{"id":2728,"date":"2026-05-09T09:56:50","date_gmt":"2026-05-09T09:56:50","guid":{"rendered":"https:\/\/coherencegeometry.com\/?page_id=2728"},"modified":"2026-05-11T14:42:07","modified_gmt":"2026-05-11T14:42:07","slug":"foundation-papers","status":"publish","type":"page","link":"https:\/\/coherencegeometry.com\/index.php\/foundation-papers\/","title":{"rendered":"Foundation Papers"},"content":{"rendered":"\n

Foundation Papers<\/h2>\n\n\n\n
<\/div>\n\n\n\n

This section collects the foundational technical papers of Coherence Geometry.<\/p>\n\n\n\n

These papers develop the core mathematical constructions behind the framework, including multi-phase structure, coherence formation, constrained refinement, basin stability, and related foundational mechanisms. They provide the technical background for the canonical definitions, demonstrations, research papers, and applied projections presented elsewhere on this site.<\/p>\n\n\n\n

The Foundation Papers are distinct from the Canonical Foundations<\/a>. The canons fix terminology, definitions, and named results. The foundation papers develop the mathematical constructions and arguments from which those canons and later applications arise. Readers looking for the current terminology should consult the Canonical Foundations alongside these papers, since some foundational documents may reflect earlier stages in the development of CG notation or presentation.<\/p>\n\n\n\n

Each entry below links to a versioned public record, usually hosted on Zenodo, together with a short description of its role in the framework.<\/p>\n\n\n\n

<\/div>\n\n\n\n

Foundation Papers by Canon Association<\/h3>\n\n\n\n
<\/div>\n\n\n\n

CDR-00: Canonical Definitions and Results<\/strong><\/h4>\n\n\n\n

A Multi-Phase Extension of Complex Numbers and the Global Coherence Theorem<\/a>
Develops \u03bc-numbers and the Global Coherence Theorem, establishing the multi-phase number framework and bounded coherence structure used throughout CG.<\/em>
Repository: Zenodo DOI<\/a><\/p>\n\n\n\n

Mathematical Foundations of Coherence Formation and Stability<\/a>
Develops coherence energy, constrained refinement, coherence basins, and stability principles, including UCCP, SCRC, and CS-SCT.<\/em>
Repository: Zenodo DOI<\/a><\/p>\n\n\n\n

CDR-01: Physics Branch Canon<\/h4>\n\n\n\n

Unified Coherence Geometry: A Common Action for Physical Fields<\/a>
Develops the Unified Coherence Action, a geometric and variational formulation for physical-field projections.<\/em>
Repostiory: Zenodo DOI<\/a><\/p>\n\n\n\n

CDR-02: Mathematics Branch Canon<\/h4>\n\n\n\n

The Unified Coherence Functional: A Closed Generative Basis for Mathematics<\/a>
Develops the Unified Coherence Functional and projection-consistency framework for mathematical structures.<\/em>
Repository: Zenodo DOI<\/a><\/p>\n\n\n\n

CDR-03: Variational\u2013Relaxation Structure Canon<\/h4>\n\n\n\n

A Variational\u2013Relaxation Framework for Coherence-Driven Structure Formation<\/a>
Develops the variational-relaxation formulation of structure formation, coherence refinement, and dissipative relaxation.<\/em>
Repository: Zenodo DOI<\/a><\/p>\n\n\n\n

CDR-04: Coherence-Geometric Information Substrate Canon<\/h4>\n\n\n\n

A Coherence-Geometric Substrate for Information, Modulation, and Inference<\/a>
Develops the pre-symbolic coherence-geometric information substrate, including basin-based modulation, inference, and recovery.<\/em>
Repository: Zenodo DOI<\/a><\/p>\n\n\n\n

CDR-05: Curvature-Driven Amplitude Relaxation Canon<\/h4>\n\n\n\n

Pattern Formation via Curvature-Driven Amplitude Relaxation in Coherence Geometry<\/a>
Develops curvature-driven amplitude relaxation as a coherence-geometric mechanism for pattern formation.<\/em>
Repository: Zenodo DOI<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Foundation Papers This section collects the foundational technical papers of Coherence Geometry. These papers develop the core mathematical constructions behind the framework, including multi-phase structure, coherence formation, constrained refinement, basin stability, and related foundational mechanisms. They provide the technical background for the canonical definitions, demonstrations, research papers, and applied projections presented elsewhere on this site….<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_kad_post_transparent":"","_kad_post_title":"hide","_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":""},"class_list":["post-2728","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/pages\/2728","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"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=2728"}],"version-history":[{"count":10,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/pages\/2728\/revisions"}],"predecessor-version":[{"id":2954,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/pages\/2728\/revisions\/2954"}],"wp:attachment":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/media?parent=2728"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}