PRCPrimeCalibrationForcesNonunitOrbitOrientationLocalProductNoMixedTarget
plain-language theorem explainer
Conjunction target packaging two prime-calibration obligations: local orientation of every nonunit ratio orbit, and a product law forbidding mixed identity/reciprocal factor orientations. Native-cost uniqueness work cites it as a product-layer sharpening of global nonunit coherence. The body is the plain logical and of those two component Props; downstream lemmas recover coherence from it, and a separate theorem refutes the package.
Claim. The statement that prime calibration of a ratio character forces both (i) a local orientation on every nonunit ratio orbit and (ii) the product no-mixed-orientation law (no mixed identity/reciprocal factor orientations under native multiplication).
background
In the Primitive Recognition Calculus, a ratio character $\chi$ assigns to each ratio orbit another orbit, subject to multiplicative structure. Prime-direction calibration means $\chi$ is fixed on prime axes in a preferred way. The local-orientation target asks that this calibration orient every nonunit orbit, not only primes. The product no-mixing target asks that under native multiplication, factors never pair an identity orientation with a reciprocal one.
The module tracks native-cost uniqueness via exact Lean targets rather than a single closed theorem. Global nonunit orientation coherence is the stronger surface goal; the doc-comment frames this definition as a product-layer sharpening once local orientation is already on the table, so branch coupling is carried by the no-mixing law alone.
Upstream, the first conjunct is the local nonunit orientation obligation under prime calibration; the second is the product no-mixing obligation under the same hypotheses.
proof idea
Definitional abbreviation only: the Prop is the conjunction of the local nonunit-orbit orientation target and the orbit product no-mixed-orientation target. No tactics or lemmas; the two conjuncts are named component targets already defined in the same module.
why it matters
Sits in the native-cost uniqueness blocker ledger: the pass-25 certificate splits unfinished uniqueness work into exact targets, and this package is one of them. Reduction theorems show that assuming the conjunction yields both the local-plus-no-mixed target and the global nonunit orientation coherence target (via the local-and-no-mixed coherence lemma). A dedicated refutation theorem then shows the conjunction is false, feeding the universal-foundation open-target ledger's negative entries for routes that cannot force the final surface. In the Recognition forcing picture this is bookkeeping on character orientation before J-cost uniqueness (T5) and the RCL can be pinned to a single native cost; it does not itself force $\phi$ or the eight-tick structure.
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