We treat intelligence the way physics treats matter. Not metaphor, not analogy. A continuous field on a Riemannian manifold, evolving under equations that yield numbers you can refute.
Intelligence is carried by a vector-valued field φ : M × Badj → Rd on a compact Riemannian manifold (M, g). Two commitments do the load-bearing work. The field is not a representation of data — it is the cognitive activity. The substrate is not a coordinate system — its metric encodes the system's inductive bias.
One equation. Δg is the Laplace-Beltrami operator on (M, g); m² sets the spectral gap; λ drives nonlinear pattern formation; η is stochastic forcing tied to fluctuation-dissipation. The free energy F[φ] is the Lyapunov function; energy-stable schemes preserve dF/dt ≤ 0 at the discrete level.
At concept-formation transitions. Power-law ξ ~ |t − tc|−ν with ν ≈ 0.71.
With β ≈ 1.22. Critical dynamics on every timescale.
εgen ≤ K / m²gap; empirical ρ ≈ −0.81 across three domains.
In the trained regime. The trained system has an operational light-cone.
Developed in the empirical-signatures chapter, the mass-robustness paper, the universal-critical-phenomena paper, the geometric-foundations paper, and the empirical-validation chapter.
The same critical exponents appear across vision, language, and reinforcement control within shared uncertainty bands. This is universality: distinct microscopic theories flow under the renormalization group to the same fixed point, where universal observables are determined.
| Domain | Transition | ν (measured) | Status |
|---|---|---|---|
| Vision | Concept boundary | 0.72 ± 0.02 | Confirmed |
| Language | Semantic phase transition | 0.70 ± 0.03 | Confirmed |
| Control | Policy collapse | 0.71 ± 0.04 | Replicating |
The corpus contains real disagreements on load-bearing claims. Three values for ν. Five functional forms for one mass-robustness law. Eight operational definitions of the mass gap. Two within-chapter formal instabilities (the synthesis chapter's Law I has a formula-vs-caption mismatch; the empirical-validation chapter's abstract disagrees with its body on the scaling-law labels). We name each one publicly and run a three-stream stabilization plan against it. External replication remains the test that matters.
Read the program audit →DFT Labs is an independent research program pursuing a physics-grade theory of intelligence. Single author at present; one secondary academic affiliation on the structural-analogies paper. The short points at how we handle that institutional shape openly.