The gap addressed

The predecessor records already contain destructive clock instruments, reference-preserving routes, and finite adaptive composition patterns. In particular, X-I-ST explicitly permits a finite adaptive tree with fresh or separately returned clock encodings XIST. X-J-ST combines selective coefficient reports with complete instruments and error margins XJST. It would therefore be incorrect to advertise X-K-ST as the first proof that finite instruments compose.

The narrower contribution is an assembled certificate with all of the following data present at once:

1. the types before and after every destructive readout;

2. the provenance of every subsequent clock input;

3. the complete public history and the distinction between public outcomes and unobserved Kraus indices;

4. the actual memory and retained residuals;

5. the causal delivery of every remotely used classical code;

6. a branchwise occupancy and storage ledger;

7. a complete-channel comparison on matching interfaces;

8. an explicit fit inside the unchanged host reserve.

The source comparisons are I-B, En09-A, X-Enter-ST, X-H-ST, X-I-ST, and the supplied X-J-ST development IB,En09,XEnterST,XHST,XIST,XJST. They are documentary precedents, not unexamined theorem premises. The finite formulas needed here are stated and proved below.

The background host and operation permissions are nevertheless explicit assumptions. Calling a citation a separation does not remove a hypothesis actually used in a proof.