A Causality–Stability Tester for Field Theories

CST (Causality–Stability Tester) is a gate-based tool paper for screening candidate field theories on a Minkowski background. The method reduces viability to auditable checks on the quadratic action and/or principal symbol: (i) symbol/units hygiene, (ii) variational well-definition, (iii) constraint/DOF sanity, (iv) ghost freedom (positive kinetic matrix), (v) gradient stability and hyperbolicity (well-posed initial value problem), (vi) tachyon/mass stability with explicit time-scale reporting, and (vii) optional luminality diagnostics.This release includes a Minkowski-specialized formalism (Fourier-mode dispersion relations) and worked benchmark classifications (Klein–Gordon, ghost scalar, Maxwell, Proca, k-essence). Output is PASS/FAIL with explicit failure localization. CST is designed to function as a “viability compiler” for theory building and as a reproducible pre-check for any model that will later be confronted with data.