PRCPrimeCalibrationForcesNonunitIdentityComparableTraceTarget_of_local_comparable_trace
plain-language theorem explainer
From the sharpened local package that pairs nonunit orbit orientation with identity-comparable finite δ-trace law, the identity-comparable-trace half drops out at once. Cited by anyone wiring nonunit coherence into native-cost uniqueness or the universal-foundation certificate. Proof is pure second-conjunct projection of the conjunction hypothesis.
Claim. If the prime-calibration package that forces both local nonunit orbit orientation and identity-respect for comparable finite $\delta$-orbit traces holds, then for every ratio-orbit map $\chi$ that is a PRC ratio character and is prime-direction calibrated, $\chi$ respects comparability of finite $\delta$-orbit traces on nonunit identity branches.
background
In the Primitive Recognition Calculus, cost uniqueness is attacked at the character/trace layer rather than by raw functional equations alone. A PRC ratio character is a map on ratio orbits encoding admissible multiplicative structure; prime-direction calibration restricts how that character behaves along prime generators.
The identity-comparable-trace target is the trace-order sharpening of nonunit identity-branch transport: under prime calibration, identity orientation must respect comparability of finite $\delta$-orbit traces on nonunit directions. The local package packages that law with a local nonunit orbit-orientation target, replacing raw identity-transport by its equivalent finite $\delta$-trace comparability law.
This module sits in the native-cost uniqueness development that feeds the Recognition Composition Law and J-cost uniqueness chain (T5), where character/trace coherence is the bridge from discrete recognition steps to a unique native cost.
proof idea
One-line wrapper. The hypothesis is definitionally a conjunction whose second factor is exactly the identity-comparable-trace target. The proof is the second projection of that conjunction; no further lemmas are applied.
why it matters
Closes the easy direction of the local-package iff identity-comparable-trace equivalence in the same module, so either formulation can be used as the active nonunit-coherence hypothesis. Downstream it is consumed by the native-cost uniqueness blocker certificate and by the universal-foundation conditional certificate, which assemble kernel, ordered-field, and trace-logic pieces into a single foundation package.
In the broader RS forcing picture this is scaffolding hygiene on the path to unique native cost (and thus to J-uniqueness / RCL), not a new physical law. It keeps the trace-layer formulation interchangeable with the identity-transport formulation without reopening the calibration hypotheses.
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