PRCPrimeCalibrationForcesPrimeReciprocalWitnessGlobalizesTarget_refuted
plain-language theorem explainer
Prime calibration does not force reciprocal orientation to spread from one native prime witness to every native prime axis. Anyone auditing native-cost uniqueness blockers or the PRC universal-foundation certificate cites this refutation. The proof is a short reduction: the globalization target is equivalent to the already-refuted no-mixed-orientation target, so it fails as well.
Claim. It is false that every ratio-orbit character $\chi$ that is prime-direction calibrated must satisfy reciprocal-witness globalization: having one reciprocal-oriented native prime witness does not force reciprocal orientation on every native prime axis.
background
In the Primitive Recognition Calculus, a ratio character $\chi$ is a map on ratio orbits encoding how multiplicative structure is read as cost. Prime-direction calibration restricts how $\chi$ orients native prime axes. Reciprocal orientation on an axis means the character treats that prime via the reciprocal branch rather than a mixed or direct-only pattern.
The reciprocal-witness globalization target asserts a strong uniformity: if calibration permits even one reciprocal-oriented native prime witness, then every native prime axis must sit on the reciprocal branch. An equivalent formulation is the no-mixed-prime-orientation target (proved equivalent in-module): calibration cannot leave some primes reciprocal and others not.
That no-mixed target is already refuted upstream. The present declaration simply transfers the refutation across the equivalence, closing one more candidate forcing route toward a unique native cost.
proof idea
Assume the reciprocal-witness globalization target. Apply the left-to-right direction of the in-module equivalence
PRCPrimeCalibrationForcesPrimeReciprocalWitnessGlobalizesTarget_iff_no_mixed_prime_orientation
to obtain the no-mixed-prime-orientation target. Discharge that assumption with the already-proved refutation
PRCPrimeCalibrationForcesNoMixedPrimeOrientationTarget_refuted.
The argument is a pure logical transfer: no new analytic content, only the iff and the prior negation.
why it matters
Native-cost uniqueness in PRC aims to force the J-cost (the unique solution of the Recognition Composition Law, T5) from calibration and character hypotheses alone. Several intermediate "forcing targets" were proposed; this one claimed that a single reciprocal prime witness globalizes under prime calibration. Refuting it removes that route.
Downstream it is recorded in prc_native_cost_uniqueness_blocker_certificate, which packages proved and refuted factorization/calibration targets as a status board for uniqueness work. It also feeds prc_universal_foundation_conditional_certificate in UniversalFoundation, so the conditional foundation stack knows this globalization claim is closed negatively rather than left open.
Within the forcing chain, this sits below T5 J-uniqueness: it is bookkeeping about which prime-orientation constraints can or cannot pin the native cost character, not a derivation of $J$ itself.
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