PDT-II: Mass Hierarchy and Sector Amplification

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 hierarchy and sector amplification relate to matter models in R09 and to calibration in R08.

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.

PDT-II develops the structural mass hierarchy implied by Phase Transport Geometry (PTG) and the finite coherence capacity introduced in PDT-I. The PTG mass functional

m_{i}

=

m_{0} \cdot C_{i} \cdot W_{i} \cdot L_{i} \cdot g_{i}^{2} \cdot S_{i} \cdot T_{i}

contains contributions from closure, winding, loading, excitation mode, sector symmetry, and return-closure invariants. PDT-II analyses how these factors combine to produce a three-tier structural hierarchy across the singlet, doublet, and triplet sectors. The return-closure invariant

T_{3}

= 9, derived in PDT-MC-1, provides the dominant amplification of the triplet structural mass functional. The hierarchy developed in this paper is the structural hierarchy of stable PTG defects; its relationship to the observed Standard Model particle spectrum is explored in later work.

Suggested citation

Graham Fincham, Daniel Hilton. “PDT-II: Mass Hierarchy and Sector Amplification.” Phase Differential Theory research programme. Version 1.1.1. 2026. https://www.phasedifferentialtheory.com/papers/pdt-ii

@misc{pdt_pdt_ii,
  title = {PDT-II: Mass Hierarchy and Sector Amplification},
  author = {Graham Fincham and Daniel Hilton},
  year = {2026},
  version = {1.1.1},
  url = {https://www.phasedifferentialtheory.com/papers/pdt-ii}
}

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