On the Structural Necessity of Effective Field Theory

Effective Field Theory (EFT) is the empirically dominant grammar of stable physics: finite parameterization, local generators, systematic suppression of higher operators, and symmetry-organized operator algebras. Unified Substrate Theory (UST) constrains physics as an admissibility protocol: stable description must be invariant under admissible regeneration (coarse-graining), preserve diagnostic completeness, and satisfy conservative infrared closure. A stable macroscopic regime is definable only as a fixed-point equivalence class of admissible regeneration, invariant up to finite reparameterization. A grammar-level necessity theorem is established: any UST-admissible fixed-point regime must be EFT-class. The core step is a distribution-support theorem: invariance (modulo a finite-dimensional reparameterization span) under a rich family of approximate identities forces the generator kernels to be supported on the coincidence diagonal, hence to be finite sums of derivatives of delta distributions. Therefore the generator is a finite-order local differential operator density and admits an EFT operator expansion. Apparent nonlocalities in effective functionals (e.g. massless logarithms) are admissible when arising from local generators by integrating out propagating degrees of freedom without introducing new independent diagnostics.