PDT-I: Axiom 0, Finite Coherence Capacity, and the Emergence of a Positive Stability Threshold

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

Revised definitionPrincipal topic: Primitives and comparison structure.

PDT I’s finite-capacity “Axiom 0” belongs to this historical paper. R01’s A0 is the current distinction axiom, a different statement; selection is treated in R03.

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 Differential Theory (PDT) provides the physical interpretation of the geometric structures developed in Phase Transport Geometry (PTG). This first paper in the PDT series introduces Axiom 0, which asserts that coherent physical systems possess a finite coherence capacity. When the total curvature loading exceeds this capacity, coherence collapses and the system transitions to a new configuration. Combined with compact transport (PTG-2), the closure-compatible metric (PTG-3), and the sector structure (PTG-4), Axiom 0 implies the existence of a positive stability threshold that is interpreted as a positive mass gap within the PTG/PDT framework. PDT-I therefore establishes the physical foundation for the mass hierarchy developed in PDT-II and the collapse dynamics formalised in PDT-III.

Suggested citation

Graham Fincham, Daniel Hilton. “PDT-I: Axiom 0, Finite Coherence Capacity, and the Emergence of a Positive Stability Threshold.” Phase Differential Theory research programme. Version 1.1.1. 2026. https://www.phasedifferentialtheory.com/papers/pdt-i

@misc{pdt_pdt_i,
  title = {PDT-I: Axiom 0, Finite Coherence Capacity, and the Emergence of a Positive Stability Threshold},
  author = {Graham Fincham and Daniel Hilton},
  year = {2026},
  version = {1.1.1},
  url = {https://www.phasedifferentialtheory.com/papers/pdt-i}
}

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