PRCPrimeCalibrationForcesNonunitOrbitOrientationLocalBranchAgreementTarget_refuted
plain-language theorem explainer
Prime calibration does not force local orientation of nonunit orbits together with two-branch agreement. That conjunction is the positive normal form of the global nonunit branch-coupling blocker in the PRC native-cost uniqueness chain. Anyone auditing which calibration targets survive would cite this. The proof is a short reduction through an equivalence to the already-refuted local identity-transport form.
Claim. It is false that prime calibration forces both local orientation on nonunit orbits and two-branch agreement. Equivalently, the positive normal form of the global nonunit branch-coupling blocker fails.
background
In the Primitive Recognition Calculus, native-cost uniqueness is organized around a ladder of calibration targets. Several of those targets encode hoped-for consequences of prime calibration on nonunit orbits: local orientation, branch agreement, identity-branch transport, and comparable-trace conditions.
The target refuted here is defined as the conjunction of local orientation on nonunit orbits with two-branch agreement. Its module doc calls that conjunction the positive normal form of the global nonunit branch-coupling blocker. A sibling equivalence identifies it with the local identity-transport form: reciprocal transport is said to follow once orientation and identity-branch transport are in hand.
Upstream, the identity-transport form is already refuted by reduction to a comparable-trace blocker. The present statement sits one step above that refutation in the same normal-form chain.
proof idea
Term-mode one-step reduction. Assume the branch-agreement target. Apply the forward direction of the equivalence that identifies branch agreement with local identity transport, obtaining the identity-transport target. Discharge by the already-proved refutation of that identity-transport target. No new analytic work; pure propositional transport along the normal-form iff.
why it matters
Closes one more positive normal form in the PRC native-cost uniqueness blocker ladder: local orientation plus two-branch agreement cannot be forced by prime calibration. Downstream it is consumed by the conditional universal-foundation certificate in UniversalFoundation, which assembles kernel, real-complete ordered field, and trace-logic certificates. In the broader Recognition forcing picture this is housekeeping inside the foundation layer that underwrites J-uniqueness and the native cost, not a direct T5–T8 step. It narrows which calibration consequences remain open versus already eliminated.
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