Finite specifiability of the ultraviolet formulation of QFT

Determine whether the small-distance (ultraviolet) formulation of realistic quantum field theories is finitely specifiable, specifically whether the bare Lagrangian requires an infinite number of irrelevant terms or admits a finite closed-form description.

Background

The paper discusses that non-renormalizable theories at the smallest scales may require infinitely many terms, raising concerns for reductionists who prefer a finite supervenience base. Even for renormalizable theories, structural features imply infinitely many possible irrelevant terms that could become significant at small distances.

Given current understanding, it is not established whether realistic QFTs at the smallest scales are finitely specifiable. Resolving this would clarify whether an ultraviolet finite basis exists or whether an infinite specification is necessary.