PRCPrimeCalibrationForcesNonunitOrbitOrientationLocalIdentityTransportTarget_of_local_comparable_trace
plain-language theorem explainer
Under prime calibration, the trace-layer nonunit package (local orbit orientation plus finite δ-trace comparability) already yields the identity-branch transport package. Anyone assembling the minimal positive normal form for nonunit coherence cites this one-way lift. The proof is a pair constructor: keep orientation and convert the second conjunct by the comparable-trace-to-identity-branch lemma.
Claim. If prime calibration forces every nonunit orbit to admit a local orientation and the finite $\delta$-trace comparability law holds on the identity branch, then prime calibration also forces the identity-branch transport law. Equivalently: the trace-layer local package implies the identity-transport local package (local orientation is unchanged; comparability upgrades to transport).
background
In the Primitive Recognition Calculus native-cost uniqueness development, nonunit coherence is packaged in two equivalent local normal forms. The identity-transport form asks for local orbit orientation together with identity-branch transport; the doc-comment calls this "the minimal positive normal form: reciprocal transport follows from these two facts."
The trace-layer form keeps the same orientation conjunct but replaces identity-branch transport by its equivalent finite $\delta$-trace comparability law. That swap is deliberate: comparability is the finite, checkable statement one proves first, while transport is the form consumed by later global coherence arguments.
Upstream, the identity half is already discharged: from the comparable-trace target one obtains the identity-branch transport target by applying the characterwise lemma that turns finite $\delta$-trace comparability into branch transport on each nonunit prime-calibrated character.
proof idea
Term-mode pair construction on the two conjuncts of the target. The hypothesis is a conjunction of local orbit orientation and the comparable-trace target. The first component is copied unchanged into the identity-transport package. The second component is obtained by applying PRCPrimeCalibrationForcesNonunitIdentityBranchTransportTarget_of_comparable_trace to the comparable-trace half, which itself reduces pointwise to the character lemma converting finite $\delta$-trace comparability into identity-branch transport. No extra orientation or calibration work is done here.
why it matters
This is one arm of the local equivalence between the identity-transport package and the trace-layer package. Downstream, the matching converse is paired with it to give the full iff, so either normal form may be used interchangeably when assembling nonunit coherence.
The same target feeds prc_universal_foundation_conditional_certificate in UniversalFoundation, which bundles kernel, real complete ordered field, and trace-logic certificates into the conditional universal-foundation certificate. In the broader Recognition forcing chain this sits inside the native-cost uniqueness route that pins the J-cost and the calibrated nonunit orbit structure before global composition laws are invoked.
It does not itself prove orientation or comparability; it only upgrades an already-proved trace package to the transport package consumers expect.
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