Declarations

dependencies. The convolution intertwining identity, zero action identity, positive witness, and real coefficient orbit are copied from X-A–Convolution. They are the classical premises of Options A–D. The ramp coordinate identity and edge integral are separately quoted from Ramp Prescription, Theorem (main) and its edge proposition, for comparison only. No ramp identity is reproved or used as a premise of Options A–D. Landmark I supplies the characterized Enter semantics. The orbit lemma, selective amplitude tests, conditional relational circuit, and quantitative bounds are proved here.

scope. The surjective orbit is an orbit of a first-order evaluated coefficient. The second-order readout test is pointwise in the gauge amplitude. No uniform coupling expansion for unbounded gauge amplitudes and no unquoted all-orders ramp identity is asserted.

boundary. The encodings are explicit mathematical interfaces. No physical device evaluating either external field functional, preparing its encoded state from fields, or supplying the independent reference coefficient is constructed. Reading an already invariant input is distinguished from proving its classical invariance.

identification. The convolution and ramp bibliography entries use separate descriptive manuscript identifiers. Their quoted mathematical premises are reproduced above. Publication dates, definitive titles, and other bibliographic metadata not supplied with those excerpts are not invented.

status. No empirical data, numerical experiment, mechanized verification, or successful source compilation is claimed. The source uses standard {} packages and requires no external graphics or bibliography database.