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

Authors: Hong, Seunghyun;

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

Abstract

https://youtu.be/3N50JTbbfFQ?si=bk9fy8oYstDMtDQF https://youtu.be/wXldrl2Fbv8?si=I2Du3bGhogWu1AWk 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.

Keywords

Phase emergence, Mathematical physics, Discrete geometry, Schrödinger equation derivation, Schrödingen, Emergent quantum mechanics, Structural dynamics, Quantum foundations, Discrete-to-continuum limit

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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