A Unified Generative Theory of Crystal Formation via Pivot–Hole Geometry and D-Modules

This paper presents a unified generative theory of crystal formation integrating pivot–hole geometry, D-modules, torsion, Frobenius angles, and derived layering, reconstructing band structures as spectral data and formalizing crystal generation as a derived functorial process.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-25
DOI
https://doi.org/10.5281/zenodo.22087280
Primary Topic
Quasicrystal Structures and Properties
Type
article
Field-Weighted Citation Impact
0.00
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article

A Unified Generative Theory of Crystal Formation via Pivot–Hole Geometry and D-Modules

Shin Tamaki
Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
article

A Unified Generative Theory of Crystal Formation via Pivot–Hole Geometry and D-Modules

Shin Tamaki
article en

Abstract

This paper presents a unified generative theory of crystal formation integrating pivot–hole geometry, D-modules, torsion, Frobenius angles, and derived layering, reconstructing band structures as spectral data and formalizing crystal generation as a derived functorial process.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 22%
Quasicrystal Structures and Properties
DOIOpen Access PDFOpenAlex
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