Research Papers
The research
library.
PDT research is presented in three collections: the current foundations, the earlier development papers and the original research series. Manuscript availability, version and journal-review status are recorded separately. Educational applications illustrate ideas and do not replace the formal papers.
Search the research index
- Foundational documents, including the R00 guide
- 14
- Earlier development papers
- 9
- Original research papers
- 14
- Files available for download
- 23
These counts describe the catalogue. They are not counts of peer-reviewed or formally released papers.
A. Current foundations
Current foundations
The R00–R13 suite: the R00 suite guide and 13 foundational papers. This is the first destination for the current axioms, definitions, mathematical results and physical assumptions of PDT. Manuscript PDFs for every paper in the suite are available on this website.
14 documents- R00Foundational suite and review guideThe guide to the suite, its reading order, the three PDT layers and the additional premises used in physical models.
- R01Core axioms and consistencyThe relational primitives, phase composition, retained history and the additional A6 realisation commitment.
- R02Phase transport and complex structureLoop phase, the minimal real phase carrier and the limits of what scalar phase information determines.
- R03Selection and persistent recordsConditions for a unique surviving candidate, symmetry obstructions and conditional record stability.
- R04Quantum states probability and dynamicsQuantum probability and dynamics under explicitly stated operational premises.
- R05Exclusion dynamics and realisationSpecified exclusion instruments, their implementations and the distinction between exact exclusion and robustness under noise.
- R06Composite systems Bell correlations and predictionComposite systems, a conditional Bell-nonlocal completion, no-signalling requirements and prediction.
- R07Spatial carriers metric and orientationConditional constructions of internal spatial carriers, metric structure and orientation persistence.
- R08Clocks scales and physical identificationThe distinction between record order, physical clocks and calibration, including the freedoms calibration leaves unresolved.
- R09Interactions matter and refinementCompatible interaction and matter models, with the assumptions and limits involved in refinement.
- R10Gravity and conditional Einstein dynamicsGravitational dynamics within a declared metric and action class, including the obligation to account for total stress.
- R11Cosmology and effective stressConditional cosmological models and the constraints imposed by stress and dilution.
- R12Joint closure and the realisation boundaryThe requirements for a common physical model and the distinction between physical closure and the adopted actuality boundary.
- R13Mathematical audit and reproducibilityThe verification record, mathematical provenance and reproducibility of the suite.
Research history
The earlier development papers and the original research series document how Phase Differential Theory developed before the R00–R13 suite. They remain available at their existing addresses, with their original titles, authorship, dates, citations and manuscripts. Read them in their original model and publication context; the R00–R13 suite provides the current formulation.
Nothing has been removed.
Status key
R00 to R13, the current formulation of PDT. Download availability, journal review and experimental evidence are recorded separately.
One of the nine earlier manuscripts, retained with its original text and available PDF.
One of the fourteen original PTG and QM manuscripts, retained with its original text and available PDF.
A dated website note identifying a specific issue in an earlier manuscript.
Interactive visual explanation available.
B. Earlier development papers
Earlier development papers
PTG 1 to 5, PDT I to III and PDT MC 1. Earlier research papers retained as part of the development of PDT.
9 papersC. Original research series
Original research series
PTG I to IX and QM I to V. The original Roman-numeral manuscripts.
14 papersRelationship guide
How the current foundations relate to the earlier papers
The foundational suite provides the current formulation of PDT. Earlier papers remain part of the research record and document the development of its ideas and model constructions. The links below identify related topics. A topic connection does not mean that every claim in an earlier paper is retained or that a new paper reproduces its proof.
| Earlier paper | Principal topic | Current foundations | Relationship | Specific correction |
|---|---|---|---|---|
| PTG 1 PTG-1: Closure Architecture and the Minimal Phase Manifold | Phase transport and representations | Historical background An earlier closure architecture and phase manifold. The current account of phase composition and the minimal phase carrier is in R01 and R02. | None recorded | |
| PTG 2 PTG-2: Compact Transport Geometry and Curvature Loading | Phase transport and representations | Related current treatment Transport geometry and curvature are treated currently through loop phase in R02 and conditional carrier constructions in R07. | None recorded | |
| PTG 3 PTG-3: Closure-Compatible Metric Selection | Internal spatial carriers and orientation | Related current treatment Metric selection is treated currently by separating internal metrics (R07) from the declared physical metric premise and action class (R10). | None recorded | |
| PTG 4 PTG-4: Sector Structure, Chirality, and Structural Algebras | Interactions, matter and refinement | Related current treatment Sector structure and chirality relate to orientation persistence in R07 and to matter models in R09. | None recorded | |
| PTG 5 PTG-5: Defect Mass Scaling and Return-Closure Invariants | Interactions, matter and refinement | Related current treatment Mass scaling relates to matter models in R09. R08 records that a calibrated mass scale is an input, not a prediction. | None recorded | |
| PDT I PDT-I: Axiom 0, Finite Coherence Capacity, and the Emergence of a Positive Stability Threshold | Primitives and comparison structure | Revised definition 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. | None recorded | |
| PDT II PDT-II: Mass Hierarchy and Sector Amplification | Interactions, matter and refinement | Related current treatment Mass hierarchy and sector amplification relate to matter models in R09 and to calibration in R08. | None recorded | |
| PDT III PDT-III: Differential Transport, Collapse Dynamics, and the Coherence Horizon | Selection and persistent records | Related current treatment Collapse dynamics are treated currently as last-survivor selection (R03) and specified exclusion instruments (R05). | None recorded | |
| PDT MC 1 PDT-MC-1: Mathematical Closure Supplement | Verification and provenance | Historical background An earlier mathematical closure supplement. Joint closure is addressed in R12 and verification and provenance in R13. | None recorded | |
| PTG I PTG I: A Metric-Free Transport Framework for Scalar Fields | Phase transport and representations | Historical background An early metric-free transport framework. Current phase transport is treated in R02. | None recorded | |
| PTG II PTG II: The Phase-Raychaudhuri Equation and Finite-Parameter Focusing | Internal spatial carriers and orientation | Historical background Focusing in a transport congruence relates to carrier geometry (R07) and gravitational dynamics (R10). | None recorded | |
| PTG III PTG III: Transport Capacity, Completeness, and Incompleteness Theorems | Internal spatial carriers and orientation | Historical background Transport capacity and completeness relate to transport structure (R02) and conditional carrier constructions (R07). | None recorded | |
| PTG IV PTG IV: Transport Horizons and Boundary Geometry | Gravitational dynamics | Specific claim corrected Transport horizons relate to gravitational dynamics in R10. | Limiting horizon requires further conditions | |
| PTG V PTG V: Quasi-Local Invariants on Transport Horizons | Gravitational dynamics | Specific claim corrected Quasi-local invariants on horizons relate to gravitational dynamics in R10. | Limiting horizon requires further conditions | |
| PTG VI PTG VI: Transport Entropy and Monotonicity | Gravitational dynamics | Specific claim corrected A transport entropy built on PTG V. Gravitational dynamics are treated in R10; verification practice in R13. | Entropy sign argument requires correction | |
| PTG VII PTG VII: Membrane Evolution on Transport Horizons | Gravitational dynamics | Historical background Membrane evolution on horizons relates to gravitational dynamics in R10. | None recorded | |
| PTG VIII PTG VIII: Structural Admissibility and Uniqueness of Transport Functionals | Gravitational dynamics | Specific claim corrected Uniqueness of transport functionals relates to the action classification in R10, which states its class and premises explicitly. | Classification requires stated assumptions | |
| PTG IX PTG IX: Constitutive Closure and Autonomy of the Framework | Joint physical closure | Historical background Constitutive closure relates to the current requirements for joint physical closure in R12. | None recorded | |
| QM I QM I: Emergence of Quantum Mechanics from Phase | Quantum probability and dynamics | Historical background An early account of quantum mechanics from phase. The current treatment uses the phase plane (R02) and stated operational premises (R04). | None recorded | |
| QM II QM II: Unified Field Structure | Internal spatial carriers and orientation | Specific claim corrected Field structure and a constructed metric relate to internal carriers (R07) and the physical metric premise (R10). | Scope of the displayed metric construction | |
| QM III QM III: Scalar Spectrum and Experimental Signatures | Interactions, matter and refinement | Specific claim corrected A scalar spectrum in a calibrated effective model relates to matter models in R09. | Model-dependent mass estimates | |
| QM IV QM IV: Interaction Dynamics of Defect States | Interactions, matter and refinement | Historical background Defect interaction dynamics relate to interaction and matter models in R09. | None recorded | |
| QM V QM V: Precision Phenomenology and Falsifiable Predictions | Interactions, matter and refinement | Specific claim corrected Proposed phenomenology relates to matter models (R09) and cosmological stress (R11). A testable prediction requires a specified model, calculation and protocol. | Prediction equations on pages 3 to 4 contain dimensional inconsistencies; the estimates are not established predictions. |
Visual route
Explore the mathematics visually
Formal papers establish the mathematics. The educational apps provide a second route into the same ideas through interactive diagrams, simulations and step-by-step explanations. Apps are explanatory aids and are never evidence for, or a substitute for, the formal paper.
5 verified current-paper educational appsConcentric phase rings
Related to the phase-propagation material
Interactive canvas showing coherent phase fronts propagating outward and coupling relational nodes.
PDT electromagnetism visual simulator
Related to electromagnetic emergence
Browser-based simulator exploring electromagnetic behaviour emerging from relational phase dynamics.
Phase evolution framework
Related to deterministic phase evolution
Numerical modelling of deterministic phase evolution across coupled relational systems.
Five checked destinations are associated with current programme papers 01 to 05. The three checked tools above are listed separately because no formal one-to-one paper relationship is documented.
Companion reading