Citations and attribution

Cite the work,
quote it cleanly.

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 the paper containing the result.

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

R00 to R13

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

Earlier papers: verified citation fields

23 papers with public manuscripts

PTG I

Original research series

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

Graham Fincham, Daniel Hilton

Version
Not recorded
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

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

BibTeX
@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

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

Graham Fincham, Daniel Hilton

Version
Not recorded
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

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

BibTeX
@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

PTG III: Transport Capacity, Completeness, and Incompleteness Theorems

Graham Fincham, Daniel Hilton

Version
Not recorded
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

Graham Fincham, Daniel Hilton. “PTG III: Transport Capacity, Completeness, and Incompleteness Theorems.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/ptg-iii

BibTeX
@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

PTG IV: Transport Horizons and Boundary Geometry

Graham Fincham, Daniel Hilton

Version
Not recorded
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

Graham Fincham, Daniel Hilton. “PTG IV: Transport Horizons and Boundary Geometry.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/ptg-iv

BibTeX
@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

PTG V: Quasi-Local Invariants on Transport Horizons

Graham Fincham, Daniel Hilton

Version
Not recorded
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

Graham Fincham, Daniel Hilton. “PTG V: Quasi-Local Invariants on Transport Horizons.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/ptg-v

BibTeX
@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

PTG VI: Transport Entropy and Monotonicity

Graham Fincham, Daniel Hilton

Version
Not recorded
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

Graham Fincham, Daniel Hilton. “PTG VI: Transport Entropy and Monotonicity.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/ptg-vi

BibTeX
@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

PTG VII: Membrane Evolution on Transport Horizons

Graham Fincham, Daniel Hilton

Version
Not recorded
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

Graham Fincham, Daniel Hilton. “PTG VII: Membrane Evolution on Transport Horizons.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/ptg-vii

BibTeX
@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

PTG VIII: Structural Admissibility and Uniqueness of Transport Functionals

Graham Fincham, Daniel Hilton

Version
Not recorded
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

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

BibTeX
@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

PTG IX: Constitutive Closure and Autonomy of the Framework

Graham Fincham, Daniel Hilton

Version
Not recorded
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

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

BibTeX
@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

QM I: Emergence of Quantum Mechanics from Phase

Graham Fincham, Daniel Hilton

Version
Not recorded
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

Graham Fincham, Daniel Hilton. “QM I: Emergence of Quantum Mechanics from Phase.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/qm-i

BibTeX
@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

QM II: Unified Field Structure

Graham Fincham, Daniel Hilton

Version
Not recorded
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

Graham Fincham, Daniel Hilton. “QM II: Unified Field Structure.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/qm-ii

BibTeX
@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

QM III: Scalar Spectrum and Experimental Signatures

Graham Fincham, Daniel Hilton

Version
Not recorded
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

Graham Fincham, Daniel Hilton. “QM III: Scalar Spectrum and Experimental Signatures.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/qm-iii

BibTeX
@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

QM IV: Interaction Dynamics of Defect States

Graham Fincham, Daniel Hilton

Version
Not recorded
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

Graham Fincham, Daniel Hilton. “QM IV: Interaction Dynamics of Defect States.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/qm-iv

BibTeX
@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

QM V: Precision Phenomenology and Falsifiable Predictions

Graham Fincham, Daniel Hilton

Version
Not recorded
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

Graham Fincham, Daniel Hilton. “QM V: Precision Phenomenology and Falsifiable Predictions.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/qm-v

BibTeX
@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

PTG-1: Closure Architecture and the Minimal Phase Manifold

Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)

Version
1.1.1
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

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

BibTeX
@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

PTG-2: Compact Transport Geometry and Curvature Loading

Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)

Version
1.1.1
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

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

BibTeX
@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

PTG-3: Closure-Compatible Metric Selection

Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)

Version
1.1.1
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

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

BibTeX
@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

PTG-4: Sector Structure, Chirality, and Structural Algebras

Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)

Version
1.1.1
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

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

BibTeX
@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

PTG-5: Defect Mass Scaling and Return-Closure Invariants

Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)

Version
1.1.1
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

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

BibTeX
@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

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

Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)

Version
1.1.1
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

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

BibTeX
@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

PDT-II: Mass Hierarchy and Sector Amplification

Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)

Version
1.1.1
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

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

BibTeX
@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

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

Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)

Version
1.1.1
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

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

BibTeX
@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

PDT-MC-1: Mathematical Closure Supplement

Graham Fincham (Delta Phi IP Ltd); Daniel Hilton (Independent Researcher)

Version
1.1.1
DOI
No DOI recorded
Journal review
Journal-review status not confirmed.

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

BibTeX
@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

When you mean the programme.

Use Phase Differential Theory on first reference and PDT thereafter. When discussing a particular result, cite the individual paper.

For reuse, translation or substantial quotation requests, use the contact page.