The optional metric gate is not entered

No finite-mode metric oscillator extension is released in this manuscript. Thus no self-adjoint joint operator ${\sum }_a{\hat{c}}_a\otimes \Phi (v_a)$ is presumed admitted.

Such an extension would require its own domain, self-adjoint realization, state moments, and classical-symbol proof. Physical graviton or constraint compatibility would remain a further identification, and a continuum or sharp-product limit would remain another theorem. B1–B5 do not depend on that optional gate.