No ultraviolet completion of the supplied series

An ultraviolet application would need a named high-energy theory, a low-energy target, matching observables and states, a regulator and renormalization prescription where relevant, approximation topology, error or remainder control, and symmetry compatibility. A scale-to-conformal statement about an already supplied QFT does not construct that package for another model.

The prepared-source and reduced-sector records XVI-A, XVI-H, XVI-I, and XVI-P retain their stated domains and imported hypotheses CheungXVIPrepared,CheungXVIP. A witness, compact kernel, extension family, two-point sector, or graph inventory is not the missing complete ultraviolet matching theorem.

The source's improvement cannot alter the hypotheses or prepared insertion of the conditional XVI-N obstruction CheungXVIN. The same word “massless” does not identify its observable with the free scalar of Section sec:stage5.