{"id":2979,"date":"2026-05-13T12:46:24","date_gmt":"2026-05-13T12:46:24","guid":{"rendered":"https:\/\/coherencegeometry.com\/?p=2979"},"modified":"2026-05-13T13:12:03","modified_gmt":"2026-05-13T13:12:03","slug":"coherence-geometry-foundations-part-i-orientation-closure-and-algebraic-foundations","status":"publish","type":"post","link":"https:\/\/coherencegeometry.com\/index.php\/2026\/05\/13\/coherence-geometry-foundations-part-i-orientation-closure-and-algebraic-foundations\/","title":{"rendered":"Coherence Geometry Foundations, Part I: Orientation, Closure, and Algebraic Foundations"},"content":{"rendered":"\n<p><strong>Internal ID:<\/strong> CGI-BKS-0001<br><strong>Document Type:<\/strong> Book<br><strong>Publication Date:<\/strong> May 2026<br><strong>Status:<\/strong> Public<br><strong>Domains:<\/strong> Mathematics, Physics<br><strong>Research Topics:<\/strong> Dark Energy, Cosmological Constant, DESI<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p><br>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).<\/p>\n\n\n\n<p>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.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Available Document<\/h3>\n\n\n\n<p><strong>DOI:<\/strong> <code>10.5281\/zenodo.20156532<\/code><\/p>\n\n\n\n<p><strong>Citation:<\/strong><br>Petersen, B. L. (2026). Coherence Geometry Foundations, Part I: Orientation, Closure, and Algebraic Foundations, Version 0.1. Zenodo.&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.20156532\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.20156532<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Source Code and Supporting Materials<\/h3>\n\n\n\n<p>N\/A<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary and Notes<\/h3>\n\n\n\n<p><strong>Scope:<\/strong><br>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.<\/p>\n\n\n\n<p><strong>Version note:<\/strong><br>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.<\/p>\n\n\n\n<p><strong>Release purpose:<\/strong><br>This release is intended to make the algebraic and structural core of Coherence Geometry publicly inspectable, citable, usable, and open to correction or extension.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Related Work<\/h3>\n\n\n\n<p><strong>Title: <\/strong><em>Coherence Geometry Foundations, Part II: Physical Projections <\/em><br><strong>Repository<\/strong>: <a href=\"https:\/\/doi.org\/10.5281\/zenodo.20156997\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.20156997<\/a><br><strong>Internal ID:<\/strong> CGI-BKS-0002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>CGI-BKS-0001 | Part I of the Coherence Geometry Foundations working reference text. It 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.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","footnotes":""},"categories":[62,57,30,31],"tags":[],"class_list":["post-2979","post","type-post","status-publish","format-standard","hentry","category-books","category-foundation-texts","category-mathematics","category-physics"],"_links":{"self":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/2979","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/comments?post=2979"}],"version-history":[{"count":4,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/2979\/revisions"}],"predecessor-version":[{"id":2998,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/2979\/revisions\/2998"}],"wp:attachment":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/media?parent=2979"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/categories?post=2979"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/tags?post=2979"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}