PRCPrimeCalibrationForcesPrimeIdentityCanonicalAddTraceTarget_refuted
plain-language theorem explainer
Prime calibration does not force identity orientation to respect the canonical additive orbit-position trace. Native-cost uniqueness and foundation-certificate work cite this as a closed negative target. The proof is a short transfer: an already-refuted branch-uniformity target is equivalent to the canonical-add-trace target, so the latter fails too.
Claim. It is false that every ratio-orbit character $\chi$ that is prime-direction calibrated must have identity orientation transport through the concrete finite common extension $\mathrm{orbitPositionTrace}(p+r)$. Equivalently, the canonical-add-trace forcing target for prime-calibrated characters does not hold.
background
In the Primitive Recognition Calculus, a ratio-orbit character is a map on ratio orbits used to build native cost. Prime-direction calibration is a local orientation condition on prime axes. The canonical-add-trace target asks that, under those hypotheses, identity orientation still respect comparability along the concrete finite common extension given by the orbit-position trace of a sum $p+r$.
A sibling target, branch uniformity, asks the same forcing in a coarser branch-uniform language. Upstream, those two targets are proved equivalent: branch uniformity holds for all such characters if and only if the canonical-add-trace condition does. Separately, branch uniformity is already refuted by an explicit two-adic axis-twist ratio character that is prime-calibrated yet breaks identity-branch uniformity.
This module sits in the native-cost uniqueness layer of the foundation stack: it records which hoped-for forcing routes from prime calibration to a unique native cost actually fail.
proof idea
Term-mode transfer of a prior refutation. Assume the canonical-add-trace target. Apply the reverse direction of the proved equivalence with branch uniformity to obtain the branch-uniformity target. Discharge by the existing theorem that branch uniformity is false, which itself rests on the constructed two-adic axis-twist ratio character. No new counterexample is built here.
why it matters
Closes one concrete forcing route in the native-cost uniqueness program: prime calibration alone does not push identity orientation through the canonical additive finite trace. Downstream, the native-cost uniqueness blocker certificate aggregates such proved and refuted targets; the universal-foundation conditional certificate likewise consumes the uniqueness-layer status. In Recognition terms this is bookkeeping on the cost side of the forcing chain (toward J-uniqueness and the native cost), not a claim about T5–T8 themselves. It tells the auditor which additive-trace strengthening is dead, so later certificates do not reopen it.
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