Theorem: X-Enter-ST release

Under Assumptions ass:host and ass:convolution, at fixed positive width:

1. full witness-orbit invariance of any scalar-only encoded complete output implies independence from that scalar;

2. the retained amplitude family has the selective visibility-or-erasure criterion, explicit discrepancy (eq:TV), and second-order diagnostic;

3. the finite supplied-evaluation dictionary has a complete destructive-clock instrument, including all unmeasured finite residuals and untouched references;

4. the relational combination and CNOT–Hadamard instrument are proved under the separate reference hypothesis, but that hypothesis is not supplied;

5. the bounded-segment trade-off is proved under an additional amplitude restriction not implied by support;

6. the ramp identity, ramp edge integral, and convolution gap retain their different prescriptions and quantifiers;

7. scheduled locality and regular reference-preserving transport hold with the resource and error contracts above.

The package is local Grade S.

No field-to-qubit preparation, independently charged second coefficient, convolution repair, interacting differential, or inherited characteristic quantum coefficient is constructed.

Proof. Theorem thm:orbit proves (i). Theorem thm:amplitude, equation (eq:TV), and Theorem thm:secondorder prove (ii). Theorem thm:clock and equation (eq:combined) prove (iii), with its interpretation limited by Proposition prop:noacquisition. Proposition prop:matching and Theorem thm:relational give exactly the conditional conclusion in (iv). Proposition prop:nocutoff and Theorem thm:tradeoff prove (v). Proposition prop:rampseparation proves (vi). Theorems thm:locality and thm:route, with (eq:errors), prove (vii). None of these constructions has the input or codomain of an excluded operation.