A Variational–Relaxation Framework for Coherence-Driven Structure Formation
Internal ID: CGI-RSR-000013
Document Type: Research Paper
Status: Public
Domains: Physics, Mathematics, Foundations
Research Topics: Variational-relaxation, structure formation
Abstract
We develop a variational framework for coherence-driven structure formation, placing phase coherent self-organization within a unified geometric description compatible with variational principles used throughout physics. Building on the Global Coherence Theorem and the Structured Coherence Refinement Corollary, we show that coherence-governed systems naturally admit an intrinsic structure functional whose extrema define stable coherent configurations. Coherence formation is not treated as a conservative Hamiltonian process; instead, structured coherence arises through dissipative relaxation toward minima of this functional. In this sense, coherence refinement follows a least-action principle understood as constraint satisfaction and landscape extremization rather than conservative energy preservation. Phase evolution is described by gradient-like flow on a coherence potential induced by shared amplitude constraints, with optional inertial extensions capturing transient dynamics without altering basin structure. This formulation clarifies the role of coherence geometry as a representational substrate underlying dynamical, informational, and organizational phenomena. It provides a principled explanation for the emergence, stability, and robustness of coherent structure across wave systems, self-organizing physical processes, and coherence-based computational models. By embedding coherence refinement within a variational–relaxation framework, this work establishes coherence structuring as a general organizing principle that is physically grounded while remaining applicable across domains.
Available Document
DOI: 10.5281/zenodo.20120588
Citation:
Petersen, B. L., & Johnson, R. K. (2026). A Variational–Relaxation Framework for Coherence-Driven Structure Formation. Zenodo. https://doi.org/10.5281/zenodo.20120588
Source Code and Supporting Materials
None
Summary and Notes
This paper is listed in the Foundation Papers section because it serves as a source document for CDR-03.
Related Work
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