{"id":1277,"date":"2025-12-17T06:35:07","date_gmt":"2025-12-17T06:35:07","guid":{"rendered":"https:\/\/coherencegeometry.com\/?page_id=1277"},"modified":"2026-05-03T07:35:35","modified_gmt":"2026-05-03T07:35:35","slug":"home-2","status":"publish","type":"page","link":"https:\/\/coherencegeometry.com\/index.php\/home-2\/","title":{"rendered":"Home &#8211; Alan Hold"},"content":{"rendered":"\n<h1 class=\"wp-block-heading has-text-align-center has-theme-palette-2-color has-text-color has-link-color wp-elements-13784811f17245dd51b02ae8a222bc5c\"><strong>A Mathematical Framework for Emergent Structure<\/strong><\/h1>\n\n\n\n<p class=\"has-text-align-center has-theme-palette-5-color has-text-color has-link-color wp-elements-90f6f5f5ec737d09af3c2bd6287429c2\"><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has--font-size\"><strong>Coherence Geometry is a tool and framing construct that assists STEM practitioners to solve challenging problems across mathematics, physics, biology, computation, and signal processing.<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-center\">Rather than prescribing domain-specific variables or symbolic rules, the framework describes a single underlying mechanism \u2014 interactions coupled through a shared amplitude, shaped by constraints \u2014 from which patterns arise, stabilize, or dissolve. Two equivalent representations provide complementary views: a geometric form emphasizing configuration and curvature, and an algebraic form emphasizing operators and compositional relations.<\/p>\n\n\n\n<p class=\"has--font-size\"><em>Coherence Geometry is not proposed as a replacement for existing mathematics or physics \u2014 it is a substrate framework from which established forms may be derived under constraint. The <a href=\"https:\/\/coherencegeometry.com\/index.php\/conceptual-overview\/\">Conceptual Overview<\/a> describes how this layered organization relates to physical, informational, and inference frameworks.<\/em><\/p>\n\n\n\n\n\n<blockquote class=\"wp-block-quote has-text-align-center is-layout-flow wp-block-quote-is-layout-flow\"><\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-text-align-center\"><em><strong>The Coherence Geometry Institute<\/strong><\/em><\/h1>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/coherencegeometry.com\/index.php\/publications\/\">Publications<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>A Mathematical Framework for Emergent Structure Coherence Geometry is a tool and framing construct that assists STEM practitioners to solve challenging problems across mathematics, physics, biology, computation, and signal processing. Rather than prescribing domain-specific variables or symbolic rules, the framework describes a single underlying mechanism \u2014 interactions coupled through a shared amplitude, shaped by constraints&#8230;<\/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-1277","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/pages\/1277","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=1277"}],"version-history":[{"count":83,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/pages\/1277\/revisions"}],"predecessor-version":[{"id":2486,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/pages\/1277\/revisions\/2486"}],"wp:attachment":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/media?parent=1277"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}