Declarations

and attribution. The author is Ngo Cheung. The analytical source results are attributed by manuscript identifier and version. The supplied X-A-ST and X-B-ST documents are cited as the predecessor manuscripts actually used, without retaining their inconsistent empty-author boilerplate.

. The underlying scalar response construction is credited to X-C and situated within the established quadratic-field and perturbative-agreement literature. The contribution claimed here is the supported completion, explicit inherited-domain ledger, and normalization, sign, defect, and finite-interface audit.

scope. The quantum field is the scalar on the flat completion. Metric coefficients remain classical and off shell. The completed background identity is through ${\kappa }^2$ on the frozen group. No general time-ordered product family is constructed.

scope. Enter consumes a finite clock encoding of supplied evaluations. No continuum-field acquisition, microscopic relativistic gate Hamiltonian, hardware synthesis, or thermodynamic implementation is derived.

status. Internal source records are cited without invented publication dates or DOIs. Comparison records do not become premises through shared terminology. The standing analytical stops are version-qualified, not a claim to have rescanned or verified the entire series.

. No successful execution, proof-assistant check, symbolic-program execution, numerical evaluation, hardware synthesis, experiment, independent referee review, or journal acceptance is asserted. The claimed mathematical results are the explicit definitions and written proofs above.