PRCPrimeCalibrationForcesPrimeIdentityBranchUniformityTarget_of_trace_coherence
plain-language theorem explainer
If prime calibration forces identity orientation to propagate across prime-axis traces, then it also forces every identity-oriented native prime axis to place all native prime axes on the identity branch. Cost-uniqueness and universal-foundation certificates cite this implication. The proof is a one-line lift of the pointwise coherence-to-uniformity lemma through the shared character and calibration hypotheses.
Claim. Assume that every ratio-orbit character that is prime-direction calibrated is prime-identity trace-coherent. Then every such character is prime-identity branch-uniform: whenever a native prime axis is identity-oriented, all native prime axes lie on the identity branch.
background
In the primitive recognition calculus, ratio-orbit characters $\chi$ encode how multiplicative structure on ratio orbits is read. Prime-direction calibration fixes the preferred orientation of native prime axes. Two residual targets remain after that calibration: trace coherence (identity orientation propagates along prime-axis trace connections) and branch uniformity (an identity-oriented native prime axis forces every native prime axis onto the identity branch).
The module packages those residual obligations as propositional targets. Trace coherence is the stronger local transport property; branch uniformity is the global, trace-free consequence one wants for native-cost uniqueness. Upstream, the pointwise lemma already shows that any single character that is prime-identity trace-coherent is automatically prime-identity branch-uniform (the proof is just reapplication of the coherence hypothesis).
proof idea
Term-mode one-line lift. Introduce a character $\chi$ together with the ratio-character and prime-direction-calibration hypotheses. Apply the assumed target to those data to obtain pointwise trace coherence of $\chi$. Feed that into the upstream lemma that converts prime-identity trace coherence into prime-identity branch uniformity. No extra algebraic work.
why it matters
Closes one direction of the equivalence between the two residual prime-calibration targets, which is recorded immediately downstream as the iff linking branch-uniformity and trace-coherence targets. That equivalence feeds the native-cost uniqueness blocker certificate and, through the same module chain, the conditional universal-foundation certificate. In the Recognition forcing picture this is bookkeeping on the way to a unique native cost (the J-cost of T5), not a new physical law: it shows the global branch-uniformity obligation is no stronger than the already-isolated trace-coherence obligation once prime axes are calibrated.
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