Fixed-regulator theorem boundary

-regulator theorem boundary{ Every theorem in this manuscript concerns the fixed nonzero $\epsilon$ in (eq:epsrange). No limit as $\epsilon \to 0$, no topology for that limit, and no identification with a sharp Cauchy insertion are asserted.

The result neither constructs nor obstructs a boundary algebra. It does not alter VII-C, identify the regulated coordinates with an IX kernel, or use a $2+1$-dimensional cone model.}