PRCPrimeCalibrationForcesGlobalOrientationTarget_refuted
plain-language theorem explainer
Prime-direction calibration of a ratio character does not force one coherent global cost orientation on all native primes. Researchers tracking native-cost uniqueness blockers in the Primitive Recognition Calculus cite this negative result. The proof is pure modus tollens: the global-orientation target implies the already-refuted prime-calibration propagation target.
Claim. It is false that every ratio-orbit character $\chi$ which is calibrated on prime directions necessarily has coherent global cost orientation: the same polarity on every native prime direction (identity throughout, or reciprocal throughout).
background
In the Primitive Recognition Calculus, costs on ratio orbits are read through characters $\chi$ on ratio orbits. Prime-direction calibration means the character matches a fixed convention on each native prime axis. Global cost orientation means one coherent polarity on every native prime: all identity, or all reciprocal.
The module asks whether native cost uniqueness follows from local prime data alone. The target proposition asserts that prime calibration already forces global orientation. Its documentation calls this a sharper propagation blocker: without that coherence, independent prime inversions can preserve prime costs while breaking composite costs.
Upstream, the same module proves that the global-orientation target would imply the weaker prime-calibration propagation target, and that the propagation target is already false.
proof idea
Assume the global-orientation target holds. Feed that hypothesis into the implication that derives the prime-calibration propagation target from global orientation: any prime-calibrated character would then satisfy the propagation rules. The propagation target has already been refuted by a prior theorem in the same module. Contradiction. The argument is a one-step modus tollens chain with no fresh case split.
why it matters
This refutation belongs to the native-cost uniqueness blocker stack. Downstream it is consumed by the native-cost uniqueness blocker certificate and, through that lineage, by the conditional universal-foundation certificate. In Recognition Science terms it separates local prime calibration from global cost coherence: uniqueness of the cost $J$ (forcing step T5, via the Recognition Composition Law) cannot be recovered from prime-axis data alone. The remaining open move is which extra global hypothesis restores uniqueness without overconstraining characters.
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