PRCPrimeCalibrationForcesPrimeIdentityBranchUniformityTarget_refuted
plain-language theorem explainer
Prime direction calibration does not force every native prime axis onto the identity branch for ratio characters. Anyone tracking native-cost uniqueness blockers or the PRC universal-foundation certificate will cite this refutation. The proof is a one-line application of the axis-twist non-implication to an explicitly constructed two-adic twist character.
Claim. The branch-uniformity target fails: it is not true that every ratio character $\chi$ that is prime-direction calibrated is automatically prime-identity branch-uniform (i.e., that calibration of identity-oriented native prime axes forces all native prime axes onto the identity branch).
background
In the Primitive Recognition Calculus, a ratio character is a map $\chi$ on ratio orbits that encodes multiplicative structure used to build native costs. Prime-direction calibration asks that identity-oriented native prime axes behave in a preferred way under $\chi$. Branch uniformity is the stronger demand that calibration on those axes forces every native prime axis onto the identity branch, with no residual twist.
The target proposition packages exactly that implication: for all ratio characters, prime-direction calibration yields prime-identity branch uniformity. It is deliberately trace-free: it does not mention doubled-trace transport or additivity, only the branch assignment of prime axes.
Upstream, a two-adic axis-twist ratio character has already been constructed, and a companion lemma shows that any such twist character is a counterexample to the target. The present declaration simply closes that gap.
proof idea
One-line term proof. Apply the general non-implication lemma (any two-adic axis-twist ratio character falsifies the branch-uniformity target) to the already-constructed witness PRCTwoAdicAxisTwistRatioCharacter_constructed. No further case analysis or algebraic work is done here.
why it matters
This refutation is a structural blocker inside native-cost uniqueness. Downstream it discharges three sibling refutations: the pair-product cost-consistency target, the trace-coherence target, and the canonical add-trace target, each reduced to branch uniformity by an iff. It also feeds the native-cost uniqueness blocker certificate and, through that chain, the conditional universal-foundation certificate.
In the Recognition Science forcing picture, uniqueness of the native cost (and ultimately of $J$ via T5) requires ruling out residual discrete twists on prime axes. Recording that bare prime calibration does not kill the two-adic twist keeps the uniqueness program honest: stronger hypotheses (zero-calibration, signed admissibility, or full trace coherence assumptions) are needed before branch uniformity can be forced.
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