Declarations

scope. XIII-C supplies the graph inventory, contact class, primitive extensions, characteristic cancellation, and four successor obligations. XIII-B supplies the tree datum, convention, properness, and ordered values. XIII-A and XIII-D supply boundaries only. XII-F's witness is copied and not recomputed.

proof scope. The new results concern the common-frequency family, its finite-regulator kernels, convergence on the admissible sets, auxiliary compact-localization independence, off-collision contact rigidity, and a conditional relative-coordinate endpoint.

scope. No convergence theorem through the full noncoincident characteristic set is asserted. No superficial degree is promoted to a scaling theorem for an undefined distribution. No isolated primitive extension is promoted to a compatible joint extension.

scope. The selected regulator does not change the frozen action inverse, the insertion sign, the Wick combinatorics, or the external backgrounds. Its positive-regulator tails are not called exact causal factorization. Ordered values are obligations of the limit.

. No successful pdflatex execution, proof-assistant check, independently executed symbolic computation, independent referee review, or journal acceptance is asserted. The manuscript releases the stated partial proofs and an explicit unresolved joint gate, not a completed quantum construction.