PRCPrimeCalibrationForcesTwoPrimeIdentityTraceConnectedTarget_of_prime_identity_trace_transport
plain-language theorem explainer
If prime calibration already forces identity orientation to stay invariant along native prime-axis trace connections, then it also forces identity at the orbit-2 prime axis to transport along any finite δ-trace link to a native prime. Native-cost uniqueness and reciprocal-transport blocker arguments cite this reduction. The proof is a one-line specialization of the general prime-identity transport hypothesis to the two-orbit case.
Claim. Assume that every ratio character that is prime-direction calibrated has identity orientation invariant along native prime-axis trace connections. Then every such character has identity orientation at the orbit-$2$ prime axis transporting along any finite $\delta$-trace connection to a native prime axis.
background
In the Primitive Recognition Calculus, a ratio character is a map on ratio orbits encoding orientation and scaling data for the native cost. Prime-direction calibration pins that character on native prime axes. Trace connections are finite $\delta$-trace paths in the prime-axis graph; identity orientation along those paths is the content of the prime-identity transport target.
The two-prime target is the same demand specialized at the orbit-$2$ prime axis: identity there must travel along any witnessed finite $\delta$-trace connection to a native prime. Pass 81 treats this as the reciprocal-transport blocker seen through reciprocal twist. The structural connectivity of the prime-axis trace graph is already available upstream; what remains is the calibration-to-invariance implication.
The smaller target (prime-identity transport under calibration) is the hypothesis here. An upstream specialization lemma already shows that any character obeying full prime-identity trace respect automatically obeys the two-prime form, by instantiating the general statement at the two-orbit.
proof idea
Term-mode reduction in three steps. Introduce a ratio character $\chi$ together with the ratio-character and prime-direction-calibration hypotheses. Instantiate the assumed prime-identity transport target at $(\chi,h_\chi,h_{\mathrm{prime}})$ to obtain prime-identity trace respect for $\chi$. Feed that fact into the upstream specialization lemma, which turns prime-identity trace respect into two-prime identity trace respect by restricting the general connection statement to the two-orbit. No extra algebraic work.
why it matters
This is one direction of the equivalence between the two-prime identity trace-connected target and the smaller prime-identity trace-transport target. That equivalence collapses two blocker formulations into one obligation inside native-cost uniqueness.
Downstream it appears in the native-cost uniqueness blocker certificate and in the conditional universal-foundation certificate, so discharging (or assuming) the smaller transport target automatically discharges the two-prime form used in those packages. In the Recognition forcing chain this sits in the foundation layer that pins the native $J$-cost before T5 uniqueness and the RCL are available as physics-facing statements; it does not itself force $J$, $\varphi$, or dimension, but clears a named obstruction on the path to a unique native cost character.
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