Declarations

. The ramp coordinate equations, density coefficients, finite-propagation prescription, kernel identity, pure-gauge law, and edge witness are premises from X-A.tex. The bare tests, scalar algebra, quotient topology, and crude upper-bound interpretation are from X-B-v3.tex. The completed tests, recursion, variation, Ward identity, and sourced diagnostic are from X-C-v3.tex. The supplied VII-C.tex is used only for the copied extension assumptions and comparison.

proof. The rate argument integrates the normal flux before estimating, derives the two exit velocities, propagates their limit, and proves convergence of the completed representatives. The finite second-order layer contribution is retained.

. The Euler coefficients are regulator independent. Green continuity is used with a justified finite seminorm loss, not an assumed universal count. Initial positions and velocities are distinguished. A possibly jumping background kernel is not a singular scalar output test. VII-C's actual quantum product hypotheses are audited without importing a quantum metric.

status. No successful pdflatex execution, proof-assistant check, numerical verification, or independent referee review is claimed. The source requires no external figures, bibliography database, or executable code.