{"id":3570,"date":"2026-05-19T06:45:01","date_gmt":"2026-05-19T13:45:01","guid":{"rendered":"https:\/\/coherencegeometry.com\/?p=3570"},"modified":"2026-05-19T06:56:23","modified_gmt":"2026-05-19T13:56:23","slug":"deterministic-protein-folding-from-coherence-fields","status":"publish","type":"post","link":"https:\/\/coherencegeometry.com\/index.php\/2026\/05\/19\/deterministic-protein-folding-from-coherence-fields\/","title":{"rendered":"Deterministic Protein Folding from Coherence Fields"},"content":{"rendered":"\n

Internal ID:<\/strong> CGI-RSR-000026
Author(s):<\/strong> Barry L. Petersen
Document Type:<\/strong> Research Paper
Publication Date:<\/strong> May 2026
Original Creation Date:<\/strong> May 18, 2025
Revised Document Date:<\/strong> N\/A
Status:<\/strong> Public
Domains:<\/strong> Biology, Chemistry, Physics
Sub-Domain:<\/strong> Biophysics
Research Topics:<\/strong> Protein Folding, Biological Structure Formation, Numerical Simulation Study<\/p>\n\n\n\n

Abstract<\/h3>\n\n\n\n

We present a deterministic, geometry-based model of protein folding using a novel variational framework called coherence geometry<\/em> (CG). In this system, residues are modeled as local phase agents embedded in a spatial field, each carrying internal biases that reflect their chemical identities. The chain folds not through stochastic search or learned potentials, but via local alignment dynamics governed by multi-channel phase interactions. Ripple-based correction events and long-range field influences\u2014such as hydrophobic attraction and directional bias\u2014enable rapid convergence into compact, protein-like structures. We demonstrate successful folding in one-dimensional chains of 50\u2013200 residues, exhibiting modular substructure, stable hydrophobic cores, and high sensitivity to residue ordering. These results suggest that protein folding may emerge from general principles of geometric coherence, without requiring energy minimization, empirical tuning, or supervised learning.<\/p>\n\n\n\n

Available Document<\/h3>\n\n\n\n

DOI:<\/strong> 10.5281\/zenodo.20285351<\/code><\/p>\n\n\n\n

Citation:<\/strong>
Petersen, B. L. (2026). Deterministic Protein Folding from Coherence Fields. Zenodo.\u00a0https:\/\/doi.org\/10.5281\/zenodo.20285351<\/a><\/p>\n\n\n\n

Source Code and Supporting Materials<\/h3>\n\n\n\n

Files included:<\/em><\/p>\n\n\n\n

    \n
  1. Deterministic_Protein_Folding_from_Coherence_Fields.pdf<\/strong>
    PDF research paper describing the CG protein-folding model, theoretical
    framework, residue representation, update dynamics, experiments, figures,
    discussion, and conclusions.<\/li>\n\n\n\n
  2. Deterministic_Protein_Folding_from_Coherence_Fields.ipynb<\/strong>
    Jupyter notebook used to generate the protein-folding images, videos, and
    plots associated with the paper. The notebook implements the discrete
    multi-phase residue model described in the Model Design section, including
    local alignment, residue identity phases, collapse pressure, hydrophobic
    attraction, charge interaction, ripple-like correction events, and phase
    evolution.<\/li>\n<\/ol>\n\n\n\n

    Code availability:<\/em>
    A Jupyter notebook is included as a research artifact associated with the paper. It is provided for inspection, experimentation, and reproducibility support, but is not packaged as maintained software. Local paths, environment setup, plotting\/video options, and parameter choices may require adjustment. No public technical support is implied.<\/p>\n\n\n\n

    Summary and Notes<\/h3>\n\n\n\n

    Document role:<\/em>
    This paper presents a deterministic, geometry-based model of protein folding within the Coherence Geometry (CG) framework. Residues are modeled as local multi-phase agents embedded in a spatial field, each carrying internal phase biases that reflect simplified chemical identities. The chain folds through local alignment dynamics, long-range field interactions, collapse pressure, identity-driven directionality, and ripple-like correction events.<\/p>\n\n\n\n

    The paper studies folding in one-dimensional chains of 50 to 200 residues and reports the emergence of compact protein-like structures, modular substructure, stable hydrophobic cores, residue-order sensitivity, phase-channel effects, single-point mutation sensitivity, identity-shuffle behavior, curvature\/ripple activity, long-chain dynamics, and residue-class differentiation.<\/p>\n\n\n\n

    Core result:<\/em>
    The model shows that protein-like folding behavior can emerge from deterministic coherence dynamics rather than stochastic search, supervised learning, or pretrained statistical potentials. Folding is treated as a coherence-driven formation process in which geometry, residue identity, phase alignment, local tension, long-range interactions, and correction events jointly guide the chain toward compact organized structures.<\/p>\n\n\n\n

    Scope:<\/em>
    This document should be read as a simulation-driven CG study of folding principles and coherent core formation. It focuses on the emergence of protein-like organization from simplified residue identities and multi-phase field dynamics. Broader all-atom modeling, quantitative biochemical calibration, native-structure prediction, and full protein-engineering applications are left to future work.<\/p>\n\n\n\n

    Historical and framework context:<\/em>
    This paper is released in its original May 2025 form. It belongs to the early simulation-driven biological phase of the Coherence Geometry research corpus, before the later canon records and Foundations texts were fully organized. Some terminology and references reflect the framework language available at the time of writing.<\/p>\n\n\n\n

    The paper defines the folding model internally, including residue representation, multi-phase alignment, ripple events, long-range interactions, and update rules. Earlier references to CG framework materials are provided as historical context, while later canon records and Foundations texts provide the current public reference layer for the underlying shared-amplitude, multi-phase, variational, and refinement concepts.<\/p>\n\n\n\n

    Related Work<\/h3>\n\n\n\n

    Relation to related CG work:<\/em>
    This paper is related to CGI-RSR-000025, “Emergent Modular Structure in
    Coherence-Driven Oscillator Fields,” which studies modular attractor-basin
    formation and ripple-like internal refinement events in oscillator lattices.
    The ripple and refinement concepts used in the protein-folding model are
    consistent with that earlier basin\/refinement mechanism.<\/p>\n\n\n\n

    The paper is also related to Coherence Geometry Foundations, Part I and Part II,
    which provide later organized reference treatments of the CG framework and its
    physical projections.<\/p>\n\n\n\n

    Related records:<\/em>
    Petersen, B. L. (2026). Emergent Modular Structure in Coherence-Driven
    Oscillator Fields: Spontaneous Phase Alignment and Internal Refinement in
    Conservative Lattices (Version 1.0). Zenodo.
    https:\/\/doi.org\/10.5281\/zenodo.20282721<\/a><\/p>\n\n\n\n

    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<\/a><\/p>\n\n\n\n

    Petersen, B. L. (2026). Coherence Geometry Foundations, Part II: Physical
    Projections (Version 0.1). Zenodo.
    https:\/\/doi.org\/10.5281\/zenodo.20156997<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

    CGI-RSR-000026 | We present a deterministic, geometry-based model of protein folding using a novel variational framework called coherence geometry (CG). In this system, residues are modeled as local phase agents embedded in a spatial field, each carrying internal biases that reflect their chemical identities. The chain folds not through stochastic search or learned potentials, but via local alignment dynamics governed by multi-channel phase interactions.<\/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":[33,32,80,31,81,56],"tags":[],"class_list":["post-3570","post","type-post","status-publish","format-standard","hentry","category-biology","category-chemistry","category-field-dynamics","category-physics","category-protein-folding","category-research-papers"],"_links":{"self":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/3570","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=3570"}],"version-history":[{"count":1,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/3570\/revisions"}],"predecessor-version":[{"id":3571,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/posts\/3570\/revisions\/3571"}],"wp:attachment":[{"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/media?parent=3570"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/categories?post=3570"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/coherencegeometry.com\/index.php\/wp-json\/wp\/v2\/tags?post=3570"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}