prc_universal_foundation
plain-language theorem explainer
The Primitive Recognition Calculus admits a closed universal-foundation certificate: kernel first-pass, promoted reals, trace logic, formal system, inevitability, recognizer bridge, and the native-cost uniqueness ledger are all assembled as one Prop. Anyone citing the PRC foundation stack as finished would point here. The proof is a pure field projection from the already-built conditional certificate.
Claim. There exists a final universal-foundation certificate for the Primitive Recognition Calculus: it packages a kernel first-pass certificate, a promoted complete ordered field of reals, a trace-logic certificate, a formal-system certificate, an inevitability certificate, a recognizer-bridge certificate, a native-cost uniqueness blocker, the repaired/refuted native-cost open-target ledger, the underlying conditional certificate, and a no-project-local-axioms audit.
background
Primitive Recognition Calculus (PRC) is the foundation layer that tries to force the Recognition Science stack from minimal recognition primitives rather than from physics postulates. The module packages that claim as certificate structures: each surface (kernel, reals, trace logic, formal system, inevitability, recognizer bridge, native cost) is a named Prop that must be inhabited.
The final certificate type records both the built surfaces and an exact native-cost ledger. Per its doc-comment, "the repaired signed/prime/zero-calibrated uniqueness route is proved, while the weaker unsigned routes are recorded as refuted targets." Upstream, the Inevitability Theorem states the no-alternatives claim: any zero-parameter framework that derives observables either reduces to RS (same cost and selection) or violates a necessity gate.
The conditional certificate already assembles those fields (kernel first-pass, promoted reals, trace logic, and the rest). This declaration is the unconditional top-level packaging of that bundle.
proof idea
Term-mode structure construction, not a new argument. Every field of the final certificate is filled by projecting the matching field of prc_universal_foundation_conditional_certificate: kernel becomes delta_kernel, then real-complete-ordered-field, trace-logic, formal-system, inevitability, recognizer-bridge, native-cost-blocker, open-targets (as the repaired/refuted ledger), the conditional certificate itself, and the no-project-local-axioms audit. No extra lemmas are applied beyond that projection.
why it matters
This is the top-level close-out theorem for the PRC universal-foundation module: it turns the conditional certificate into the final certificate Prop that the foundation stack presents as finished. The native-cost half is the ledger split already described upstream: repaired signed/prime/zero-calibrated uniqueness is in, weaker unsigned routes stay as refuted open targets rather than silent gaps.
In the broader Recognition Science forcing picture this sits under the foundation/inevitability layer (the "no alternatives" claim), not under a later T5–T8 physics step. It does not itself derive $J$, $\varphi$, the eight-tick octave, or $D=3$; it certifies that the PRC surfaces and cost-uniqueness blocker needed before those steps are packaged. Downstream use count is currently zero, so the declaration is an export boundary rather than an intermediate lemma inside a longer proof chain.
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