PRCPrimeCalibrationForcesPrimeIdentityWitnessExcludesReciprocalTarget_iff_no_mixed_prime_orientation

In the Primitive Recognition Calculus, a ratio character $\chi$ assigns to each ratio orbit another orbit and is required to behave like a multiplicative character on the native cost side. Prime-direction calibration means that on each prime axis the character is forced to pick a consistent orientation: either the identity orientation or the reciprocal orientation.

Two target propositions package what prime calibration is supposed to enforce. The no-mixed target says calibration forbids independent mixed identity/reciprocal choices on different prime axes. The one-sided witness-exclusion target says that once any identity-oriented prime witness exists, no reciprocal-oriented prime witness may remain. Both are universal statements over characters $\chi$ that are ratio characters and prime-direction calibrated.

This module develops native-cost uniqueness by reducing candidate cost functionals to doubled-trace d'Alembert data and then constraining prime orientations. The two targets above are intermediate blockers in that reduction chain.

Term-mode Iff constructor. The forward direction applies the already-proved implication from identity-witness exclusion to no-mixed orientation (introduces $\chi$, the character and calibration hypotheses, then invokes the character-level no-mixed lemma). The reverse direction applies the dual implication from no-mixed orientation to identity-witness exclusion, again discharging at the character level. No new algebra is done here; the declaration only records that the two targets are interchangeable.

Native-cost uniqueness needs a clean accounting of which prime-orientation constraints are the same proposition under different packaging. This equivalence lets later certificates and refutations move freely between the one-sided witness-exclusion form and the global no-mixed form.

Downstream, the refutation of the identity-witness-exclusion target routes through this Iff and the already-refuted no-mixed target. A sibling Iff then chains reciprocal-witness globalization through the same no-mixed core. The native-cost uniqueness blocker certificate and the conditional universal-foundation certificate sit further up the same dependency cone.

In the broader Recognition forcing picture this is bookkeeping inside the cost-uniqueness layer that feeds J-uniqueness (T5) and the Recognition Composition Law, not a new physical constant claim. It closes a scaffolding seam: two named targets are now known to be the same obstruction.