Corrections and subsequent obligations

Authorization begins only after a surviving complete singularity or a constructed limit is known.

A mathematical singular primitive does not become permitted because it removes a divergent test pairing. The supplied XV-B lifting theorem tests membership in a specified correction image; it does not enlarge that image XVB. The supplied Em01-E authorization theorem also requires reference, support, tensor, growth, microlocal, and overlap conditions EmE. They have not been discharged here.

A fixed-kernel calculation is not an operator theorem. An operator domain must preserve the actual physical relationships responsible for cancellation and must support continuous input seminorm estimates. The reconstruction criterion and an operator Dini interface are retained in Appendix app:upgrades.

A local limit does not by itself give the later joint section, contact compatibility, proper pushforward, output wavefront bound, or observable normalization. In particular,

is not established.

The supplied source comparisons do not identify the application data of Em01-F or Em01-G with the inherited weighted family EmF,EmG. The En01 recorded-circuit and decoherence materials are a different track and are not used as input definitions or premises.

boundary. The source below is self-contained and intended for pdfLaTeX. The proofs are mathematical arguments for the displayed objects. No compiler execution, machine verification, independent symbolic computation, exhaustive corpus search, registration verification, referee approval, or acceptance is claimed.