Theorem: X-K-ST mathematical release

For the retained host of Assumption ass:host:

1. each declared destructive clock has the complete channel identity of Theorem thm:oneclock;

2. every finite well-typed instruction certificate has the complete adaptive history law (eq:completehistory);

3. no later quantum use of a clock follows from the consumed name or from its classical record;

4. the regular route is the identity on the entire payload–reference state, while remote use of a record requires its own readiness certificate;

5. every fitting certificate stays on the same host, chart, signature ledger, fixed positive width, and regulator;

6. the complete network obeys scheduled locality, and metric containment follows only from its separately certified causal edges;

7. matched complete-channel errors obey (eq:telescope) and the adaptive bound (eq:patherror); specified-input trace errors have only the qualified state-specific conclusion;

8. the explicit two-readout, two-route experiment has the complete law (eq:twoclock), the stated nonzero failure branch, and the proved finite resource requirements;

9. no classical obstruction, sharp-limit question, BV transport problem, or characteristic quantum admission is repaired by the composed instrument.

A resource-fitting instance with these data is local Grade S. It is not continuum field acquisition, not gravity-generated entanglement, not a Page curve, not ultraviolet completion, and not spacetime emergence.

In particular, it is not quantized relational time without an external clock or external scheduling time.

Proof. Theorem thm:oneclock proves (i). Theorem thm:compose proves (ii), and its type audit with Proposition prop:noreturn proves (iii). Theorem thm:route and Definition def:readiness prove (iv). Theorem thm:noenlarge proves (v). Theorem thm:locality proves (vi). Theorems thm:error and thm:adaptiveerror, with Proposition prop:stateerror, prove (vii). Theorem thm:twoclock and Corollary cor:examplefit prove (viii). Section sec:boundaries records precisely the non-interference in (ix).

The external-time limitation follows from the declared inputs and Section sec:time; no stronger physical identification appears in the construction.