PTG-2: Compact Transport Geometry and Curvature Loading

Daniel Hilton

Earlier research paper

This paper remains available as part of the development of Phase Differential Theory. The R00–R13 foundational suite provides the current formulation of the theory. Read this paper in its original model and publication context.

Current foundations Research history

Current foundational treatment

Related current treatmentPrincipal topic: Phase transport and representations.

Transport geometry and curvature are treated currently through loop phase in R02 and conditional carrier constructions in R07.

A topic connection does not mean that every claim in this paper is retained or that a current paper reproduces its proof.

Original abstract

Preserved from the original manuscript.

Phase Transport Geometry (PTG) models coherent physical evolution using compact, periodic transport on the minimal phase manifold (

S^{1}

)^6 established in PTG-1. This paper introduces the compact transport potential T(

\theta

) = K(1 − cos

\theta

), adopted as the minimal smooth periodic potential satisfying periodicity, symmetry, boundedness, and quadratic behaviour near equilibrium. The associated curvature operator distinguishes local spectral instability from global coherence loading. The separation between the spectral quantity

\lambda

max(K) and the aggregate quantity Tr(K) is a defining structural feature of PTG dynamics. This distinction provides the structural motivation for introducing finite coherence capacity in PDT-I and underlies the mass-scaling and collapse dynamics developed in PTG-5, PDT-II, and PDT-III.

Suggested citation

Graham Fincham, Daniel Hilton. “PTG-2: Compact Transport Geometry and Curvature Loading.” Phase Differential Theory research programme. Version 1.1.1. 2026. https://www.phasedifferentialtheory.com/papers/ptg-2-2026

@misc{pdt_ptg_2_2026,
  title = {PTG-2: Compact Transport Geometry and Curvature Loading},
  author = {Graham Fincham and Daniel Hilton},
  year = {2026},
  version = {1.1.1},
  url = {https://www.phasedifferentialtheory.com/papers/ptg-2-2026}
}

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