Phase Differential Theory
Phase Differential
A Framework for Reality

The library

The
papers.

Two arcs. Fourteen documents. Reader summary, abstract, falsifiable predictions, and BibTeX on every page.

Reader path →Physicist path →

PTG I — IX

Phase, Tilt, and Geometry.

Nine papers that build the geometry of phase and the dynamics that live on it.

PTG I

PTG I: A Metric-Free Transport Framework for Scalar Fields

PTG I lays the foundation. Strip a manifold down to the bare minimum: a smooth scalar field (the phase), a cone of allowed transport directions at every point, and a torsion-free c…

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PTG II

PTG II: The Phase-Raychaudhuri Equation and Finite-Parameter Focusing

PTG II derives PDT's version of the Raychaudhuri equation, the workhorse identity that controls how bundles of trajectories spread or focus. We do it without a metric. With only a …

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PTG III

PTG III: Transport Capacity, Completeness, and Incompleteness Theorems

PTG III turns local focusing into a global obstruction. We define transport capacity, a non-negative measure on hypersurfaces compatible with the transport cone, and a notion of tr…

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PTG IV

PTG IV: Transport Horizons and Boundary Geometry

PTG IV asks what the failure of completeness leaves behind. Each incomplete congruence ends on a canonical terminal hypersurface, the transport horizon, that carries a limiting tra…

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PTG V

PTG V: Quasi-Local Invariants on Transport Horizons

PTG V equips the transport horizon with three quasi-local invariants: a transverse area, a capacity-weighted invariant, and a curvature-type invariant built from the limiting shear…

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PTG VI

PTG VI: Transport Entropy and Monotonicity

PTG VI builds a single scalar functional, the transport entropy, by weighting the three quasi-local invariants from PTG V. The entropy is non-negative, finite on every transported …

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PTG VII

PTG VII: Membrane Evolution on Transport Horizons

PTG VII makes the horizon dynamical. The entropy gradient, combined with a shear-dissipating term, defines a canonical vector field on the transport horizon. The resulting first-or…

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PTG VIII

PTG VIII: Structural Admissibility and Uniqueness of Transport Functionals

PTG VIII proves that PDT's transport functionals are not arbitrary choices. The focusing functional, the capacity density, and the entropy weights are uniquely determined, up to fi…

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PTG IX

PTG IX: Constitutive Closure and Autonomy of the Framework

PTG IX closes the programme. Every admissible focusing functional and capacity density arises from a single constitutive tensor; no other admissible scalar, vector, or tensor funct…

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QM I — V

Quantum mechanics from phase.

Five papers. The Born rule, the effective Lagrangian, and the predictions QM V bets on.

QM I

QM I: Emergence of Quantum Mechanics from Phase

Standard quantum mechanics works, but it sits on assumptions no one has ever justified from a deeper picture. QM I takes a different starting point. It assumes the universe is made…

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QM II

QM II: Unified Field Structure

If QM I shows that the Schrödinger equation can be derived rather than postulated, QM II asks a much bigger question. Can the rest of physics, gravity, particles, the Standard Mode…

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QM III

QM III: Scalar Spectrum and Experimental Signatures

A theory is only physics if it can be wrong. QM III makes PDT wrong-able. It takes the defect picture from QM II, computes the spectrum of small wobbles around the defect, and read…

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QM IV

QM IV: Interaction Dynamics of Defect States

Particles in PDT are not point-like. They are stable knots in the phase manifold. So where do forces come from? QM IV answers that. When one defect moves or wobbles, it disturbs t…

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QM V

QM V: Precision Phenomenology and Falsifiable Predictions

QM V is the scorecard. It collects everything PDT predicts into one place and pins each prediction to a number, an experiment and a sensitivity. The organising quantity is a single…

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