PRCPrimeCalibrationForcesNonunitOrbitOrientationLocalComparableTraceTarget_of_identity_comparable_trace
plain-language theorem explainer
Prime calibration that forces identity orientation to respect finite δ-orbit trace comparability on nonunit directions already yields the full local-orientation-plus-comparable-trace target. Native-cost uniqueness and universal-foundation certificates cite this packing step. The proof is a one-line pair: derive local orientation from the identity law, then conjoin the hypothesis.
Claim. If prime calibration forces identity orientation to respect comparability of finite $\delta$-orbit traces on nonunit directions, then it forces the conjunction of (i) local nonunit orbit orientation under prime calibration and (ii) that same identity comparable-trace law.
background
In the primitive recognition calculus, ratio characters $\chi$ assign orientations on ratio orbits. Prime-direction calibration restricts how $\chi$ behaves on prime generators. The identity-branch comparable-trace target asserts that any such calibrated character respects comparability of finite $\delta$-orbit traces on nonunit directions: identity orientation cannot mix incomparable traces.
The full target packaged here is the conjunction of that identity law with local nonunit orbit orientation (every nonunit direction admits a coherent local branch choice). The module treats the identity-transport half as interchangeable with finite $\delta$-trace comparability, so the conjunction is the trace-layer form of the active local identity-transport goal.
Upstream, a sibling theorem already derives local orientation from the identity comparable-trace hypothesis by reducing to a proved local prime-orientation fact and a product-local orientation lemma.
proof idea
Term-mode pair constructor. The goal is a conjunction. The left conjunct is obtained by applying the upstream theorem that turns the identity comparable-trace hypothesis into local nonunit orbit orientation. The right conjunct is the hypothesis itself. No further rewriting or case analysis.
why it matters
Closes one direction of the iff equating the full orientation-plus-comparable-trace target with the bare identity comparable-trace target, so later certificates may assume either form. Feeds the native-cost uniqueness blocker certificate (factorization and signed-admissible refutation side) and the universal-foundation conditional certificate (kernel, real complete ordered field, and trace-logic bundle). In the Recognition forcing chain this sits inside native J-cost uniqueness infrastructure that supports T5-style cost uniqueness and the Recognition Composition Law, without yet discharging the identity law itself.
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