Declarations

scope. The new coefficients are compact classical response moments on smooth off-shell scalar data. Their independence and local charges are proved explicitly. No new interacting action, fourth-order completion, Koszul–Tate resolution, physical cohomology, or interacting free-carrier transport is claimed.

scope. The finite instruments are specified on supplied register inputs, all declared selective outputs, and untouched references. They do not acquire the input coefficient from a continuum field or derive a microscopic detector.

. The classical vertex and BV interface are those of the supplied X-I-ST source. The amplitude and conditional phase-instrument mechanisms are credited to X-Enter/X-Enter-ST. The present continuation constructs the explicit moment pair, its independent charges and local matching boundary, and the failure-retaining finite-dictionary assembly.

. No successful execution, numerical quadrature, symbolic-program execution, proof-assistant verification, hardware implementation, repository registration, independent execution, independent referee approval, or journal acceptance is asserted. The source is standalone and intended for pdfLaTeX; the mathematical claims are the written proofs above.