PTG-3: Closure-Compatible Metric Selection

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: Internal spatial carriers and orientation.

Metric selection is treated currently by separating internal metrics (R07) from the declared physical metric premise and action class (R10).

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) requires a metric on the minimal phase manifold (

S^{1}

)^6 that respects the closure hierarchy established in PTG-1 and the compact transport dynamics introduced in PTG-2. This paper constructs the closure-compatible metric, which projects out closure directions in the triplet and doublet sectors and retains only physically relevant phase differences. The resulting reduced metric defines the primitive curvature scale and provides the geometric backbone for curvature loading, excitation structure, sector organisation (PTG-4), mass scaling (PTG-5), and the physical interpretation developed in the PDT series. A formal uniqueness theorem is stated here and proved in the mathematical closure supplement PDT-MC-1.

Suggested citation

Graham Fincham, Daniel Hilton. “PTG-3: Closure-Compatible Metric Selection.” Phase Differential Theory research programme. Version 1.1.1. 2026. https://www.phasedifferentialtheory.com/papers/ptg-3-2026

@misc{pdt_ptg_3_2026,
  title = {PTG-3: Closure-Compatible Metric Selection},
  author = {Graham Fincham and Daniel Hilton},
  year = {2026},
  version = {1.1.1},
  url = {https://www.phasedifferentialtheory.com/papers/ptg-3-2026}
}

No DOI recorded. No repository record verified. Journal-review status not confirmed.