Coherence Geometry Foundations, Part I: Orientation, Closure, and Algebraic Foundations

Internal ID: CGI-BKS-0001
Document Type: Book
Publication Date: May 2026
Status: Public
Domains: Mathematics, Physics
Research Topics: Dark Energy, Cosmological Constant, DESI

Abstract

This document is Part I of the Coherence Geometry Foundations working reference text. It develops the orientation, closure principles, projection language, and algebraic foundations of Coherence Geometry (CG).

Part I introduces multi-phase numbers, shared-amplitude phase structure, mathematical closure, projection, coherence relations, coherence matrices, coherence manifolds, projective coherence objects, morphisms, operators, and the canonical convergence and stability results governing coherent systems.

Available Document

DOI: 10.5281/zenodo.20156532

Citation:
Petersen, B. L. (2026). Coherence Geometry Foundations, Part I: Orientation, Closure, and Algebraic Foundations, Version 0.1. Zenodo. https://doi.org/10.5281/zenodo.20156532

Source Code and Supporting Materials

N/A

Summary and Notes

Scope:
This volume develops the internal algebraic and structural framework of CG. It does not attempt to contain the full set of physical or applied projections. Later volumes and related research papers develop projections into physical, informational, computational, and other domain-level settings.

Version note:
This is Version 0.1 of a working reference text. It has not undergone external editorial review or peer review. Terminology, organization, examples, derivations, and explanatory framing may be revised in later versions.

Release purpose:
This release is intended to make the algebraic and structural core of Coherence Geometry publicly inspectable, citable, usable, and open to correction or extension.

Related Work

Title: Coherence Geometry Foundations, Part II: Physical Projections
Repository: https://doi.org/10.5281/zenodo.20156997
Internal ID: CGI-BKS-0002