PRCPrimeCalibrationForcesPrimeIdentityCommonTraceExtensionTarget_refuted
plain-language theorem explainer
Prime calibration of a ratio character does not force identity orientation to respect a witnessed common finite δ-trace extension. Anyone auditing which native-cost uniqueness targets fail cites this negation. The proof is a short transport: the common-extension target is equivalent to the trace-coherence target, already refuted upstream.
Claim. It is false that every ratio-orbit map $\chi$ that is a ratio character and is prime-direction calibrated has identity orientation respecting an explicitly witnessed common finite $\delta$-trace extension.
background
In the Primitive Recognition Calculus native-cost uniqueness module, candidate cost characters on ratio orbits are constrained by calibration and trace-transport axioms. A ratio character is a structure-preserving map on ratio orbits; prime-direction calibration fixes how that character behaves on prime generators.
The target being negated is the sharper trace-transport demand: prime calibration should force identity orientation to respect an explicitly witnessed common finite $\delta$-trace extension. Upstream, that common-extension target is proved equivalent to a coarser trace-coherence target, and the coherence form is already refuted by reduction to a failed branch-uniformity target.
Local setting: native cost uniqueness tries to pin the Recognition cost (the $J$-cost lineage) by forcing character identity from calibration hypotheses. This declaration records that one concrete forcing route is blocked.
proof idea
Assume the common-trace-extension target. Apply the reverse direction of the proved equivalence …TraceCoherenceTarget ↔ …CommonTraceExtensionTarget to obtain the coherence target, then invoke the already-proved coherence refutation. Pure transport of a negation across an iff; no new analytic work.
why it matters
Closes one named forcing route in the native-cost uniqueness ledger: the sharper common finite $\delta$-trace extension demand under prime calibration is false. Downstream it feeds prc_native_cost_uniqueness_blocker_certificate, which packages proved versus refuted factorization and calibration targets, and appears in the conditional universal-foundation certificate chain.
In framework terms this is housekeeping inside the foundation layer that eventually supports $J$-uniqueness (T5) and the Recognition Composition Law, not a direct derivation of $\phi$, the eight-tick octave, or $D=3$. It tells auditors which identity-forcing sketch cannot be the uniqueness proof, so effort shifts to surviving targets (for example zero-calibrated factorization routes still marked proved in the blocker certificate).
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