A Groupoid-Level Equivalence of Phase, Null, and Galois Structures

We show that layered circle, null, and Galois structures become isomorphic groupoids within a reduced model. Using pushout encounters and a discrete pivot, phase geometry, causal propagation, and Galois symmetry collapse into a single algebraic pattern.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-25
DOI
https://doi.org/10.5281/zenodo.22086753
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
article
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article

A Groupoid-Level Equivalence of Phase, Null, and Galois Structures

Shin Tamaki
Zenodo (CERN European Organization for Nuclear Research)
Homotopy and Cohomology in Algebraic Topology
article

A Groupoid-Level Equivalence of Phase, Null, and Galois Structures

Shin Tamaki
article en

Abstract

We show that layered circle, null, and Galois structures become isomorphic groupoids within a reduced model. Using pushout encounters and a discrete pivot, phase geometry, causal propagation, and Galois symmetry collapse into a single algebraic pattern.

Zenodo (CERN European Organization for Nuclear Research)
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Homotopy and Cohomology in Algebraic Topology
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A Groupoid-Level Equivalence of Phase, Null, and Galois Structures — Shin Tamaki · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS