PRCPrimeCalibrationForcesTwoPrimeBranchControlsPrimesTarget_refuted
plain-language theorem explainer
Prime calibration of ratio characters does not force the branch chosen at the distinguished orbit 2 to control every native prime branch. Researchers tracking native-cost uniqueness blockers in the Primitive Recognition Calculus cite this as a closed negative. The proof is a short reduction through an equivalence to a previously refuted identity-iff-two target.
Claim. It is false that every ratio character $\chi$ which is prime-direction calibrated has the property that the branch chosen at the orbit of $2$ controls every native prime branch.
background
In the Primitive Recognition Calculus, ratio characters are maps on ratio orbits that encode admissible multiplicative structure for native cost. Prime-direction calibration is a normalization that fixes orientation data along prime axes. The target proposition asserts a strong normal form: once a character is so calibrated, the branch choice at the distinguished orbit of $2$ would determine the branch on every native prime.
That claim is one of several equivalent "blocker" formulations standing between local calibration hypotheses and uniqueness of the native cost. An upstream equivalence identifies it with the identity-iff-two target: prime calibration forces identity orientation on an arbitrary prime axis exactly when it forces identity on the orbit-$2$ prime axis. The identity-iff-two form is already refuted upstream, so the two-prime-branch-controls form falls with it.
The local module develops native-cost uniqueness infrastructure (doubled-trace d'Alembert structure, character-trace matching, and a lattice of calibration targets). This declaration sits in the negative half of that lattice: it records that a particular forcing claim does not hold.
proof idea
Term-mode one-liner. Assume the two-prime-branch-controls target. Apply the forward direction of the recorded equivalence to obtain the prime-identity-iff-two target. Discharge by the already-proved refutation of that identity-iff-two target. No new analytic or combinatorial work occurs here; the content is pure transport along the iff.
why it matters
This closes one normal form of the prime-calibration blocker in the native-cost uniqueness program. Downstream, the coherent-prime-orientation target is refuted by the same pattern: reduce via its own equivalence to this statement, then apply the present refutation. The native-cost uniqueness blocker certificate aggregates such proved and refuted targets into a single structured witness used by the universal-foundation conditional certificate.
In framework terms the result is negative bookkeeping inside the foundation layer that prepares J-cost uniqueness and the forcing chain, not a direct hit on T5--T8. It tells the auditor which calibration slogans cannot be assumed when arguing that the native cost is forced. The open residual is whatever remains after the blocker certificate is fully assembled: which positive factorization or orientation claims still hold under weaker hypotheses.
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