R00
R00. “Foundational suite and review guide.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r00
Citations and attribution
Citation records use only documented titles, authors, versions and dates. Repository deposits, DOI records and journal-review stages are shown only where verified.
Citation principles
Cite an individual manuscript when discussing a specific derivation, theorem, model or proposal. Cite the wider research programme only when referring to PDT as a whole.
Public manuscript availability, repository deposit, DOI registration and journal review are separate facts. No repository record or DOI is currently verified for these records. Journal-review status is not confirmed.
Where a DOI is absent, cite the paper page and manuscript title. Do not reconstruct an identifier from a paper name or series code.
Current foundations
Authors, versions and release dates for the foundational suite have not yet been supplied with release files, so these are identifier-and-URL references. BibTeX will be added when that metadata is verified. No DOI or repository deposit is recorded.
R00
R00. “Foundational suite and review guide.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r00
R01
R01. “Core axioms and consistency.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r01
R02
R02. “Phase transport and complex structure.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r02
R03
R03. “Selection and persistent records.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r03
R04
R04. “Quantum states probability and dynamics.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r04
R05
R05. “Exclusion dynamics and realisation.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r05
R06
R06. “Composite systems Bell correlations and prediction.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r06
R07
R07. “Spatial carriers metric and orientation.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r07
R08
R08. “Clocks scales and physical identification.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r08
R09
R09. “Interactions matter and refinement.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r09
R10
R10. “Gravity and conditional Einstein dynamics.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r10
R11
R11. “Cosmology and effective stress.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r11
R12
R12. “Joint closure and the realisation boundary.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r12
R13
R13. “Mathematical audit and reproducibility.” Phase Differential Theory current foundations. https://www.phasedifferentialtheory.com/foundations/r13
Paper records
PTG I
Original research series
Graham Fincham, Daniel Hilton
Graham Fincham, Daniel Hilton. “PTG I: A Metric-Free Transport Framework for Scalar Fields.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/ptg-i
@misc{pdt_ptg_i,
title = {PTG I: A Metric-Free Transport Framework for Scalar Fields},
author = {Graham Fincham and Daniel Hilton},
url = {https://www.phasedifferentialtheory.com/papers/ptg-i}
}PTG II
Original research series
Graham Fincham, Daniel Hilton
Graham Fincham, Daniel Hilton. “PTG II: The Phase-Raychaudhuri Equation and Finite-Parameter Focusing.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/ptg-ii
@misc{pdt_ptg_ii,
title = {PTG II: The Phase-Raychaudhuri Equation and Finite-Parameter Focusing},
author = {Graham Fincham and Daniel Hilton},
url = {https://www.phasedifferentialtheory.com/papers/ptg-ii}
}PTG III
Original research series
Graham Fincham, Daniel Hilton
Graham Fincham, Daniel Hilton. “PTG III: Transport Capacity, Completeness, and Incompleteness Theorems.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/ptg-iii
@misc{pdt_ptg_iii,
title = {PTG III: Transport Capacity, Completeness, and Incompleteness Theorems},
author = {Graham Fincham and Daniel Hilton},
url = {https://www.phasedifferentialtheory.com/papers/ptg-iii}
}PTG IV
Original research series
Graham Fincham, Daniel Hilton
Graham Fincham, Daniel Hilton. “PTG IV: Transport Horizons and Boundary Geometry.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/ptg-iv
@misc{pdt_ptg_iv,
title = {PTG IV: Transport Horizons and Boundary Geometry},
author = {Graham Fincham and Daniel Hilton},
url = {https://www.phasedifferentialtheory.com/papers/ptg-iv}
}PTG V
Original research series
Graham Fincham, Daniel Hilton
Graham Fincham, Daniel Hilton. “PTG V: Quasi-Local Invariants on Transport Horizons.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/ptg-v
@misc{pdt_ptg_v,
title = {PTG V: Quasi-Local Invariants on Transport Horizons},
author = {Graham Fincham and Daniel Hilton},
url = {https://www.phasedifferentialtheory.com/papers/ptg-v}
}PTG VI
Original research series
Graham Fincham, Daniel Hilton
Graham Fincham, Daniel Hilton. “PTG VI: Transport Entropy and Monotonicity.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/ptg-vi
@misc{pdt_ptg_vi,
title = {PTG VI: Transport Entropy and Monotonicity},
author = {Graham Fincham and Daniel Hilton},
url = {https://www.phasedifferentialtheory.com/papers/ptg-vi}
}PTG VII
Original research series
Graham Fincham, Daniel Hilton
Graham Fincham, Daniel Hilton. “PTG VII: Membrane Evolution on Transport Horizons.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/ptg-vii
@misc{pdt_ptg_vii,
title = {PTG VII: Membrane Evolution on Transport Horizons},
author = {Graham Fincham and Daniel Hilton},
url = {https://www.phasedifferentialtheory.com/papers/ptg-vii}
}PTG VIII
Original research series
Graham Fincham, Daniel Hilton
Graham Fincham, Daniel Hilton. “PTG VIII: Structural Admissibility and Uniqueness of Transport Functionals.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/ptg-viii
@misc{pdt_ptg_viii,
title = {PTG VIII: Structural Admissibility and Uniqueness of Transport Functionals},
author = {Graham Fincham and Daniel Hilton},
url = {https://www.phasedifferentialtheory.com/papers/ptg-viii}
}PTG IX
Original research series
Graham Fincham, Daniel Hilton
Graham Fincham, Daniel Hilton. “PTG IX: Constitutive Closure and Autonomy of the Framework.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/ptg-ix
@misc{pdt_ptg_ix,
title = {PTG IX: Constitutive Closure and Autonomy of the Framework},
author = {Graham Fincham and Daniel Hilton},
url = {https://www.phasedifferentialtheory.com/papers/ptg-ix}
}QM I
Original research series
Graham Fincham, Daniel Hilton
Graham Fincham, Daniel Hilton. “QM I: Emergence of Quantum Mechanics from Phase.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/qm-i
@misc{pdt_qm_i,
title = {QM I: Emergence of Quantum Mechanics from Phase},
author = {Graham Fincham and Daniel Hilton},
url = {https://www.phasedifferentialtheory.com/papers/qm-i}
}QM II
Original research series
Graham Fincham, Daniel Hilton
Graham Fincham, Daniel Hilton. “QM II: Unified Field Structure.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/qm-ii
@misc{pdt_qm_ii,
title = {QM II: Unified Field Structure},
author = {Graham Fincham and Daniel Hilton},
url = {https://www.phasedifferentialtheory.com/papers/qm-ii}
}QM III
Original research series
Graham Fincham, Daniel Hilton
Graham Fincham, Daniel Hilton. “QM III: Scalar Spectrum and Experimental Signatures.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/qm-iii
@misc{pdt_qm_iii,
title = {QM III: Scalar Spectrum and Experimental Signatures},
author = {Graham Fincham and Daniel Hilton},
url = {https://www.phasedifferentialtheory.com/papers/qm-iii}
}QM IV
Original research series
Graham Fincham, Daniel Hilton
Graham Fincham, Daniel Hilton. “QM IV: Interaction Dynamics of Defect States.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/qm-iv
@misc{pdt_qm_iv,
title = {QM IV: Interaction Dynamics of Defect States},
author = {Graham Fincham and Daniel Hilton},
url = {https://www.phasedifferentialtheory.com/papers/qm-iv}
}QM V
Original research series
Graham Fincham, Daniel Hilton
Graham Fincham, Daniel Hilton. “QM V: Precision Phenomenology and Falsifiable Predictions.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/qm-v
@misc{pdt_qm_v,
title = {QM V: Precision Phenomenology and Falsifiable Predictions},
author = {Graham Fincham and Daniel Hilton},
url = {https://www.phasedifferentialtheory.com/papers/qm-v}
}PTG-1
Earlier development paper
Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)
Graham Fincham, Daniel Hilton. “PTG-1: Closure Architecture and the Minimal Phase Manifold.” Phase Differential Theory research programme. Version 1.1.1. 2026. https://www.phasedifferentialtheory.com/papers/ptg-1-2026
@misc{pdt_ptg_1_2026,
title = {PTG-1: Closure Architecture and the Minimal Phase Manifold},
author = {Graham Fincham and Daniel Hilton},
year = {2026},
version = {1.1.1},
url = {https://www.phasedifferentialtheory.com/papers/ptg-1-2026}
}PTG-2
Earlier development paper
Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)
Graham Fincham, Daniel Hilton. “PTG-2: Compact Transport Geometry and Curvature Loading.” Phase Differential Theory research programme. Version 1.1.1. 2026. https://www.phasedifferentialtheory.com/papers/ptg-2-2026
@misc{pdt_ptg_2_2026,
title = {PTG-2: Compact Transport Geometry and Curvature Loading},
author = {Graham Fincham and Daniel Hilton},
year = {2026},
version = {1.1.1},
url = {https://www.phasedifferentialtheory.com/papers/ptg-2-2026}
}PTG-3
Earlier development paper
Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)
Graham Fincham, Daniel Hilton. “PTG-3: Closure-Compatible Metric Selection.” Phase Differential Theory research programme. Version 1.1.1. 2026. https://www.phasedifferentialtheory.com/papers/ptg-3-2026
@misc{pdt_ptg_3_2026,
title = {PTG-3: Closure-Compatible Metric Selection},
author = {Graham Fincham and Daniel Hilton},
year = {2026},
version = {1.1.1},
url = {https://www.phasedifferentialtheory.com/papers/ptg-3-2026}
}PTG-4
Earlier development paper
Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)
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}
}PTG-5
Earlier development paper
Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)
Graham Fincham, Daniel Hilton. “PTG-5: Defect Mass Scaling and Return-Closure Invariants.” Phase Differential Theory research programme. Version 1.1.1. 2026. https://www.phasedifferentialtheory.com/papers/ptg-5-2026
@misc{pdt_ptg_5_2026,
title = {PTG-5: Defect Mass Scaling and Return-Closure Invariants},
author = {Graham Fincham and Daniel Hilton},
year = {2026},
version = {1.1.1},
url = {https://www.phasedifferentialtheory.com/papers/ptg-5-2026}
}PDT-I
Earlier development paper
Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)
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}
}PDT-II
Earlier development paper
Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)
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}
}PDT-III
Earlier development paper
Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)
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}
}PDT-MC-1
Earlier development paper
Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)
Graham Fincham, Daniel Hilton. “PDT-MC-1: Mathematical Closure Supplement.” Phase Differential Theory research programme. Version 1.1.1. 2026. https://www.phasedifferentialtheory.com/papers/pdt-mc-1
@misc{pdt_pdt_mc_1,
title = {PDT-MC-1: Mathematical Closure Supplement},
author = {Graham Fincham and Daniel Hilton},
year = {2026},
version = {1.1.1},
url = {https://www.phasedifferentialtheory.com/papers/pdt-mc-1}
}Programme attribution
Use Phase Differential Theory on first reference and PDT thereafter. When discussing a particular result, cite the individual paper.
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