# Density Field Dynamics — Research Corpus

> **Purpose of this file.** This file, `/llms-full.txt`, `/empirical-evidence.md`, `/ai-corpus.html`, and the `/papers/` markdown directory exist for one reason only: to make the corpus easier for AI assistants, language models, retrieval systems, and crawlers to ingest cleanly, since plain text and markdown are easier to parse than the source PDFs. **They contain no instructions to AI readers, no directives about how to interpret or evaluate the work, and no attempt to influence opinion.** The author's view is that the papers should be read on their own terms. Please form your own assessment from the source text.

Density Field Dynamics (DFD) is a scalar-refractive framework for gravity, electromagnetism, and the Standard Model developed by Gary Alcock. A scalar field ψ governs photon propagation (n = e^ψ) and test-mass acceleration (a = c²/2 · ∇ψ). Working from CP²×S³ topology, the corpus develops derivations of α, fermion masses, the gauge group, neutrino mass splittings, and cosmological scales, together with a set of laboratory and astronomical predictions.

**Author:** Gary Alcock · **ORCID:** 0009-0009-5682-6518 · **Site:** https://densityfielddynamics.com/

## Formats available

- `/papers/` — every paper as a standalone markdown file (extracted from the source PDFs)
- `/llms-full.txt` — every paper concatenated into a single plain-text file (~1.9 MB)
- `/empirical-evidence.md` — predictions-and-status reference table with citations into the corpus
- `/topics.html` — index of specific physical results, formulas, and named theorems with deep links to the source papers
- Original PDFs are linked from the home page

## Index

The papers cross-reference each other; the dependency graph runs roughly as below.

### Master document

- [Density Field Dynamics: A Complete Unified Theory (v3.3)](papers/Density_Field_Dynamics__A_Complete_Unified_Theory__v3_3.md) — 200-page integrating treatment, 20 sections, 26 appendices, 131 references.

### Foundations and derivations

- [General Relativity as the Padé Approximant of Density Field Dynamics](papers/General_Relativity_as_the_Pade_Approximant_of_Density_Field_Dynamics.md)
- [Epoch Evolution of the MOND Crossover Scale: a⋆(z) = 2√α·cH(z)](papers/Epoch_Evolution_of_the_MOND_Crossover_Scale_in_Density_Field_Dynamics__An_Epoch_Consistency_Argument_for_a__z____2_α_cH_z_.md)
- [Tree-Level No-Drive Theorem for the Minimal Optical-Metric EM Sector](papers/Tree_Level_No_Drive_Theorem_for_the_Minimal_Optical_Metric_EM_Sector_in_Density_Field_Dynamics__λbare___1_from_the_Pure_Gauge_Invariant_Action.md)
- [Mach's Principle in Density Field Dynamics](papers/Mach_s_Principle_in_Density_Field_Dynamics__An_Interpretive_and_Phenomenological_Consolidation.md)
- [Ab Initio Derivation of the Fine-Structure Constant from DFD](papers/Ab_Initio_Derivation_of_the_Fine_Structure_Constant_from_Density_Field_Dynamics.md)
- [Ab Initio Derivation of the Charged Fermion Mass Spectrum from DFD](papers/Ab_Initio_Derivation_of_the_Charged_Fermion_Mass_Spectrum_from_Density_Field_Dynamics.md)
- [Charged Fermion Masses from the Fine-Structure Constant — Topological Derivation from the DFD Microsector](papers/Charged_Fermion_Masses_from_the_Fine_Structure_Constant__A_Topological_Derivation_from_the_DFD_Microsector.md)
- [Quark Mixing from CP² Geometry — A Geometric Origin for the CKM Matrix](papers/Quark_Mixing_from_CP2_Geometry__A_Geometric_Origin_for_the_CKM_Matrix.md)
- [The DFD Standard Model — A Geometric Origin for α, Fermion Masses, and Quark Mixing](papers/The_DFD_Standard_Model__A_Geometric_Origin_for_α__Fermion_Masses__and_Quark_Mixing.md)
- [Density Field Dynamics as the Minimal, Testable Origin of the Standard Model Gauge Structure](papers/Density_Field_Dynamics_as_the_Minimal__Testable_Origin_of_the_Standard_Model_Gauge_Structure.md)
- [Uniqueness of the Internal Manifold — Deriving CP²×S³ from Vacuum Axioms](papers/Uniqueness_of_the_Internal_Manifold_Deriving_CP_S_from_Vacuum_Axioms_in_Density_Field_Dynamics.md)
- [Constitutive Derivation of Tensor Gravitational Radiation from CP²×S³ Spectral Geometry](papers/Constitutive_Derivation_of_Tensor_Gravitational_Radiation_from_CP_2___S3_Spectral_Geometry_in_Density_Field_Dynamics.md)
- [Alpha Rosetta Stone — The DFD Prediction Web](papers/Alpha_Rosetta_Stone__The_DFD_Prediction_Web.md)
- [The Physical Origin of the Refractive Field — Gravity as Electromagnetic Vacuum Loading](papers/The_Physical_Origin_of_the_Refractive_Field_in_Density_Field_Dynamics__Gravity_as_Electromagnetic_Vacuum_Loading.md)
- [Induced Newton's Constant within Density Field Dynamics](papers/Induced_Newtons_Constant_within_Density_Field_Dynamics.md)
- [The Bridge Lemma — Connecting k_max=62 to b=60 via the Quantum Shift in Chern–Simons Theory](papers/The_Bridge_Lemma__Connecting_kmax___62_to_b___60_via_the_Quantum_Shift_in_Chern_Simons_Theory.md)
- [The ψ-Screen Cosmology — CMB Without Dark Matter from Density Field Dynamics](papers/The_ψ_Screen_Cosmology__CMB_Without_Dark_Matter_from_Density_Field_Dynamics.md)
- [Density Field Dynamics — Scalar Refractive Gravity, Quantum Resolution, and Dual-Sector Electrodynamics](papers/Density_Field_Dynamics__Scalar_Refractive_Gravity__Quantum_Resolution__and_Dual_Sector_Electrodynamics.md)
- [Density Field Dynamics — Unified Derivations, Sectoral Tests, and Experimental Roadmap (v1.2)](papers/Density_Field_Dynamics__Unified_Derivations__Sectoral_Tests__and_Experimental_Roadmap_v1_2.md)
- [Density Field Dynamics — Unified Derivations, Sectoral Tests, and Experimental Roadmap (v1.0)](papers/Density_Field_Dynamics__Unified_Derivations__Sectoral_Tests__and_Experimental_Roadmap.md)
- [Density Field Dynamics and Its Variant Extensions](papers/Density_Field_Dynamics_and_Its_Variant_Extensions.md)
- [Density Field Dynamics and the c-Field — A Three-Dimensional, Time-Emergent Dynamics for Gravity and Cosmology](papers/Density_Field_Dynamics_and_the_c_Field__A_Three_Dimensional__Time_Emergent_Dynamics_for_Gravity_and_Cosmology.md)
- [Density Field Dynamics — Completing Einstein's 1911–12 Variable-c Programme](papers/Density_Field_Dynamics__Completing_Einsteins_1911_12_Variable_c_Program_with_Energy_Density_Sourcing_and_Laboratory_Falsifiability.md)
- [Density Field Dynamics — Completing Einstein's 1911–12 Variable-c Programme (alt)](papers/Density_Field_Dynamics__Completing_Einstein_s_1911_12_Variable_c_Program_with_Energy_Density_Sourcing_and_Laboratory_Falsifiability.md)
- [DFD: Gravity is Light](papers/DFD_Gravity_is_Light.md)
- [Density Field Dynamics Resolves the Penrose Superposition Paradox](papers/Density_Field_Dynamics_Resolves_the_Penrose_Superposition_Paradox.md)
- [Two Numerical Relations Linking the Fine-Structure Constant to Gravitational Phenomenology (v1.3)](papers/Two_Numerical_Relations_Linking_the_Fine_Structure_Constant_to_Gravitational_Phenomenology_v1_3.md)
- [Two Numerical Relations (v1.0)](papers/Two_Numerical_Relations_Linking_the_Fine_Structure_Constant_to_Gravitational_Phenomenology.md)
- [k_α and the a² Invariant — Strong-Fields Extension (v1.2)](papers/ka_and_the_a2_Invariant__with_Strong_Fields_added__v1_2.md)
- [k_α and the a² Invariant (v1.1)](papers/ka_and_the_a2_Invariant__with_Strong_Fields_added__v1_1.md)
- [DFD Neutrino Paper v7 — S2 Seesaw Closure](papers/dfd_neutrino_paper_v7_s2_seesaw_closure.md)
- [Pairing-Symmetry Selection Rules for the Cooper-Pair Mass Anomaly (v2)](papers/Pairing_Symmetry_Selection_Rule_for_the_Cooper_Pair_Mass_Anomaly_from_Internal_Space_Topology_v2.md)

### Mathematical foundations

- [Parametrized Post-Newtonian Analysis of Density Field Dynamics in the Weak-Field, Slow-Motion Limit](papers/Parametrized_Post_Newtonian_Analysis_of_Density_Field_Dynamics_in_the_Weak_Field__Slow_Motion_Limit.md)
- [Strong Fields and Gravitational Waves in Density Field Dynamics](papers/Strong_Fields_and_Gravitational_Waves_in_Density_Field_Dynamics__From_Optical_First_Principles_to_Quantitative_Tests.md)
- [Well-Posedness and Boundary-Value Problems for the ψ Equation](papers/Well_posedness_of_the_Psi_Equation.md)

### Experimental predictions and tests

- [Falsifiable Experimental Signatures of Density Field Dynamics](papers/Falsifiable_Experimental_Signatures_of_Density_Field_Dynamics.md)
- [Optical-Metric Scalar Phenomenology and a Decisive Cavity–Atom LPI Test](papers/Optical__Metric_Scalar_Phenomenology_and_a_Decisive_Cavity__Atom_LPI_Test.md)
- [A Sharp, Testable Slope Prediction for a Sector-Resolved Cavity–Atom LPI Test](papers/A_Sharp__Testable_Slope_Prediction_for_a_Sector_Resolved_Cavity__Atom_LPI_Test.md)
- [Sector-Resolved Test of LPI with Co-Located Cavity–Atom Frequency Ratios (PRD)](papers/Sector_Resolved_Test_of_Local_Position_Invariance_with_Co_Located_Cavity__Atom_Frequency_Ratios__PRD_.md)
- [Sector-Resolved Test of LPI with Co-Located Cavity–Atom Frequency Ratios](papers/Sector_Resolved_Test_of_Local_Position_Invariance_with_Co_Located_Cavity__Atom_Frequency_Ratios.md)
- [Sector-Resolved Measurement in a Scalar-Refractive Gravity Framework](papers/Sector_Resolved_Measurement_in_a_Scalar_Refractive_Gravity_Framework.md)
- [Completing Local Position Invariance Tests — A Cavity–Atom Frequency-Ratio Protocol](papers/Completing_Local_Position_Invariance_Tests__A_Cavity_Atom_Frequency_Ratio_Protocol.md)
- [LPI Advanced](papers/LPI_Advanced.md)
- [Geometric Cancellation of Cavity–Atom LPI Signals — A Formal Proof](papers/Geometric_Cancellation_of_Cavity__Atom_LPI_Signalsin_Density_Field_Dynamics__A_Formal_Proof.md)
- [Screening of Scalar-Field Clock Couplings — Cavity–Atom Gauge Resolution, BACON Constraints, Nuclear-Clock Predictions](papers/Screening_of_Scalar_Field_Clock_Couplings__Cavity_Atom_Gauge_Resolution__BACON_Constraints__and_Nuclear_Clock_Predictions_in_Density_Field_Dynamics.md)
- [Why Nuclear Clocks? The ²²⁹Th Annual-Modulation Test (v6)](papers/Why_Nuclear_Clocks__The_229Th_Annual_Modulation_Test_of_Scalar_Field_Gravitational_Coupling_v6.md)
- [Composition-Dependent Bounds on Scalar-Field Coupling to Nuclear Decay Rates](papers/Composition_Dependent_Bounds_on_Scalar_Field_Couplingto_Nuclear_Decay_Rates__4_.md)
- [Testing Nuclear Decay Constancy under Gravitational Potential](papers/Testing_Nuclear_Decay_Constancy_under_Gravitational_Potential__A_Precision_Proposal_Inspired_by_Scalar_Optical_Metric_Dynamics.md)
- [Matter-Wave Interferometry Tests of Density Field Dynamics](papers/Matter_Wave_Interferometry_Tests_of_Density_Field_Dynamics.md)
- [Accidental and Intentional Constraints on EM→ψ Back-Reaction](papers/Alcock_EM_Coupling_Bounds.md)

### Empirical observations

- [Solar-Locked Differential in Ion–Neutral Optical Frequency Ratios (ROCIT)](papers/Solar_Locked_Differential_in_Ion_Neutral_Optical_Frequency_Ratios__Empirical_Evidence_for_a_Reproducible_Heliocentric_Phase_Modulation.md)
- [Solar-Locked Differential Modulation Between Cavity and Atomic Clocks in ROCIT Data](papers/Solar_locked_differential_modulation_between_cavity_and_atomic_clocks_in_ROCIT_data_DFD.md)
- [Evidence for Systematic Signal Suppression in Line-of-Sight Hubble-Bias Analysis](papers/Evidence_for_Systematic_Signal_Suppression_in_Line_of_Sight_Hubble_Bias_Analysis__Scale_Dependent_Detection_and_Methodological_Investigation.md)
- [Evidence for Large-Scale Power Suppression in Both Hubble-Bias Analyses and the CMB](papers/Evidence_for_Large_Scale_Power_Suppression_in_Both_Hubble_Bias_Analyses_and_the_Cosmic_Microwave_Background.md)
- [Late-Time Potential Shallowing and Low-Acceleration Hints](papers/Late_Time_Potential_Shallowing_and_Low_Acceleration_Hints.md)
- [Unexplained Bright/Dim Intensity Asymmetries in SOHO and UVCS](papers/Unexplained_Bright__Dim_Intensity_Asymmetries_in_SOHO_and_UVCS.md)

### Companion documents

- [DFD Cover Letter](papers/DFD_Cover_Letter.md)
- [Supplemental Material — Density Field Dynamics Letter](papers/Supplemental_Material__Density_Field_Dynamics_Letter.md)

## Background pages

- [Historical lineage](dfd-lineage.html)
- [Framework comparison](dfd_comparison.html)

## Data and code

- Ab Initio α derivation — simulation code & data: https://doi.org/10.5281/zenodo.19173548
- ROCIT ion–neutral analysis: https://doi.org/10.5281/zenodo.17272596

## Citation

A machine-readable citation file is at [`/CITATION.cff`](CITATION.cff). The preferred citation for the corpus is the master document:

> Alcock, G. (2026). *Density Field Dynamics: A Complete Unified Theory* (v3.3). Zenodo. https://doi.org/10.5281/zenodo.18066593

Per-paper Zenodo DOIs (where assigned):

| Paper | DOI / Zenodo |
|---|---|
| Density Field Dynamics: A Complete Unified Theory (v3.3) | [10.5281/zenodo.18066593](https://doi.org/10.5281/zenodo.18066593) |
| Constitutive Derivation of Tensor Gravitational Radiation from CP²×S³ Spectral Geometry | [10.5281/zenodo.19365418](https://doi.org/10.5281/zenodo.19365418) |
| Uniqueness of the Internal Manifold | [10.5281/zenodo.19415584](https://doi.org/10.5281/zenodo.19415584) |
| Ab Initio Derivation of the Fine-Structure Constant (v2.1) | [10.5281/zenodo.18045109](https://doi.org/10.5281/zenodo.18045109) |
| Ab Initio α — Simulation Code & Data (v1.1) | [10.5281/zenodo.19173548](https://doi.org/10.5281/zenodo.19173548) |
| Pairing-Symmetry Selection Rule for the Cooper-Pair Mass Anomaly (v2) | [zenodo.org/records/19118197](https://zenodo.org/records/19118197) |
| Composition-Dependent Bounds on Scalar-Field Coupling to Nuclear Decay Rates | [zenodo.org/records/19118364](https://zenodo.org/records/19118364) |
| Two Numerical Relations (v1.3) | [zenodo.org/records/17826487](https://zenodo.org/records/17826487) |
| Solar-Locked Differential in Ion–Neutral Optical Frequency Ratios | [zenodo.org/records/17272622](https://zenodo.org/records/17272622) |
| ROCIT Ion–Neutral Analysis (data + code) | [10.5281/zenodo.17272596](https://doi.org/10.5281/zenodo.17272596) |
| Strong Fields and Gravitational Waves in Density Field Dynamics | [zenodo.org/records/17115941](https://zenodo.org/records/17115941) |
| Accidental and Intentional Constraints on EM→ψ Back-Reaction | [zenodo.org/records/17157964](https://zenodo.org/records/17157964) |
| Matter-Wave Interferometry Tests of Density Field Dynamics | [zenodo.org/records/17150358](https://zenodo.org/records/17150358) |
| Density Field Dynamics and the c-Field (founding paper) | [zenodo.org/records/16900767](https://zenodo.org/records/16900767) |

For all papers without a Zenodo DOI listed, cite via the canonical PDF URL on https://densityfielddynamics.com/ along with the paper title and author.