Declarations

correction. The production specification identified the two relative transverse directions with clean excess two before checking clean matching. This identification is replaced by the proved rank-two tangent-defect statement. The frozen pair, propagators, source, and ambiguity class are not changed.

scope. Only XIV-E, XIV-D, XIV-C, XIII-C, XIII-B, XII-E, and XII-C are analytic manuscript inputs. Their quoted handoffs retain their predecessor scope. Recorded classical boundaries and the prior regulator attempt are not product, phase, or subtraction data.

calculus. Definitions of clean matching and composition excess are used to test the stated geometric construction. No clean-composition, paired-distribution, stationary-phase, or extension theorem is invoked with unchecked hypotheses. The new results are the displayed intrinsic geometric proofs.

of exclusion. The exclusion concerns direct clean-excess-two composition of the specified unrepaired fiber product. It is not a universal obstruction to every paired representation or characteristic prescription, and it does not prove nonvanishing of the complete six-branch amplitude.

scope. The differentiated source is the actual density-weighted Euler source. No layer coefficient or lower-order term is set to zero, and no hidden internal vertex is identified with a retained external point.

scope. No characteristic distribution, renormalized quantum coefficient, Ward defect, interacting differential, state, numerical loop value, or sharp-width limit is constructed.

. No successful pdflatex execution, proof-assistant verification, independently executed symbolic computation, independent referee review, or journal acceptance is asserted. The mathematical release consists of the displayed proofs and the explicit unresolved composition gate.