{"id":4043,"date":"2026-06-09T18:39:55","date_gmt":"2026-06-10T01:39:55","guid":{"rendered":"https:\/\/coherencegeometry.com\/?p=4043"},"modified":"2026-06-09T18:39:57","modified_gmt":"2026-06-10T01:39:57","slug":"constraint-driven-formation-of-coherence-structures-and-their-inverse-square-exterior-flux","status":"publish","type":"post","link":"https:\/\/coherencegeometry.com\/index.php\/2026\/06\/09\/constraint-driven-formation-of-coherence-structures-and-their-inverse-square-exterior-flux\/","title":{"rendered":"Constraint-Driven Formation of Coherence Structures and Their Inverse-Square Exterior Flux"},"content":{"rendered":"\n

Internal ID:<\/strong> CGI-RSR-000031
Author(s):<\/strong> Barry L. Petersen
Document Type:<\/strong> Research Paper
Publication Date:<\/strong> June 2026
Original Creation Date:<\/strong> April 20, 2026
Revised Document Date:<\/strong> June 10, 2026
Status:<\/strong> Public
Domains:<\/strong> Physics
Sub-Domain:<\/strong> Cosmology
Research Topics:<\/strong> Cosmology, Galactic Dynamics, Flux Scaling Model<\/p>\n\n\n\n

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


We establish a dynamical mechanism by which coherence-driven structure formation produces the inverse-square scaling behavior associated with galactic rotation curves and gravitational lensing. Within the framework of Coherence Geometry, constrained variational\u2013relaxation dynamics generate stable coherence basins corresponding to local minima of an intrinsic structure functional. We show that, when realized in spatially extended systems, these basins form curvature-confined structures whose exterior dynamics satisfy flux conservation, leading to an inverse-square scaling of outward energy transport. This scaling implies an effective density profile \\(\\rho(r) \\sim r^{-2}\\), reproducing the leading-order gravitational signatures typically attributed to dark matter halos. The result provides a direct link between underlying phase dynamics, structure formation, and observable gravitational behavior, without requiring a prescribed mass distribution.<\/p>\n\n\n\n

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

DOI:<\/strong> 10.5281\/zenodo.20618890<\/code><\/p>\n\n\n\n

Citation:<\/strong>
Petersen, B. L. (2026). Constraint-Driven Formation of Coherence Structures and Their Inverse-Square Exterior Flux<\/em>. Zenodo.\u00a0https:\/\/doi.org\/10.5281\/zenodo.20618890<\/a><\/p>\n\n\n\n

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

N\/A.<\/p>\n\n\n\n

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

Document role:<\/em>
This paper investigates a coherence-driven mechanism for generating the inverse-square scaling behavior commonly associated with galactic rotation curves and gravitational lensing.<\/p>\n\n\n\n

Within the framework of Coherence Geometry, constrained variational-relaxation dynamics generate stable coherence basins corresponding to local minima of an intrinsic structure functional. When realized in spatially extended systems, these basins form curvature-confined structures whose exterior dynamics satisfy flux conservation.<\/p>\n\n\n\n

The resulting exterior flux exhibits inverse-square scaling, producing an effective density profile<\/p>\n\n\n\n

rho(r) ~ r^-2,<\/p>\n\n\n\n

and thereby reproducing the leading-order gravitational signatures commonly attributed to dark matter halos.<\/p>\n\n\n\n

Core result:<\/em>
The paper establishes the following chain:<\/p>\n\n\n\n

coherence dynamics -> coherence basins -> localized structures -> conserved exterior flux -> rho(r) ~ r^-2 -> rotation curves and lensing.<\/p>\n\n\n\n

The result provides a direct connection between coherence-driven structure formation and observable gravitational behavior without requiring a prescribed mass distribution.<\/p>\n\n\n\n

Scope:<\/em>
This paper focuses on the dynamical origin of inverse-square exterior flux within the Coherence Geometry framework.<\/p>\n\n\n\n

It does not attempt to provide a complete cosmological model, dark matter theory, numerical structure-formation simulation, or detailed comparison with observational survey data. Its purpose is to identify a coherence-driven mechanism capable of producing the scaling behavior examined in the preceding papers.<\/p>\n\n\n\n

Relation to previous work:<\/em>
This paper builds directly on Conserved Flux and Inverse-Square Density Profiles in Galactic Rotation Curves<\/a><\/em> and Inverse-Square Density Profiles and Gravitational Lensing from Conserved Flux<\/a><\/em>. <\/p>\n\n\n\n

The first paper showed that conserved outward flux naturally produces inverse-square density scaling and flat galactic rotation curves. The second paper showed that the same density profile reproduces the leading-order lensing behavior associated with standard halo models.<\/p>\n\n\n\n

The present paper investigates the dynamical origin of the structures supporting such conserved exterior flux.<\/p>\n\n\n\n

Relation to Coherence Geometry:<\/em>
This paper is the first paper in the sequence to make substantial use of the Coherence Geometry framework.<\/p>\n\n\n\n

The analysis draws upon the variational-relaxation principle, coherence basins, constrained coherence dynamics, and the formation of stable structured configurations described in the Coherence Geometry canons and foundations documents.<\/p>\n\n\n\n

Within this framework, coherence structures provide a candidate mechanism for generating the conserved exterior flux responsible for the scaling behavior examined in the preceding papers.<\/p>\n\n\n\n

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

Petersen, B. L. (2026). Conserved Flux and Inverse-Square Density Profiles in Galactic Rotation Curves. Zenodo. https:\/\/doi.org\/10.5281\/zenodo.20618642<\/a><\/p>\n\n\n\n

Petersen, B. L. (2026). Inverse-Square Density Profiles and Gravitational Lensing from Conserved Flux. Zenodo. https:\/\/doi.org\/10.5281\/zenodo.20618733<\/a><\/p>\n\n\n\n","protected":false},"excerpt":{"rendered":"

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