PRCPrimeCalibrationForcesCoherentPrimeOrientationTarget_refuted
plain-language theorem explainer
Prime-direction calibration of a ratio-orbit character does not force one coherent orientation on all native prime axes. The universal claim that every calibrated character is orientation-coherent is false. Native-cost uniqueness and blocker-certificate work cite this. Proof reduces via an equivalence to the already-refuted two-prime branch-control target.
Claim. It is not the case that every ratio-orbit character $\chi$ which is prime-direction calibrated is necessarily prime-orientation coherent. Equivalently, prime cost calibration does not force a single coherent orientation across all native prime axes.
background
In the Primitive Recognition Calculus, a ratio-orbit character $\chi$ is a map on ratio orbits encoding multiplicative structure used to build native costs. Prime-direction calibration means the character has been fixed so that each native prime axis has a chosen branch (direction). Orientation coherence is the stronger demand that those branch choices agree globally: one coherent orientation across all native primes, with no mixed independent prime inversions.
The target proposition asserts that calibration alone forces that coherence for every such character. Its doc frames it as "sharper orientation blocker A": the place where mixed independent prime inversions must be ruled out if uniqueness is to go through in that form.
Upstream, the same module proves an equivalence between this coherent-orientation target and a two-prime branch-control target (the distinguished-prime normal form: the branch at orbit $2$ controls every native prime branch). That two-prime form is already refuted.
proof idea
Term-mode reduction in three steps. Assume the coherent-orientation target. Apply the forward direction of the equivalence ...Target_iff_two_prime_branch_controls to obtain the two-prime branch-controls target. Discharge by the prior refutation of that two-prime target. No new arithmetic or character construction appears here; the work is pure logical transport along the iff.
why it matters
This closes one link in the native-cost uniqueness blocker chain: a proposed forcing principle (calibration implies coherent prime orientation) does not hold. Downstream, the no-mixed-prime-witnesses target is refuted by the same pattern, reducing through an iff to this result. The native-cost uniqueness blocker certificate aggregates such proved and refuted targets to record what uniqueness can and cannot claim. The universal-foundation conditional certificate also depends on this module's certificate surface.
In Recognition Science terms this sits in foundation work on native cost uniqueness (J-cost / character-trace side), not in the T5–T8 forcing chain itself. It clarifies that prime-axis orientation coherence is not automatic from calibration, so uniqueness arguments must either weaken the claim or add hypotheses that rule out mixed inversions by other means.
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