PRCPrimeCalibrationForcesNonunitNoMixedWitnessesTarget_of_identity_witness_excludes

In the Primitive Recognition Calculus, a ratio character $\chi$ is a map on ratio orbits that encodes how recognition cost transforms under multiplicative structure. Prime-direction calibration fixes the orientation of $\chi$ along prime generators so that local sign/orientation choices cannot freely flip when witnesses are globalized.

Two witness-side targets appear here. The one-sided exclusion target asserts that, once $\chi$ is a ratio character and prime-calibrated, any identity-oriented nonunit witness rules out every reciprocal-oriented nonunit witness. The existential no-mixed-witnesses target is weaker in surface form: it only forbids simultaneous existence of one identity-oriented and one reciprocal-oriented nonunit witness. Both are quantified over all such calibrated characters.

Upstream, the character-level lemma already shows that identity-witness exclusion implies no mixed witnesses for a fixed $\chi$. This declaration lifts that implication to the quantified prime-calibration targets used by the native-cost uniqueness certificate stack.

Term-mode specialization, not a new argument. Introduce an arbitrary ratio character $\chi$ together with the hypotheses that it is a ratio character and prime-direction calibrated. Apply the assumed target hypothesis to obtain identity-witness exclusion for that $\chi$. Then invoke the character-level theorem that identity-witness exclusion implies no mixed witnesses, and discharge the goal. No extra algebraic identities or case splits appear.

This is one direction of the equivalence between the one-sided exclusion target and the existential no-mixed-witnesses target under prime calibration. The sibling iff theorem packages both directions; the native-cost uniqueness blocker certificate and the universal-foundation conditional certificate sit downstream of that witness-split infrastructure.

In the Recognition framework the point is orientation hygiene: prime calibration is meant to strip local orientation out of witness globalization so that cost uniqueness cannot be spoiled by mixed identity/reciprocal nonunit witnesses. That hygiene feeds the PRC path toward a unique native cost functional, which is the foundation-layer counterpart of J-uniqueness (T5) and the Recognition Composition Law. The declaration itself is a proved bridge, not an open scaffold; it closes the target-level implication once the character-level exclusion lemma is in hand.