The corpus
Where the work lives.
The DFT corpus has three pillars. A 25-chapter book that develops the theory from first principles. Sixteen papers that treat focused topics in depth. The dft-solver, a Python implementation of the numerical machinery. A 28-claim patent draft sits alongside, covering the algorithmic and hardware contributions. Nothing here claims finished status; every piece is open to external scrutiny.
01
PAPERS
Sixteen manuscripts.
The geometric-framework paper on Riemannian-manifold learning has been accepted in Frontiers in Big Data. The remaining manuscripts are in preparation; pre-publication drafts are available on request for academic peer review. Each row below names the question the paper takes up; the full title and the publication target sit below.
- P-01 The Parrondo Paradox as a Non-Equilibrium Phase Transition in Data Field Theory In prep
- P-02 Data Field Theory: An Axiomatic Framework for Intelligence with Testable Physical Signatures In prep
- P-03 Data Field Theory: A Geometric Framework for Learning on Riemannian Manifolds with Synthetic Validation and Limitation Analysis Frontiers in Big Data · DOI 10.3389/fdata.2026.1752468 Published
- P-04 The Mass-Robustness Law: A Field-Theoretic Principle for Generalization, Mathematical Foundations and Experimental Validation In prep
- P-05 Advanced Mathematical Extensions of Data Field Theory: Hyperbolic Geometry, Gauge Theory, and Higher Structures In prep
- P-06 Energy-Based Learning as Field Dynamics: Geometric Foundations and Symmetry-Aware Filtering in Data Field Theory In prep
- P-07 The Data Field Processor: A Computing Stack for Field-Theoretic Learning In prep
- P-08 Universal Critical Phenomena in Learning Systems: Comprehensive Experimental Validation of Data Field Theory Across Domains In prep
- P-09 Structural Analogies Between Data Field Theory and Quantum Field Theory: A Mathematical Framework for Cross-Domain Method Transfer In prep
- P-10 Hierarchical Parrondo Paradoxes in Data Field Theory: Rigorous Framework, Validated Scaling, and Design Principles In prep
- P-11 Data Field Thermodynamics: A Unified Framework for Intelligence, through Geometric Field Theory and Thermodynamic Principles In prep
- P-12 Data Field Theory: A Unified Mathematical Framework for Physics-Grade Intelligence In prep
- P-13 Unified Theory of Critical Learning and Data Field Processing: Bridging Statistical Physics with Specialized Computing Architecture In prep
- P-14 Advanced Mathematical Foundations of the Mass-Robustness Law: Hyperbolic Geometry, Gauge Theory, and Spectral Analysis In prep
- P-15 Quantum-Enhanced Hierarchical Systems: A Field-Theoretic Framework for Emergent Optimization In prep
- P-16 Data Field Theory: A Geometric and Field-Theoretic Foundation for Emergent Intelligence In prep
02
THE BOOK
Twenty-five chapters.
From the diagnosis of modern AI's heuristic plateau to the empirical-validation chapter, the book moves through the mathematical foundations, the theory, the numerical methods, the empirics, the applications, the safety layer, and the integration. Six AGI-variant chapters (CH19AGI–CH24AGI) repackage chapters 19–24 for a different audience.
| Chapter | Title | Part |
|---|---|---|
| CH1 | Introduction: The Quest for a Physics of Intelligence | I. Diagnosis |
| CH2 | Mathematical Foundations: Manifolds, Fields, and Operators | II. Mathematical foundations |
| CH3 | Physics Primer: Field Theory and Critical Phenomena | II. Mathematical foundations |
| CH4 | Core Axioms of Data Field Theory | III. The theory |
| CH5 | The Data Field and its Manifold Substrate | III. The theory |
| CH6 | Dynamical Laws: From Ginzburg-Landau to Generic Learning Flows | III. The theory |
| CH7 | Observables in DFT: How to Measure "Intelligent" Behavior | III. The theory |
| CH8 | Symmetry and Equivariance in Field Dynamics | III. The theory |
| CH9 | Rigorous Mathematical Foundations of Data Field Theory | IV. Geometric structure |
| CH10 | Advanced Extensions of Data Field Theory | IV. Geometric structure |
| CH11 | From Theory to Computation: The DFT Solver | V. Numerical methods |
| CH12 | DFT Learning Stack: From PDEs to Trainable Systems | V. Numerical methods |
| CH13 | Critical Phenomena in the Wild: Universal DFT Signatures Across Domains | VI. Empirics |
| CH14 | Non-Equilibrium Learning: Parrondo Switching in Practice | VI. Empirics |
| CH15 | From Principles to Product: The Data Field Processor (DFP) | VII. Implementation |
| CH16 | Geometry and Topology of Concepts: Hyperbolic Embeddings and Gauge-Theoretic Extensions | VIII. Applications |
| CH17 | Agents as Fields: DFT for Reinforcement Learning and Planning | VIII. Applications |
| CH18 | Conclusion and Synthesis: The Data Field Theory of Intelligence | IX. Synthesis |
| CH19 | Integrating DFT with Large-Scale Foundation Models: Geometric Priors, Spectral Regularization | X. Foundation models |
| CH20 | DFT-Native World Models: Architectures, Benchmarks, and Scaling | XI. Agents and environments |
| CH21 | Field-Theoretic Agents for General-Scope Tasks: From Continuous Control to AGI | XI. Agents and environments |
| CH22 | Scaling Geometric and Topological Concept Stacks: End-to-End Pipelines for Web-Scale Knowledge | XII. Topological aspects |
| CH23 | DFT as a Safety and Alignment Layer: Diagnostic Monitoring and Control for AGI Systems | XIII. Safety |
| CH24 | Full-Stack DFT Systems with Hardware Co-Design: End-to-End AGI Platforms | XIV. Integration |
| CH25 | Empirical Validation of DFT Predictions at Scale: Large-Scale Experiments and Reproducibility Kits | XV. Validation |
Computational framework
dft-solver
A Python implementation of the numerical machinery of DFT: spectral, finite-element, and graph-Laplacian discretizations; energy-stable IMEX time integration with discrete dF/dt ≤ 0 guarantee; adaptive timestep respecting finite-speed CFL; and an MMS + convergence + spectral + boundary-condition validation harness.
The solver is under active development. Distribution is currently limited; access is available for academic collaboration on request.
dft-solver v1.0 ───────────────────────────────────── discretization spectral · FEM · graph time integration IMEX · adaptive · symplectic operators Δ_g · ∇_g · GL[m², λ] validation MMS · convergence · spectral · BC diagnostics m_gap · ξ · v_c · 1/f^β
03
FEATURED RESULT
Non-equilibrium Parrondo switching.
Two training regimes, each individually counterproductive, can be alternated at the right frequency to produce a net improvement in the loss function. The phenomenon, borrowed from the Parrondo paradox in stochastic dynamics, is a first-of-its-kind application to learning. The optimal switching rate is derived from a Floquet / joint-spectral-radius analysis of the combined operator.
Non-equilibrium Parrondo switching. Two regimes (orange, blue) each increase loss when run alone. Alternating between them at the Floquet-resonant switching frequency (dashed vertical marks) produces a net decrease, the joint spectral radius of the alternation falls below unity even when each regime individually has spectral radius above unity. The Parrondo-switching chapter develops the spectral diagnostics; the hierarchical-Parrondo paper extends to multi-scale stacks.
04
PATENT DRAFT
Patent draft: 28 claims.
The patent draft covers six categories: the core field-theoretic learning method (claims 1-9), discretization and solver techniques (10-12), the learning stack with mass-gap regularization, RG schedules, and Parrondo switching (17-21), agents and world models (13-14, 26), foundation models (23), and the safety / alignment layer (27).
Filing strategy, provisional vs non-provisional, jurisdictions, continuations, is being finalized. Coverage matrix maps each claim to the chapters and papers that develop it.