PRCPrimeCalibrationForcesNonunitReciprocalBranchTransportTarget_of_branch_agreement
plain-language theorem explainer
If prime calibration forces two-branch agreement on nonunit directions for every ratio character, then it also forces reciprocal branch transport across those directions. Downstream pair-transport and the universal foundation certificate cite this reduction. The proof is a one-line specialization: apply the character-level reciprocal-from-agreement lemma to the calibrated agreement hypothesis.
Claim. Assume that every ratio character $\chi$ that is prime-direction calibrated has nonunit branch agreement (identity and reciprocal branches agree across all nonunit directions). Then every such $\chi$ has reciprocal branch transport: reciprocal orientation at one nonunit direction transports to every other nonunit direction.
background
In the Primitive Recognition Calculus, ratio characters are maps $\chi$ on ratio orbits that encode multiplicative recognition data. Nonunit directions are the orbits away from the unit class. Branch agreement says that a nonunit branch choice (identity or reciprocal) fixed at one such direction must match the corresponding choice at every other nonunit direction.
The reciprocal transport target is the one-way half of that coupling: if the reciprocal orientation is chosen at one nonunit direction, it must be chosen at all of them. The agreement target packages both identity and reciprocal halves under the hypothesis that $\chi$ is a ratio character and is prime-direction calibrated.
Upstream, the character-level lemma already shows that nonunit branch agreement implies reciprocal branch transport for a fixed $\chi$, by projecting the second component of the agreement pair. This declaration only lifts that implication to the quantified prime-calibration targets.
proof idea
Term-mode one-liner after introducing the character data. Specialize the agreement-target hypothesis at $\chi$, the ratio-character proof, and the prime-direction calibration proof to obtain nonunit branch agreement for that $\chi$. Feed the result into the character-level lemma that extracts reciprocal branch transport from agreement. No extra algebraic work.
why it matters
Closes the reciprocal half of the split nonunit branch-transport targets under prime calibration. The immediate parent pairs this with the identity-transport half to obtain the full branch-transport pair target from agreement alone. That pair target sits on the path into the conditional universal foundation certificate, which assembles kernel, real-complete ordered field, and trace-logic pieces for the PRC foundation stack.
In the broader Recognition Science forcing picture this is bookkeeping inside native cost uniqueness: once prime calibration pins branch choices, reciprocal orientation cannot freeload on a single direction. It does not itself force $J$-uniqueness (T5) or $\phi$, but it removes a blocker on the way to a unique native cost functional compatible with the Recognition Composition Law.
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