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Differential Global Coherence: Intrinsic Jet Persistence, Transport Covariance, and Projection Noncreation

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Internal ID: CGI-RSR-000042
Author(s): Barry L. Petersen
Document Type: Research Paper
Publication Date: September 29, 2026
Original Creation Date: September 24, 2026
Revised Document Date: September 29, 2026
Status: Public
Domains: Mathematics, Mathematical Physics, General
Sub-Domain: Differential Source Geometry / Regularity / Projection
Research Topics: Differential Global Coherence, Source Regularity, Source Jets, Transport Covariance, Spatial Refinement, Projection Noncreation, Complete Source Dynamics, Hodge Reaction, Persistent Source Lifts

Abstract

This paper develops Differential Global Coherence as an extension of the Global Coherence framework from bounded coherent states to persistence of their spatial differential structure.

The Global Coherence architecture controls the evolution of coherent states at the state-space level. Differential Global Coherence asks the next question: when a complete Source is spatially distributed, under what conditions does finite differential structure remain finite during its evolution?

The analysis develops finite Source-jet persistence under intrinsic Source evolution, positive spatial refinement, and regular material transport. It distinguishes state confinement from differential persistence and studies the mechanisms by which bounded complete-Source dynamics propagate first and higher spatial derivatives.

The paper also develops transport-covariant differential coherence, fixed-Eulerian transport diagnostics, Source stress and Hodge reaction, finite-order projection noncreation, and persistent admissible Source lifts.

The resulting framework provides a general differential regularity layer connecting bounded complete-Source evolution to the finite spatial structure required by downstream physical and observable projections.

Available Document

DOI: 10.5281/zenodo.23040056

Citation:
Petersen, B. L. (2026). Differential Global Coherence: Intrinsic Jet Persistence, Transport Covariance, and Projection Noncreation (Version 1.0). Coherence Geometry Institute. Zenodo. https://doi.org/10.5281/zenodo.23040056

Source Code and Supporting Materials

No separate computational package is included with this archival release.

The principal results are analytic and geometric and do not require a separate numerical dataset, computational notebook, or software package.

Primary file:
Differential_Global_Coherence.pdf

Version 1.0 archival research paper.

A README file accompanying the Zenodo deposit records document provenance, scope, citation information, file integrity, and archival metadata.

Summary and Notes

Scope:

Differential Global Coherence extends the state-level coherence architecture into the spatial differential geometry of a complete Source.

A bounded Source state does not by itself guarantee bounded spatial derivatives. A spatially distributed Source may remain inside a regular region of coherence-state space while developing increasingly sharp spatial structure. The paper therefore treats state confinement and differential persistence as distinct mathematical questions.

The analysis develops several levels of Source regularity:

  • persistence of the first Source differential;
  • persistence of higher finite Source jets;
  • differential evolution under intrinsic complete-Source dynamics;
  • positive spatial refinement;
  • transport-covariant preservation of Source differential structure;
  • fixed-Eulerian transport diagnostics;
  • Source stress and Hodge reaction;
  • finite-order projection noncreation; and
  • persistent admissible Source lifts.

For intrinsic complete-Source evolution, the first Source differential satisfies a tangent evolution equation controlled by the derivative of the intrinsic Source generator. Under bounded Source evolution through a regular region and bounded Source variation, finite initial differential structure therefore remains finite on finite intervals.

The same structure extends to higher finite Source jets through a triangular variational hierarchy.

Positive spatial refinement supplies an additional regularizing mechanism. In the canonical flat or product coherence sector, positive Source stiffness contributes a non-amplifying differential term and therefore preserves first-order differential coherence rather than generating differential blow-up.

For material Source transport, the paper distinguishes intrinsic Source growth from distortion produced by the chosen spatial representation. With the naturally transported domain geometry, regular material transport preserves Source differential magnitude covariantly. Fixed-Eulerian growth may still serve as a useful diagnostic of representation distortion without constituting intrinsic growth of the Source itself.

The paper also establishes a projection principle: a regular finite-order observable projection cannot create a singularity solely from a complete Source jet that remains finite in a regular region. This gives the directional hierarchy

This gives the directional hierarchy:

finite regular Source geometry → regular finite-order projection → finite observable geometry

The result is formulated at the complete-Source level and is not restricted to one physical realization. It supplies a general differential regularity layer for later Source-geometric, fluid, transport, and projection-based developments within Coherence Geometry.

Related Work

Foundational framework:

Petersen, B. L. (2026). Coherence Geometry Foundations, Part I: Orientation, Closure, and Algebraic Foundations(Version 0.1). Zenodo.
https://doi.org/10.5281/zenodo.20156531

Petersen, B. L. (2026). Coherence Geometry Foundations, Part II: Physical Projections. Zenodo.
https://doi.org/10.5281/zenodo.20156996

Related Source, projection, and fluid work:

Petersen, B. L. (2026). Projection-Covariant Dynamics in Coherence Geometry: Presymplectic Reduction, Mapping-Space Evolution, and Observable Descent (Version 1.0). Coherence Geometry Institute. Zenodo.
https://doi.org/10.5281/zenodo.23040342

Petersen, B. L. (2026). Coherence Geometry as a Structured Generalization of Fluid Dynamics (Version 1.0). Coherence Geometry Institute. Zenodo.
https://doi.org/10.5281/zenodo.23043221

Petersen, B. L. (2026). Coherence Geometry Foundations, Volume II: Source Curvature, Book I: Source Geometry, Fluid Projection, and Regularity (Version 0.1). Coherence Geometry Institute. Zenodo.
https://doi.org/10.5281/zenodo.23056935

Petersen, B. L. (2026). Rank-One Coherence Obstructions in High–High Navier–Stokes Interactions (Version 2.0). Zenodo.
https://doi.org/10.5281/zenodo.23054930

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