Declarations

scope. XII-F's witness and remainder are copied with their hypotheses. XII-E supplies the assembled coefficient and the differentiable completion formulas. XII-D supplies the inherited roots and causal plateau proposition. XII-A-v2 supplies the product, full-shell ideal, brackets, and ordering class. XI-B supplies the free normalization and differential. The commutator, compact detecting smearings, new-ideal obstruction, and rank-one ordering calculation are proved here.

correction. The defect set is indexed by the frozen observation, switch, and parameter region. Its strictness is asserted only for detecting data. Properness of ${\mathcal{C}}_W$ and failure of the naive quantum quotient hold for every nonempty $W$.

scope. The conditional cocycle equation requires a specified representation preserving the equation ideal. Constant compact metric translations do not supply that representation. No conclusion about every possible reduction or completion is claimed.

. The manuscript is a standalone analytic proof relative to its stated inputs. No successful pdflatex execution, proof-assistant verification, independently executed symbolic computation, independent referee review, or journal acceptance is asserted.