PTG-5: Defect Mass Scaling and Return-Closure Invariants

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: Interactions, matter and refinement.

Mass scaling relates to matter models in R09. R08 records that a calibrated mass scale is an input, not a prediction.

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) interprets mass as the coherence burden required to sustain a stable compact defect on the phase manifold (

S^{1}

)^6. Earlier papers established the closure hierarchy (PTG-1), compact transport and curvature loading (PTG-2), the closure-compatible metric (PTG-3), and the sector structure and structural algebras (PTG-4). PTG-5 introduces the structural mass functional implied by these geometric and algebraic ingredients. Each factor in the mass expression is motivated by the preceding PTG papers, and the multiplicative structure reflects the independent contributions of closure, winding, loading, excitation mode, sector symmetry, and return-closure invariants.

Suggested citation

Graham Fincham, Daniel Hilton. “PTG-5: Defect Mass Scaling and Return-Closure Invariants.” Phase Differential Theory research programme. Version 1.1.1. 2026. https://www.phasedifferentialtheory.com/papers/ptg-5-2026

@misc{pdt_ptg_5_2026,
  title = {PTG-5: Defect Mass Scaling and Return-Closure Invariants},
  author = {Graham Fincham and Daniel Hilton},
  year = {2026},
  version = {1.1.1},
  url = {https://www.phasedifferentialtheory.com/papers/ptg-5-2026}
}

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