recovers

The module sits in the Primitive Recognition Calculus (PRC) layer of Foundation: native costs on ratio orbits, selected by minimality and uniqueness under signed admissibility. The base two-calibration is the ratio orbit $2$ (numerator the signed orbit of two, denominator the unit distinction). Pair fields supply the two-point character data that, after a case split, force prime-axis calibration.

Signed-admissible rigidity is the existing constraint that admissible signed native costs cannot freely rescale per prime once the global calibration is fixed. Zero-calibration means the cost vanishes at the neutral/unit orbit, so residual freedom is only in how primes are weighted. The local uniqueness target packages these constraints into a single proposition that the selected native cost is the canonical $J$-type cost on the ratio lattice.

Upstream scaffolding in the same file includes the pair/two case split and the lemma that character pair plus two-calibration forces prime calibration; those are the substantive inputs this recovery step consumes.

No separate proof body is attached at the declaration site (zero-line body in the render). Mathematically the step is a recovery bridge, not a fresh computation: apply the pair/two case split, invoke the sibling that character-pair data plus base two-calibration force per-prime calibration, then close with the already-proved signed-admissible rigidity for the zero-calibrated strengthened native-cost class. The lemma therefore packages those reductions into the uniqueness-target language used by the proved uniqueness theorem in the same module.

Native-cost uniqueness is the PRC-side reason the Recognition Composition Law cost $J(x)=(x+x^{-1})/2-1$ (T5) is the selected ledger cost rather than an arbitrary prime-weighted variant. Recovering per-prime calibration from only pair-field data and the base two-orbit removes residual gauge freedom before mass-ladder and coupling extractions.

Downstream, the same uniqueness package is cited across Constants (alpha residual load), Cosmology (graded-rung and polarized birth costs, neighborhood Euler corrections), and further Foundation arithmetic/winding developments. In the forcing chain this is pre-physics bookkeeping: it locks the cost functional that later feeds $\phi$-ladder rungs, eight-tick structure, and $D=3$ gap identities. Sibling refutations of stronger unsigned or non-zero-calibrated targets mark the boundary of what can be forced.