PTG-4: Sector Structure, Chirality, and Structural Algebras

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.

Sector structure and chirality relate to orientation persistence in R07 and to matter models in R09.

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) organises the six phase degrees of freedom on the minimal phase manifold (

S^{1}

)^6 into triplet, doublet, and singlet closure sectors. These sectors support distinct classes of phase defects: collective closure defects in the triplet sector, orientation (chirality) defects in the doublet sector, and winding defects in the singlet sector. Each sector is canonically associated with a structural endomorphism algebra: End(

C^{3}

), End(

C^{2}

), and C respectively. These algebras classify the internal symmetry of the closure sectors and should not be interpreted as physical gauge groups. PTG-4 develops the geometric and algebraic structure of the closure sectors and states the Sector Algebra Theorem, proved in full in PDT-MC-1.

Suggested citation

Graham Fincham, Daniel Hilton. “PTG-4: Sector Structure, Chirality, and Structural Algebras.” Phase Differential Theory research programme. Version 1.1.1. 2026. https://www.phasedifferentialtheory.com/papers/ptg-4-2026

@misc{pdt_ptg_4_2026,
  title = {PTG-4: Sector Structure, Chirality, and Structural Algebras},
  author = {Graham Fincham and Daniel Hilton},
  year = {2026},
  version = {1.1.1},
  url = {https://www.phasedifferentialtheory.com/papers/ptg-4-2026}
}

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