PRCPrimeCalibrationForcesMixedNonunitWitnessesReflectPrimeWitnessesTarget_proved
plain-language theorem explainer
Under prime-direction calibration, every ratio character has the property that its mixed nonunit witnesses reflect onto mixed prime-axis witnesses. Native-cost uniqueness and the prime-witnesses-control step cite this composite bridge. The proof is a one-line application of the split-to-target lemma to the already-proved identity and reciprocal halves.
Claim. For every map $\chi$ on ratio orbits that is a ratio character and is prime-direction calibrated, the mixed nonunit witnesses of $\chi$ reflect down to mixed prime-axis witnesses.
background
In the Primitive Recognition Calculus, cost uniqueness is approached through ratio characters: maps $\chi$ on ratio orbits that encode multiplicative structure compatible with the native cost. Prime-direction calibration restricts how $\chi$ behaves along prime axes of the ratio lattice.
The target here is the reflection form of a composite bridge: mixed nonunit witnesses (composite, non-unit ratio data) must reflect down to mixed witnesses living on the prime axes. The module packages this as a single Prop quantifying over characters that are ratio characters and prime-calibrated.
Upstream, the claim is split into an identity half and a reciprocal half; both halves are already proved, and a bridge lemma reassembles any such split into the composite reflection target.
proof idea
One-line term proof. Apply the bridge lemma that turns a split target into the composite reflection target, feeding it the already-proved split (the pair of identity-half and reciprocal-half theorems). No further case analysis is done at this layer.
why it matters
This closes the mixed-nonunit reflection bridge under prime calibration. Immediately downstream, the prime-witnesses-control theorem is obtained by applying the mixed-reflects-to-control bridge to this result, so prime witnesses control nonunit witnesses once calibration holds.
It is also wired into the native-cost uniqueness blocker certificate and, through that stack, into the conditional universal-foundation certificate. In the Recognition forcing picture this is foundation scaffolding for uniqueness of the native cost (the J-cost side of the T5 uniqueness story), not a direct citation of T5–T8 themselves.
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