Part 9_The Structural Origin of Schrödinger-Type Dynamics from JS–SH Discrete Geometry

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.