PRCPrimeCalibrationForcesPrimeIdentityCanonicalAddTraceTarget_of_trace_transport
plain-language theorem explainer
If prime calibration forces identity orientation to be invariant along native prime-axis trace connections, then it also forces identity to transport through the concrete finite common extension orbitPositionTrace(p+r). Anyone closing the native-cost uniqueness or universal-foundation certificates cites this implication. The proof is a one-line application of the already-proved connectivity of the prime-axis trace graph.
Claim. Assume that every ratio character $\chi$ that is prime-direction calibrated has identity orientation invariant along native prime-axis trace connections. Then every such $\chi$ has identity orientation that transports through the concrete finite common extension given by the orbit-position trace of $p+r$.
background
In the Primitive Recognition Calculus, ratio characters $\chi$ act on ratio orbits and encode orientation data used to build native cost. Prime-direction calibration is the hypothesis that $\chi$ is correctly oriented on the prime axis. Two related targets package what calibration should force about identity orientation.
The smaller target (trace transport) asks only that identity orientation be invariant along native prime-axis trace connections; structural connectivity of that graph is already proved in-module. The canonical-add-trace target asks the sharper concrete statement: identity transports through the finite common extension orbitPositionTrace(p+r).
Upstream, PRCCharacterPrimeIdentityRespectsCanonicalAddTrace_of_trace_connected already shows that any character respecting the abstract trace-connected identity property automatically respects the canonical add-trace property, by feeding in the proved connectivity witness for primes $p,r$.
proof idea
Term-mode proof by introducing a character $\chi$ with the ratio-character and prime-calibration hypotheses, then applying the upstream lemma that converts trace-connected identity respect into canonical-add-trace respect. The hypothesis htransport supplies exactly the trace-connected respect for that $\chi$; connectivity of the prime-axis graph is already baked into the upstream lemma, so no further work is needed.
why it matters
This is one direction of the equivalence between the trace-transport target and the canonical-add-trace target (the sibling iff theorem packages both directions). Downstream it feeds the native-cost uniqueness blocker certificate and the conditional universal-foundation certificate, which assemble kernel, ordered-field, and trace-logic obligations for the PRC foundation layer.
In the Recognition Science forcing picture, native cost uniqueness is the bridge from the J-cost functional equation (T5) and the Recognition Composition Law toward a unique cost character on ratio orbits. Closing the prime-calibration identity-transport obligation removes a structural blocker before mass-ladder and constant extractions can be treated as forced rather than postulated.
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