PRCPrimeCalibrationForcesNonunitBranchTransportPairTarget_refuted
plain-language theorem explainer
The split target claiming both one-way nonunit branch transports under prime calibration is false. Native-cost uniqueness and universal-foundation audits cite it when closing the nonunit branch-agreement ladder. Proof is a one-line projection: the reciprocal half is already refuted, so the conjunction fails.
Claim. It is not the case that prime calibration forces both one-way nonunit branch transports: the identity-orientation transport target and the reciprocal-orientation transport target cannot both hold.
background
In the Primitive Recognition Calculus, native cost uniqueness is organized around character-trace matching and prime-direction calibration. A recurring pattern is to state a strong "forces transport" target as a Prop, then either prove or refute it.
The pair target is the conjunction of two one-way nonunit branch transport claims: identity-branch transport (identity orientation should respect comparability of finite $\delta$-orbit traces on nonunit directions) and reciprocal-branch transport (the reciprocal orientation analogue). The module treats these as split targets so each half can be attacked separately.
Upstream, the reciprocal half is already refuted: PRCPrimeCalibrationForcesNonunitReciprocalBranchTransportTarget_refuted shows that prime calibration does not force the reciprocal nonunit branch transport, via a two-adic axis-twist character that is prime-direction calibrated yet breaks the reciprocal claim.
proof idea
Term-mode one-liner. Assume the pair target $H$. Project to the second conjunct (reciprocal nonunit branch transport) and apply the already-proved reciprocal refutation. The conjunction is therefore false. No new analytic work; pure logical projection from the reciprocal half.
why it matters
Closes the pair-level nonunit branch-transport claim in the PRC native-cost uniqueness stack. Immediately feeds the next refutation: nonunit branch-agreement is equivalent (via an iff) to the transport pair, so agreement is refuted by applying this result. That ladder sits inside the conditional universal-foundation certificate, which packages kernel, real-complete ordered field, and trace-logic certificates. In framework terms this is housekeeping on the cost-uniqueness side of the forcing chain (J-cost / RCL uniqueness), not a new physical constant: it records that a natural "prime calibration forces both branch transports" strengthening is too strong and must be dropped or replaced.
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