{"id":3979,"date":"2026-06-09T03:33:30","date_gmt":"2026-06-09T10:33:30","guid":{"rendered":"https:\/\/coherencegeometry.com\/?p=3979"},"modified":"2026-06-10T16:22:08","modified_gmt":"2026-06-10T23:22:08","slug":"emergent-duplex-helicity-from-coherence-alignment-and-transport","status":"publish","type":"post","link":"https:\/\/coherencegeometry.com\/index.php\/2026\/06\/09\/emergent-duplex-helicity-from-coherence-alignment-and-transport\/","title":{"rendered":"Emergent Duplex Helicity from Coherence Alignment and Transport"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>Internal ID:<\/strong> CGI-RSR-000028<br><strong>Author(s):<\/strong> Barry L. Petersen<br><strong>Document Type:<\/strong> Research Paper<br><strong>Publication Date:<\/strong> June 2026<br><strong>Original Creation Date:<\/strong> June 9, 2026<br><strong>Status:<\/strong> Public<br><strong>Domains:<\/strong> Biology, Chemistry, Physics<br><strong>Sub-Domain:<\/strong> Molecular Structure, DNA<br><strong>Research Topics:<\/strong> DNA, Duplex helicity, Transport, Operator dynamics<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><br>Helical structures are commonly modeled by prescribing a rotational geometry, a preferred twist angle, or an equivalent geometric construction rule. In this work, we investigate an alternative approach in which helicity emerges from local coherence dynamics rather than from an explicitly imposed helical instruction. We introduce a minimal duplex model consisting of a three-channel coherence state and a fixed (\\( 3\\times3 \\)) coherence operator. Admissible local states align with the coherence mode supported by the operator. A transport observable is obtained by projecting the resulting response onto an axis determined by the antisymmetric part of the operator, and the resulting transport increment is applied recursively as a local frame rotation during duplex growth. The construction produces stable duplex helicity without an imposed global helical scaffold, target curve, or prescribed twist angle. Diagnostic examples demonstrate complete transport cycles, persistent long-range helical organization, and operator-controlled handedness. Numerical experiments further indicate that a broad range of admissible initial states converge toward nearly identical response directions, implying that the resulting transport behavior is determined primarily by the operator rather than by the particular incoming state. Although the model is intended as a minimal transport construction rather than a realistic biochemical simulation, it illustrates how local coherence dynamics can generate observable geometric structure through recursive transport. In this framework, the helical twist appears as a derived consequence of the operator-supported transport dynamics rather than as an externally prescribed geometric parameter.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Available Document<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>DOI:<\/strong> <code>10.5281\/zenodo.20607906<\/code><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Citation:<\/strong><br>Petersen, B. L. (2026). Emergent Duplex Helicity from Coherence Alignment and Transport. Zenodo. <a href=\"https:\/\/doi.org\/10.5281\/zenodo.20607906\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.20607906<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Representative Figure<\/h3>\n\n\n\n<div style=\"height:38px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<style>.kb-image3979_7ae648-57.kb-image-is-ratio-size, .kb-image3979_7ae648-57 .kb-image-is-ratio-size{max-width:506px;width:100%;}.wp-block-kadence-column > .kt-inside-inner-col > .kb-image3979_7ae648-57.kb-image-is-ratio-size, .wp-block-kadence-column > .kt-inside-inner-col > .kb-image3979_7ae648-57 .kb-image-is-ratio-size{align-self:unset;}.kb-image3979_7ae648-57 figure{max-width:506px;}.kb-image3979_7ae648-57 .image-is-svg, .kb-image3979_7ae648-57 .image-is-svg img{width:100%;}.kb-image3979_7ae648-57:not(.kb-image-is-ratio-size) .kb-img, .kb-image3979_7ae648-57.kb-image-is-ratio-size{padding-top:var(--global-kb-spacing-sm, 1.5rem);padding-right:var(--global-kb-spacing-sm, 1.5rem);padding-bottom:var(--global-kb-spacing-sm, 1.5rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kb-image3979_7ae648-57 .kb-image-has-overlay:after{opacity:0.3;border-top-left-radius:10px;border-top-right-radius:10px;border-bottom-right-radius:10px;border-bottom-left-radius:10px;}.kb-image3979_7ae648-57 img.kb-img, .kb-image3979_7ae648-57 .kb-img img{border-top:2px solid var(--global-palette5, #4A5568);border-right:2px solid var(--global-palette5, #4A5568);border-bottom:2px solid var(--global-palette5, #4A5568);border-left:2px solid var(--global-palette5, #4A5568);background-color:#ffffff;border-top-left-radius:10px;border-top-right-radius:10px;border-bottom-right-radius:10px;border-bottom-left-radius:10px;box-shadow:10px 10px 30px 0px rgba(0, 0, 0, 0.2);}@media all and (max-width: 1024px){.kb-image3979_7ae648-57 img.kb-img, .kb-image3979_7ae648-57 .kb-img img{border-top:2px solid var(--global-palette5, #4A5568);border-right:2px solid var(--global-palette5, #4A5568);border-bottom:2px solid var(--global-palette5, #4A5568);border-left:2px solid var(--global-palette5, #4A5568);}}@media all and (max-width: 767px){.kb-image3979_7ae648-57 img.kb-img, .kb-image3979_7ae648-57 .kb-img img{border-top:2px solid var(--global-palette5, #4A5568);border-right:2px solid var(--global-palette5, #4A5568);border-bottom:2px solid var(--global-palette5, #4A5568);border-left:2px solid var(--global-palette5, #4A5568);}}<\/style>\n<div class=\"wp-block-kadence-image kb-image3979_7ae648-57\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"480\" height=\"480\" src=\"https:\/\/coherencegeometry.com\/wp-content\/uploads\/2026\/06\/Fig3_Minus_Grid_Right_Handedness_N55_5inx5in_96dpi.png\" alt=\"\" class=\"kb-img wp-image-3982\" srcset=\"https:\/\/coherencegeometry.com\/wp-content\/uploads\/2026\/06\/Fig3_Minus_Grid_Right_Handedness_N55_5inx5in_96dpi.png 480w, https:\/\/coherencegeometry.com\/wp-content\/uploads\/2026\/06\/Fig3_Minus_Grid_Right_Handedness_N55_5inx5in_96dpi-300x300.png 300w, https:\/\/coherencegeometry.com\/wp-content\/uploads\/2026\/06\/Fig3_Minus_Grid_Right_Handedness_N55_5inx5in_96dpi-150x150.png 150w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/figure><\/div>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><em>3D numerically simulated image of helicity emerging from local coherence dynamics<\/em>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Source Code and Supporting Materials<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Notebook availability:<br>Three Jupyter notebooks are included as research artifacts associated with the<br>paper. Two notebooks generate the video frames and visualizations used for the<br>website and paper imagery, while one notebook generates the diagnostic plots<br>shown in the paper.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Files included:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>DNA_Formation_Video_Frames_Creator-v8.ipynb<\/strong><br>Jupyter notebook used to generate longer duplex-strand video frames and site<br>visualizations associated with the paper. This notebook produces extended<br>recursive-growth structures showing persistent long-range helical organization.<\/li>\n\n\n\n<li><strong>DNA_Formation_Video_Frames_Creator-Initial-v8.ipynb<\/strong><br>Jupyter notebook used to generate early-growth duplex video frames and the<br>early-growth DNA image used in the paper. This notebook focuses on the initial<br>formation stage of the recursive duplex-growth process.<\/li>\n\n\n\n<li><strong>Minimal_Recursive_Duplex_Growth_v8_Plots.ipynb<\/strong><br>Jupyter notebook used to generate the diagnostic figures shown in the paper,<br>including plots associated with recursive duplex growth, transport behavior,<br>response direction, operator-controlled handedness, and convergence of the<br>state, response, and transport observables.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">The notebooks are provided for inspection, experimentation, figure-generation<br>context, and reproducibility support. They are not packaged as maintained<br>software. Local paths, environment setup, plotting\/video options, frame export<br>settings, and parameter choices may require adjustment. No public technical<br>support is implied.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary and Notes<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">PDF research paper describing the minimal duplex transport model, three-channel coherence state, fixed coherence operator, antisymmetric transport axis,<br>recursive frame rotation, diagnostic examples, long-range helical organization,<br>operator-controlled handedness, and convergence behavior across admissible<br>initial states.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Related Work<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Petersen, B. L. (2026). Atomic Orbitals via Coherence Geometry. Zenodo.<br><a href=\"https:\/\/doi.org\/10.5281\/zenodo.20270492\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.20270492<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Petersen, B. L. (2026). Atomic Bonding via Coherence Geometry. Zenodo.<br><a href=\"https:\/\/doi.org\/10.5281\/zenodo.20287269\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.20287269<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Petersen, B. L. (2026). Deterministic Protein Folding from Coherence Fields. Zenodo.<br><a href=\"https:\/\/doi.org\/10.5281\/zenodo.20285351\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.20285351<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Petersen, B. L. (2026). Coherence Geometry Foundations, Part I: Orientation,<br>Closure, and Algebraic Foundations (Version 0.1). Zenodo.<br><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<p class=\"wp-block-paragraph\">Petersen, B. L. (2026). Coherence Geometry Foundations, Part II: Physical<br>Projections (Version 0.1). Zenodo.<br><a href=\"https:\/\/doi.org\/10.5281\/zenodo.20156997\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.20156997<\/a><\/p>\n\n\n\n","protected":false},"excerpt":{"rendered":"<p>CGI-RSR-000028 | Helical structures are commonly modeled by prescribing a rotational geometry, a preferred twist angle, or an equivalent geometric construction rule. In this work, we investigate an alternative approach in which helicity emerges from local coherence dynamics rather than from an explicitly imposed helical instruction.<\/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":[84,33,32,83,31,56],"tags":[],"class_list":["post-3979","post","type-post","status-publish","format-standard","hentry","category-dna-and-molecular-geometry","category-biology","category-chemistry","category-molecular-structure","category-physics","category-research-papers"],"_links":{"self":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/3979","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=3979"}],"version-history":[{"count":4,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/3979\/revisions"}],"predecessor-version":[{"id":3986,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/3979\/revisions\/3986"}],"wp:attachment":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/media?parent=3979"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/categories?post=3979"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/tags?post=3979"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}