PRCTwoCalibrationForcesPrimeCalibrationTarget_refuted

In the Primitive Recognition Calculus, ratio characters are maps $\chi$ on ratio orbits that preserve the multiplicative structure used to build a candidate native cost via costFromCharacter. Calibration means the character-derived cost agrees with the native cost on a given orbit (cross-equality of ratio orbits). The orbit $2$ is the distinguished two-adic direction; prime orbits such as the three-step orbit are independent axes under unique factorization of distinction naturals.

Sharper target A asserts that two-calibration alone already forces calibration on every prime direction. The module treats this as the exact control gap: independent prime axes are not yet pinned by the two-point data. A concrete witness is the three-to-five rebase character, which rewrites rational ratios by a $3\mapsto 5$ rebase and remains a ratio character that is two-calibrated.

Upstream facts used here: $3$ is a prime orbit, the rebase map is a ratio character and two-calibrated, and its cost fails cross-equality on the prime-$3$ direction.

Assume the target proposition. Instantiate it at the three-to-five rebase character, feeding the already-proved facts that this map is a ratio character, is two-calibrated, and that the three-orbit is prime. The target then yields prime-direction calibration for that character. That conclusion contradicts the lemma that the rebase character is not calibrated on the prime-$3$ direction. Hence the target is false. The argument is a pure counterexample discharge: no algebraic expansion beyond applying those five named facts.

This refutation is the first mixed-composite cut in the two-adic obstruction story: calibration at $2$ does not police the prime-$3$ axis, so native-cost character rigidity cannot be obtained from two-calibration alone. Downstream, the sharpened rigidity target is refuted by projecting to this conjunct, and the native-cost uniqueness blocker certificate records the obstruction for the foundation stack. The universal-foundation conditional certificate consumes that blocker surface when stating what remains open.

In Recognition Science terms, J-uniqueness (T5) and the Recognition Composition Law still force the cost shape once a genuine native character is fixed; the gap exposed here is only about which calibration data pin that character on the rational lattice. Closing uniqueness therefore needs either stronger prime-axis control or a different calibration package than two-point data at orbit $2$.