PRCPrimeFloorSuccessorTransportLocalAdjacentTarget
plain-language theorem explainer
The local adjacent form of the prime-floor successor blocker is the conjunction of two calibration demands: prime calibration orients every nonunit orbit direction locally, and adjacent nonunit directions never mix identity with reciprocal orientation. Native-cost uniqueness work cites it as the Pass-39 sharpening that unbundles successor transport into those two facts. The body is a pure Prop conjunction with no proof content.
Claim. The local adjacent prime-floor successor target holds precisely when both of the following are true: (i) every prime-calibrated ratio character orients all nonunit orbit directions locally, and (ii) under that calibration, no adjacent pair of nonunit orbit directions carries opposite identity/reciprocal orientations.
background
In the Primitive Recognition Calculus, a ratio character assigns an identity-or-reciprocal orientation along each ratio orbit. Prime-direction calibration already fixes the character on prime axes; the remaining question is how far that forces orientation on the rest of the nonunit lattice.
The first conjunct is the local nonunit-orientation target: prime calibration should orient every nonunit orbit direction, not only prime axes. The second is the adjacent no-mixing target: adjacent nonunit orbit directions cannot carry opposite identity/reciprocal orientations. The module packages these as separate Lean targets rather than a single bundled successor-transport claim.
This sits in the native-cost uniqueness program, which reduces uniqueness of the RS cost $J(x)=(x+x^{-1})/2-1$ (the T5 J-cost) to exact named Prop targets instead of one closed theorem.
proof idea
Definitional conjunction only. The target is the meet of the local nonunit-orientation target and the prime-floor no-adjacent-mixed-orientation target. There is no tactic proof and no lemma application; downstream results project the pair or rebuild successor transport from it.
why it matters
Pass-39 refinement of the corrected successor blocker: it separates local nonunit orientation from adjacent no-mixing instead of bundling both under successor transport. Downstream, it feeds the native-cost uniqueness blocker certificate and the bridge theorems that recover prime-floor successor transport and nonunit orientation coherence from the local adjacent form (including the iff with the coherent-orientation target). It is packaging infrastructure on the path toward T5 J-uniqueness, not a closed uniqueness proof.
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