Declarations

scope. The analytic predecessor is XIII-C. XIV-A and XIV-B are recorded only and are not hypotheses of any product or extension theorem here.

correction. The full eleven-branch observable is denoted $\mathcal{O}$. The scalar-linear lift ${{\Phi }^{(2)}}_{\mathrm{D}}$ retains its original meaning. The scalar-sourced slot is included once, before any diagnostic calculation.

scope. The branch inventory, primitive extension statements, partial-contact class, tree datum, and support control are copied from the supplied XIII-C handoff. The characteristic rank calculation, conormal relation, explicit component check, and contact-support rigidity are proved here.

scope. No joint characteristic distribution or cancellation theorem for the complete pair is supplied. J3–J5 are not opened. The manuscript is an exact analytic stop report, not a claim of completed renormalization.

scope. No renormalized quantum output, quantum master equation, Ward defect, state, residue subtraction, interacting differential, or sharp-width limit is constructed.

. No successful pdflatex execution, proof-assistant check, independently executed symbolic computation, independent referee review, or journal acceptance is asserted. The new calculations are the displayed analytic ones.