Deterministic Protein Folding from Coherence Fields

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. 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. The model treats folding as a coherence-driven formation process in which geometry, residue identity, phase alignment, local tension, long-range interaction, and correction events jointly guide the chain toward compact organized structures. The paper should be read as a simulation-driven CG study of folding principles and coherent core formation. Broader all-atom modeling, quantitative biochemical calibration, native-structure prediction, and full protein-engineering applications are left to future work. This paper is released in its original May 2025 form and belongs to the early simulation-driven biological phase of the CG corpus. The paper defines the folding model internally, including residue representation, multi-phase alignment, ripple events, long-range interactions, and update rules. Later canon records and Foundations texts provide the current public reference layer for the underlying CG framework. The Zenodo record includes a Jupyter notebook used to generate the protein-folding images, videos, and plots associated with the paper. The notebook is provided as a research artifact for inspection, experimentation, and reproducibility support, not as maintained software. Internal reference: CGI-RSR-000026.