Test for Fundamental Theories

This document introduces an external and theory-agnostic Variational Integrity Test designed to assess whether a given theoretical construction satisfies the minimal requirements of mathematical completeness demanded by a closed variational framework. The test is formulated independently of any specific model and applies uniformly to field theories, effective theories, and foundational proposals. The assessment is based on six non-negotiable criteria: (i) variational closure without externally imposed potentials or background structures; (ii) self-generated operator content with no imported symmetries or ansätze; (iii) intrinsic stability of coherent sectors under second variation; (iv) absence of patchwork renormalization procedures; (v) fully emergent spectral structure derived from functional variation alone; and (vi) emergence, rather than postulation, of all symmetries. Each criterion is binary: failure of any single test implies that the construction is not mathematically self-contained and therefore cannot qualify as a fundamental theory under a closed variational standard. The test does not evaluate phenomenological success, experimental agreement, or interpretive appeal. Its sole purpose is to determine structural admissibility. Applied as a benchmark, the test reveals that most conventional theoretical frameworks operate as open systems dependent on external assumptions, free parameters, imposed symmetries, or ad hoc regularization schemes. Such constructions may remain phenomenologically effective, but they do not satisfy the criteria of variational completeness required for ontological closure. This work does not propose an alternative model, nor does it argue for empirical falsification of existing theories. Instead, it establishes a minimal admissibility filter that any candidate for fundamental physics must pass in order to claim internal mathematical integrity.