twoAdicGeneratedNativeCost_sans_pair_hypotheses

In the Primitive Recognition Calculus, a native cost is a map $F$ on ratio orbits obeying reciprocity and related ledger axioms (the native-cost hypotheses). The slim sans-pair class keeps those base axioms and adds two calibrations: the signed unit (so $F$ treats $\pm 1$ correctly) and the zero orbit under the doubled-trace display. It deliberately omits the prime-pair product field.

The two-adic generated native cost is built from the two-adic axis-twist character: on the unit orbit it returns zero, and elsewhere it evaluates the character-derived cost. Upstream work already shows this $F$ meets the native hypotheses, calibrates the signed unit, and calibrates zero. The present declaration packages those three facts into the single sans-pair structure.

Term-mode structure construction. The three fields of the sans-pair hypotheses are filled by name: native from the existing native-cost hypotheses theorem for this $F$, signed_unit from the signed-unit calibration theorem, and zero_calibrated from the doubled-trace zero-calibration theorem. No new algebra is done here.

This membership is the positive half of the pair-field necessity argument. Downstream, the uniqueness target for the sans-pair class is refuted by feeding this $F$ into that target and invoking the already-proved failure of prime-pair product calibration at the mixed $(2,3)$ orbit. The doc-comment on the parent states the moral: base + sign + zero admit the two-adic twist, so the pair field cannot be dropped.

In the broader Recognition stack this protects the full native-cost uniqueness story that underwrites the J-cost and the forcing chain (T5 J-uniqueness and the Recognition Composition Law). Without the pair field, a non-J competitor survives the slim axioms.