathology half is immediate once the predicate is constantly true.
In the Recognition foundation layer this is scaffolding for hard-problem certificate hygiene (prime critical line, Navier–Stokes energy, Yang–Mills gap, Hodge algebraicity appear as sibling audit targets). It does not itself encode a physical law from the forcing chain; it only standardizes how continuum displays are marked pathological when the native witness is finite.
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