PRCPrimeFloorSuccessorTransportLocalAdjacentTarget_refuted
plain-language theorem explainer
The local prime-floor successor-transport target is false: local nonunit orbit orientation cannot hold together with adjacent no-mixing under prime calibration. Native-cost uniqueness and universal-foundation certificates cite this refutation as a closed blocker. The proof is a one-step transport through an equivalence to a previously refuted coherent-orientation target.
Claim. The conjunction of (i) local nonunit orbit orientation forced by prime calibration and (ii) absence of adjacent mixed orientations on the prime floor is false.
background
In the Primitive Recognition Calculus, native cost uniqueness is blocked by a family of orientation and transport targets on the prime-calibrated orbit. The local adjacent target packages two demands: local nonunit orbit orientation, and no mixed orientation between adjacent prime-floor cells. Its doc-comment calls this "the exact local version of the corrected successor blocker," separating local orientation from adjacent no-mixing rather than bundling both under successor transport.
An in-module equivalence identifies this local adjacent package with the coherent nonunit-orbit orientation target. That coherent target is already refuted upstream by reduction to a failed identity-witness globalization. The present declaration simply closes the local adjacent form of the same blocker.
proof idea
Assume the local adjacent target. Apply the forward direction of the equivalence PRCPrimeFloorSuccessorTransportLocalAdjacentTarget ↔ PRCPrimeCalibrationForcesNonunitOrbitOrientationCoherentTarget to obtain the coherent orientation target. Discharge by the already-proved refutation of that coherent target. Pure transport; no new arithmetic.
why it matters
Closes one concrete successor-blocker leaf in the native-cost uniqueness ledger. Downstream, prc_native_cost_uniqueness_blocker_certificate aggregates proved and refuted factorization targets into a single certificate object; this refutation supplies a negative leaf of that ledger. The same certificate chain feeds prc_universal_foundation_conditional_certificate in UniversalFoundation, which packages kernel, real-complete ordered field, and trace-logic passes. Within the forcing picture, native cost uniqueness sits under the J-uniqueness and Recognition Composition Law layer (T5/RCL): ruling out mixed prime-floor orientations keeps the cost character from admitting non-native factorizations. No open scaffold remains on this particular target.
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