PRCPrimeFloorSuccessorTransportSharpenedTarget
plain-language theorem explainer
Conjunction packaging the two sharpened prime-floor successor obligations: local nonunit orbit orientation coherence, and no adjacent mixed identity/reciprocal orientations on calibrated ratio characters. Cited by the native-cost uniqueness blocker ledger and by the implication that recovers ordinary successor transport from the split. Definitional pairing only; no new mathematics.
Claim. The sharpened prime-floor successor-transport target is the conjunction of (i) the sharpened local nonunit-orbit product-orientation obligation (nonunit orientation coherence on calibrated ratio characters) and (ii) the obligation that adjacent nonunit orbit directions never carry opposite identity/reciprocal orientations under prime-direction calibration.
background
In the Primitive Recognition Calculus native-cost uniqueness development, ratio characters $\chi$ assign identity or reciprocal orientation along ratio orbits. Prime-direction calibration forces how those orientations sit on prime floors of the orbit lattice. Successor transport is the claim that orientation data on a floor determines the next floor coherently.
Earlier passes bundled local orientation with adjacent no-mixing into a single successor-transport target. Pass-39 splits them. The first conjunct is the Pass-45 product-local orientation sharpening: same-orientation products are algebraic via canonical normalization, and the remaining commitment is nonunit orientation coherence (which implies product no-mixing). The second conjunct states that adjacent nonunit orbit directions cannot carry opposite identity/reciprocal orientations once $\chi$ is a ratio character with prime-direction calibration.
This module sits in the foundation layer that tries to force the native cost (the $J$-cost side of Recognition Composition) uniquely from character/trace data.
proof idea
Pure definitional abbreviation: the target is literally the $\wedge$ of the two named component Props. No tactics, no lemmas applied at this site. Downstream, the recovery theorem assumes the conjunction and feeds the first conjunct into the local-orientation-from-coherence lemma, then applies the local-adjacent-nomix successor-transport lemma to obtain the unsharpened successor-transport target.
why it matters
This is the Pass-39 split of the prime-floor successor blocker inside native-cost uniqueness. It feeds the Pass-25 blocker certificate (exact Lean targets for what remains open), the Pass-27 prime-calibration propagation sharpening (this conjunct plus global coherent-orientation propagation), and the universal-foundation open-target ledger.
A direct refutation theorem shows the conjunction is false by refuting the first conjunct (nonunit orbit product-local orientation). The split therefore isolates a dead route: successor transport cannot be forced by packaging local nonunit orientation with adjacent no-mixing in this form. That negative result is part of closing which character-factorization paths can still force native $J$-cost uniqueness (T5 landmark) versus which are permanently blocked.
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