Intelligence is a field,
not a heuristic.
We build Data Field Theory: a physics-grade account of intelligence as a continuous field on a Riemannian manifold, evolving by Ginzburg–Landau dynamics. One equation, four falsifiable predictions, each with a number attached and each refutable on its own.
The starting move
One equation.
Four predictions.
Contemporary AI treats data as discrete points and learning as a search through parameter space. DFT starts elsewhere. The cognitive activity of a learning system is a continuous field on a geometric substrate; learning is that field's evolution under a free energy functional. From this single starting point follow a small number of specific, quantitative, falsifiable predictions about what every learning system does.
- φ
- Data field on a Riemannian manifold (M, g)
- Δg
- Laplace–Beltrami operator on the substrate
- m²
- Mass parameter, controls spectral gap and robustness
- λ
- Quartic coupling, drives pattern formation
- η
- Stochastic forcing (fluctuation–dissipation)
From the axioms chapter, the dynamical-laws chapter, and the geometric-foundations paper.
What follows
Four cardinal
predictions.
These are not four separate findings. They are four windows onto the same underlying field dynamics, each with a number attached, each refutable on its own.
Diverging correlation length
Near concept-formation transitions the correlation length ξ of the field diverges as |t − tc|−ν with universal exponent ν = 0.71 ± 0.018.
From the empirical-signatures chapter, the universal-critical-phenomena paper, and the empirical-validation chapter.
Mass-gap generalization bound
Generalization under distribution shift is bounded by the smallest Hessian eigenvalue: εgen ≤ K / mgap². Empirical correlation ρ ≈ −0.81 across vision, language, and reinforcement control.
From the mass-robustness paper, the observables chapter, and the learning-stack chapter.
Finite effective causal speed
In the trained regime, information propagates at a finite effective speed, not instantaneously. The cone is set by amplitude threshold and mass parameter; under hyperbolic regularization the continuum equation itself becomes finite-speed.
From the geometric-foundations paper, the agents-as-fields chapter, and the safety chapter.
Cross-domain universality
The same critical exponents appear across vision, language, and reinforcement control within shared uncertainty bands. Universality is the structural reason: distinct microscopic theories flow under RG to the same fixed point.
| Domain | ν | β | γ |
|---|---|---|---|
| Vision | 0.710 ± 0.018 | 0.348 ± 0.011 | 1.386 ± 0.028 |
| Language | 0.714 ± 0.022 | 0.351 ± 0.013 | 1.389 ± 0.031 |
| Control | 0.706 ± 0.025 | 0.345 ± 0.015 | 1.383 ± 0.035 |
From the empirical-signatures chapter, the empirical-validation chapter, and the universal-critical-phenomena paper.
The substrate
The manifold is not a coordinate system.
It is an active component of the theory.
DFT's substrate (M, g) encodes the inductive bias and relational structure of the system. Its geometry determines how information propagates, how concepts relate, and how scaling laws emerge.
Spherical substrate.
On a sphere the eigenfunctions of Δg are the spherical harmonics Yℓm. They are the natural basis for a rotation-invariant field. The brand mark is one of them: (ℓ, m) = (2, ±2).
Toroidal substrate.
On a flat torus the eigenfunctions are products of sines and cosines indexed by integer wavenumbers (k1, k2). Periodicity encodes translational symmetry; the spectrum is discrete and the propagation is wave-like.
Data-manifold substrate.
For applications the substrate is a learned data manifold embedded in ℝᵏ with a metric derived from the data itself. The same field equation now produces RG flow toward the same fixed point. that is the structural reason cross-domain universality holds.
Program audit
The disagreements
we document publicly.
DFT is a young program, and its corpus contains real disagreements on load-bearing claims, the kind any honest reader will encounter on the first careful pass. We name them in writing rather than smooth them over, and we run a stabilization plan against each one.
Three values for ν
The headline critical exponent is reported at three distinct values in the corpus: 0.71 ± 0.02 (Lineage A, four-source internal replication), 0.63 ± 0.04 (Lineage B, citing 3D Ising universality), and 0.85 ± 0.04 (the empirical-validation chapter's finite-size scaling collapse). Reconciling them is the first item on the stabilization plan.
Five forms for one law
The mass-robustness relationship appears as exponential, power-law, Lipschitz inverse-linear, linear-cone, and hybrid forms in different papers, differing by 3–4 orders of magnitude in their applied predictions. A regime map and a model-comparison run on the 25,000-model dataset would settle which form applies when.
Validation that doesn't yet adjudicate
The empirical-validation chapter reports a tight scaling collapse (Q = 0.94) and a strong mass-gap-to-robustness correlation (ρ ≈ −0.89). But its Lipschitz bound derives without the full field-theoretic apparatus, so the chapter as written cannot choose among the candidate functional forms it could in principle distinguish.
Join the work
The corpus is open. The predictions are testable. We want to hear from anyone who engages seriously.
Twenty-five book chapters, sixteen papers, a Python solver, an empirical-validation chapter across twenty-five thousand model variants, and a twenty-eight-claim patent draft. The corpus names what it gets wrong in the same voice it uses to argue what it gets right.