Substrate Physics: A Geometric Origin of Quantum Phase, Gravitation, and Cosmological Structure

We show that Planck’s constant ℏ, the Schr¨odinger equation, the hydrogen spectrum, and the Karlsson cosmological redshift spacing ∆z ≈ 0.089 all emerge from a single geometric object, a periodic one-form bµ, derived from path composition consistency, locality, and single-valued amplitudes. No quantum postulates are assumed. Closed-loop phase winding produces Bohr–Sommerfeld quantization and atomic spectra, while open-path phase accumulation yields statistical redshift clustering. General relativity arises as the isotropic limit bµ -> 0. The theory predicts cross-scale consistency between atomic and cosmological measurements of the same periodicity scale, along with falsifiable signatures including weak equivalence principle violation at the 10−¹⁵ level and directional cosmological anisotropies. Three independent observational channels, equivalence principle measurement (MICROSCOPE), cosmological redshift periodicity scatter (Karlsson statistics), and intergalactic magnetic field bounds (γ-ray cascade), converge on this scale without parameter tuning.