Part 7The Structural Origin of Schrödinger-Type Dynamics from JS–SH Discrete Geometry

https://youtu.be/3N50JTbbfFQ?si=bk9fy8oYstDMtDQF Updated Zenodo Description (Revised) This work derives a Schrödinger-type evolution equation from first principles, starting exclusively from a discrete structural framework composed of JS-cells and SH-hub couplings.No quantum-mechanical postulates, complex wavefunctions, canonical quantization rules, or predefined physical constants are assumed at any stage. Each JS-cell carries a minimal two-channel real internal state, and neighboring cells interact locally through SH-hubs.Imposing a single universal requirement — strict conservation of a global quadratic structural norm — uniquely constrains the admissible dynamics. From these premises, we derive a discrete structural master equation, governing real two-channel wave–rotation dynamics above the Schrödinger level.This master equation is closed, local, norm-preserving, and fully defined at the discrete level, without reference to complex amplitudes or quantum axioms. We show that: Norm preservation enforces an internal SO(2)SO(2)SO(2) symmetry, The unique generator of this symmetry is a real antisymmetric matrix JJJ, Complex numbers and phase emerge only as a compact notation for this real rotational structure, Local SH-hub connectivity forces a discrete Laplacian form, The ordered continuum limit uniquely selects a first-order conservative time evolution. Only at the final stage is the resulting continuum equation identified as belonging to the Schrödinger universality class, as a structure-hiding, long-wavelength, phase-open limit of the underlying master dynamics.Planck’s constant, mass, and potential appear as emergent structural parameters, fixed by discrete spatial and temporal scales rather than postulated a priori. The derivation is non-circular, fully constructive, and independent of standard quantum axioms.An explicit numerical implementation confirms exact norm preservation and Schrödinger-class dispersion directly from the discrete update rule. In addition to the main theoretical manuscript, a companion predictive and validation paper is provided, which develops falsifiable higher-order corrections beyond the Schrödinger limit (including quartic dispersion terms), identifies concrete experimental platforms, and supplies reproducible numerical codes for direct testing. Together, these works provide a structural explanation for why Schrödinger dynamics exists, rather than assuming it as a foundational principle.