PDT-III: Differential Transport, Collapse Dynamics, and the Coherence Horizon

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: Selection and persistent records.

Collapse dynamics are treated currently as last-survivor selection (R03) and specified exclusion instruments (R05).

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-III develops the dynamical consequences of finite coherence capacity (Axiom 0) introduced in PDT-I. The compact transport potential of PTG-2 induces a gradient-flow dynamical system on the minimal phase manifold (

S^{1}

)^6, and the curvature operator generates a loading accumulation that grows along the flow. When the total loading exceeds the coherence capacity

C_{max}

, the system undergoes coherence collapse. PDT-III formalises this behaviour, defines the coherence horizon, and shows that the collapse time is a stopping time determined entirely by the transport dynamics together with finite coherence capacity. Existence and uniqueness of solutions to the differential transport system are established in PDT-MC-1.

Suggested citation

Graham Fincham, Daniel Hilton. “PDT-III: Differential Transport, Collapse Dynamics, and the Coherence Horizon.” Phase Differential Theory research programme. Version 1.1.1. 2026. https://www.phasedifferentialtheory.com/papers/pdt-iii

@misc{pdt_pdt_iii,
  title = {PDT-III: Differential Transport, Collapse Dynamics, and the Coherence Horizon},
  author = {Graham Fincham and Daniel Hilton},
  year = {2026},
  version = {1.1.1},
  url = {https://www.phasedifferentialtheory.com/papers/pdt-iii}
}

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