The Past-Completeness Theorem

This work establishes a structural restriction on homogeneous classical gravity under finite quadratic closure. Assuming classical covariance, finiteness of a conserved quadratic field norm, orthogonality of response sectors, and homogeneous–isotropic symmetry, it is shown that admissible gravitational configurations cannot terminate at a finite past time. The result is classificatory rather than dynamical: finite-time past boundaries are excluded by incompatibility with admissibility once symmetry exhausts functional freedom, independently of particular field equations, matter models, or phenomenological cosmological assumptions. The document is presented as a standalone theorem and serves as a priority-asserting pre-publication.