PRCPrimeCalibrationForcesNonunitNoMixedWitnessesTarget_refuted
plain-language theorem explainer
Prime-direction calibration of a ratio-orbit character does not force the absence of mixed nonunit witnesses (identity-oriented together with reciprocal-oriented). Anyone auditing native-cost uniqueness blockers or the PRC universal-foundation certificate cites this negative result. The proof is a short reduction: the nonunit target is equivalent to the prime-witness target, which is already refuted.
Claim. It is false that every ratio-orbit character $\chi$ that is prime-direction calibrated necessarily satisfies the nonunit no-mixed-witnesses property: that is, prime calibration does not forbid the coexistence of an identity-oriented nonunit witness with a reciprocal-oriented nonunit witness.
background
In the Primitive Recognition Calculus, a ratio-orbit character $\chi$ is a map on ratio orbits obeying the algebraic laws of a recognition character. Prime-direction calibration restricts how $\chi$ orients prime generators. The nonunit no-mixed-witnesses property asks that no such calibrated character admit both an identity-oriented nonunit witness and a reciprocal-oriented nonunit witness at once.
The target proposition packages that hope as a universal claim: every prime-calibrated character is free of mixed nonunit witnesses. A parallel, weaker target asks only that mixed prime witnesses be forbidden. An in-module equivalence identifies the two targets: nonunit no-mixing under prime calibration is equivalent to prime no-mixing under the same calibration.
The prime-witness target has already been refuted upstream. The present declaration lifts that negative result across the equivalence.
proof idea
Assume the nonunit target. Apply the forward direction of the equivalence ...Target_iff_no_mixed_prime_witnesses to obtain the prime-witness target. Discharge the assumption by the already-proved refutation of the prime-witness target. The whole argument is a three-line reduction; no new analytic or combinatorial work appears here.
why it matters
This closes one branch of the native-cost uniqueness blocker stack: the hoped-for forcing from prime calibration to nonunit no-mixed witnesses fails. Downstream, the split-target refutation quotes this lemma directly, and the native-cost uniqueness blocker certificate records related calibration failures as part of its negative ledger. The universal-foundation conditional certificate in UniversalFoundation sits on the same certificate spine.
In the broader Recognition forcing chain, native cost uniqueness is the bridge from the J-cost (T5) and the composition law toward a unique continuum cost. Refuting over-strong calibration claims keeps the uniqueness program honest: only the surviving positive targets (for example zero-calibrated factorization) remain as candidate routes. The result does not touch T6--T8 directly; it prunes a false shortcut inside the PRC uniqueness layer.
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