PRCPrimeCalibrationForcesGlobalOrientationTarget_of_prime_orientation_targets
plain-language theorem explainer
Prime cost calibration forces a single global cost orientation on every ratio orbit, once two sharper blockers hold: calibration makes all native prime axes share one orientation, and that coherent prime orientation propagates to every composite ratio. Anyone assembling the native-cost uniqueness certificate or the sharpened propagation target cites this. The proof is pure composition: apply the coherence blocker, then the propagation blocker.
Claim. Assume that every ratio character $\chi$ whose prime directions are cost-calibrated is coherent on native primes (all identity or all reciprocal). Assume further that every such character with coherent prime orientation has global cost orientation on every ratio orbit. Then every prime-calibrated ratio character has global cost orientation: for all $\chi$, if $\chi$ is a ratio character and is prime-direction calibrated, then $\chi$ is globally cost-oriented.
background
In the Primitive Recognition Calculus, cost uniqueness is obstructed by orientation freedom: a multiplicative character $\chi$ on ratio orbits can invert some prime axes independently while preserving prime costs, yet break composite costs. The module isolates this as a propagation blocker.
Three Prop-targets package the obstruction. The coherent-prime target says prime calibration forces one shared orientation on every native prime axis (ruling out mixed independent prime inversions). The propagation target says that once primes are coherent, the multiplicative character law and native rational factorization push that orientation to every ratio direction. The global target is their composite: prime calibration alone yields global cost orientation.
Upstream docs fix the meaning: blocker A is "the place where mixed independent prime inversions must be ruled out"; blocker B requires that "the multiplicative character law and native rational factorization must propagate that orientation to every ratio direction." The global target warns that without it, "independent prime inversions can preserve prime costs while breaking composite costs."
proof idea
Term-mode composition, three lines. Introduce a ratio character $\chi$ together with the ratio-character and prime-calibration hypotheses. Apply the coherent-prime target to obtain prime-orientation coherence, then feed that into the propagation target to conclude global cost orientation. No extra algebraic work: the two named hypotheses are chained by function application.
why it matters
This is the glue step that turns the two sharpened orientation blockers into the single global orientation target used by the uniqueness pipeline. Downstream, PRCPrimeCalibrationPropagationTarget_of_sharpened_orientation applies it (via the global-orientation route) to discharge the older propagation target from the sharpened package. The native-cost uniqueness blocker certificate also sits on this chain: without global orientation forced by prime calibration, composite cost matching can fail even when primes match.
In Recognition Science terms this protects the J-cost uniqueness story (T5 / RCL): the cost functional on ratio orbits must not admit independent prime-axis flips. Closing the orientation gap is a prerequisite for claiming a unique native cost character before constants and the phi-ladder are read off.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.