Declarations

of the proofs. All special formulas needed from the supplied companion manuscripts have been written out and proved here. No identification with an unspecified series construction, record observable, or implementation is used.

and computation. No empirical data or numerical integration is used. The existence and nonzero witnesses are analytic. No code execution or successful pdflatex compilation is asserted.

inputs. The only external functional-analytic theorem used to close an operator argument is the stated analytic-vector criterion. The compact-current argument is proved directly from flat wave Green identities. References below identify the standard observable class and perturbative terminology; no supplied companion paper is cited.