Double-Slit Interference and Feynman Path Integrals from the UCM Membrane Network: Schrödinger's Equation Without Postulates

UCM Paper 36 (Theoretical). Derives the Schrödinger equation from the UCM substrate action in the non-relativistic limit (Theorem 1). The Feynman path integral is identified with the sum over membrane phase paths (Proposition 2). Double-slit interference follows from instantaneous membrane phase propagation (κₘem >> κcell, Paper 31): both slits simultaneously acquire the global phase pattern without hidden variables (Proposition 3). The de Broglie relation follows from the dispersion relation; confirmed against the Davisson-Germer experiment at 0. 1%. The substrate quantum mass m₀ = E_Λ/c² is the U-cell rest mass; composite particle masses arise from substrate binding energy. UCM preprint series on Zenodo, ORCID 0009-0005-5088-4339.