Declarations

and attribution. The author name follows the supplied X-D-ST and X-E-ST source metadata. The action and three-tree mechanism are attributed separately to Cheung's X-E and X-F. No priority claim is made for those parent results.

status. The supplied adaptations, rendered parent records, and documentary comparisons are distinguished. No publication date, DOI, registration, or external proof verification is invented for an internal manuscript. The X-G variational caution is used at the level of the supplied record; the local formal-adjoint calculation is proved here.

scope. The construction is a finite-order, fixed-width polynomial response calculation on the completion. Classical backgrounds remain off shell. There is no all-order, loop, sharp joint-metric, or characteristic cross-line admission theorem.

scope. A finite dictionary encodes supplied evaluations. The clock consumes finite names, not geometric time. Transport uses declared regular finite-operation permissions and preserves existing reference correlations.

. No successful execution, proof-assistant verification, numerical evaluation, symbolic-program execution, hardware synthesis, repository installation, independent execution, experiment, independent referee review, or journal acceptance is asserted. The mathematical release consists of the explicit definitions and written proofs in this source.