PRCPrimeCalibrationForcesNonunitBranchAgreementTarget_of_coherent
plain-language theorem explainer
If prime calibration forces a single coherent orientation on every nonunit orbit direction, then it also forces two-branch agreement across those directions. Anyone assembling the native-cost uniqueness or universal-foundation certificates cites this implication. The proof is a one-line pointwise reduction: apply the given coherence target, then the character-level coherence-to-branch-agreement lemma.
Claim. Assume that every ratio-orbit character $\chi$ that is prime-direction calibrated has a single coherent nonunit orbit orientation (all identity or all reciprocal). Then every such $\chi$ also has nonunit branch agreement: the identity (resp. reciprocal) branch choice at any nonunit direction agrees with the same branch at every other nonunit direction.
background
In the Primitive Recognition Calculus, ratio characters $\chi$ act on ratio orbits and are the algebraic carriers of native cost. Prime-direction calibration is the hypothesis that $\chi$ is pinned on prime generators. Nonunit orbit directions are those not the unit class; each may be oriented either as the identity branch or as the reciprocal branch.
The coherence target asserts that prime calibration forces one global orientation across all nonunit directions (no mixed identity/reciprocal factors). The branch-agreement target is the two-branch form of the same idea: a branch choice at one nonunit direction must match every other nonunit direction, for both branches. The module develops these as Prop-valued targets that feed native-cost uniqueness.
Upstream, the character-level lemma already shows that orbit-orientation coherence of a single $\chi$ implies its nonunit branch agreement. The present declaration lifts that implication from one character to the quantified prime-calibration targets.
proof idea
One-line wrapper. Introduce a character $\chi$ together with the ratio-character and prime-calibration hypotheses. Apply the assumed coherence target at $(\chi,h_\chi,h_{\mathrm{prime}})$ to obtain nonunit orbit-orientation coherence of $\chi$. Feed that into the upstream lemma that coherence implies nonunit branch agreement. The resulting pointwise statement is exactly the branch-agreement target.
why it matters
This closes the gap between the stronger orientation-coherence target and the two-branch agreement target used in the native-cost uniqueness stack. Downstream, the local-branch-agreement packaging theorem applies the same pattern, and the universal-foundation conditional certificate consumes the resulting target chain. In the Recognition forcing picture this is bookkeeping inside the J-cost uniqueness lane (T5): once prime calibration forbids mixed nonunit orientations, branch choices cannot disagree, so the native cost extracted from the character is forced to a single branch normal form. It does not itself prove calibration; it only converts one calibration consequence into another.
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