The evidence

Four cardinal signatures.

DFT predicts a small number of specific, quantitative, falsifiable observables. They appear across vision, language, and reinforcement control with shared uncertainty bands, not four separate findings but four windows onto the same underlying field dynamics. Below: each signature with its number attached and the audit context where it matters.

01Diverging ξ 02Power-law fluctuations 03Mass-gap scaling 04Causal speed 05Universality 06Falsification

SIGNATURE 01

DIVERGING ξ

Diverging correlation length at concept formation

Near concept-formation transitions, the correlation length ξ of the field diverges:

ξ(t) ~ |t − t_c|^−ν, ν = 0.71 ± 0.018

The exponent ν ≈ 0.71 is reported across the empirical-signatures chapter, the synthesis chapter, and the universal-critical-phenomena paper with four-source intra-corpus replication. The disciplinary note: Lineage B reports ν = 0.63 ± 0.04; the empirical-validation chapter's finite-size scaling collapse reports ν = 0.85 ± 0.04. Reconciling these clusters is on the program's stabilization plan (see audit).

From the empirical-signatures chapter, synthesis chapter, and universal-critical-phenomena paper.

SIGNATURE 02

POWER-LAW F^−β

Power-law temporal fluctuations

Near the critical surface, the temporal power spectrum of the field's activity exhibits the 1/f^β structure of critical dynamics:

S(f) ~ f^−β, β = 1.22 ± 0.06

Fluctuations span all timescales; the system has no characteristic timescale of its own; the spectral exponent is universal across the cardinal universality class. Reported in the universal-critical-phenomena paper's Power-Law Spectra section and the empirical-validation chapter's cross-domain run, with consistent exponents across modalities.

From the universal-critical-phenomena paper and the empirical-validation chapter.

SIGNATURE 03

MASS-GAP SCALING

Mass-gap scaling for robustness

The mass-gap m_gap, the smallest non-zero Hessian eigenvalue at a learned configuration, controls generalisation under distribution shift:

ε_gen ≤ K / m_gap²

The mass-robustness paper reports empirical correlations ρ = −0.812 ± 0.041 for vision (N=200), ρ = −0.788 ± 0.048 for language (N=156), and ρ = −0.776 ± 0.055 for reinforcement control (N=189). The fitted scaling exponent α = 1.8 ± 0.6 is consistent with α = 2 within the uncertainty band.

The mass-gap object is operationally polysemous in the corpus (eight definitions; see audit). The empirical-validation chapter anchors it as m_gap = λ_min(H), the smallest non-zero Hessian eigenvalue.

From the mass-robustness paper and the empirical-validation chapter.

Vision Language Control —— K/m²

SIGNATURE 04

EFFECTIVE CAUSAL CONE

Finite effective causal speed

Information in the trained regime propagates at a finite effective speed, not instantaneously. The continuum TDGL is parabolic, formally infinite propagation speed, but effective causal constraints emerge in the trained regime from three mechanisms.

Operational cone (from the geometric-foundations paper). A perturbation propagates to a region within time t only if its amplitude there exceeds a detection threshold within that time. The cone has finite effective speed depending on m² and noise scale.
Lattice discretisation. Information cannot cross a graph edge faster than one timestep per neighbour.
Hyperbolic regularisation (Lineage B). A modified Axiom II adds a second time-derivative, giving a hyperbolic continuum with finite formal speed c_eff = √(Γ/τ).

From the geometric-foundations paper, the unified-framework paper, and the dynamical-laws chapter.

UNIVERSALITY

UNIVERSALITY TABLE

The same exponents across vision, language, and control.

The Renormalization Group says: the long-distance behaviour of a field theory is governed by the fixed points of the RG flow, and many microscopic theories flow to the same fixed point. DFT's empirical claim is that learning systems built on very different architectural substrates flow to fixed points within one universality class.

Domain	ν (correlation)	β (order parameter)	γ (susceptibility)	Sample size
Vision	0.710 ± 0.018	0.348 ± 0.011	1.386 ± 0.028	N = 200
Language	0.714 ± 0.022	0.351 ± 0.013	1.389 ± 0.031	N = 156
Control	0.706 ± 0.025	0.345 ± 0.015	1.383 ± 0.035	N = 189

From the empirical-signatures chapter, the universal-critical-phenomena paper, and the empirical-validation chapter's universality table.

The Rushbrooke identity α + 2β + γ = 2 and Josephson identity νd = 2 − α are satisfied within the reported uncertainty bands across all three domains (residuals < 0.08). This is the structural reason the cross-domain consistency is possible: the cardinal exponents are universal data of the same RG fixed point.

Renormalization-group flow on the (m², λ) plane. Distinct microscopic theories, different architectures, datasets, parameter initializations, flow to the same Wilson–Fisher-like fixed point (WF*). At the fixed point, the universal exponents ν, β, γ are determined by the linearised flow matrix. This is the structural reason DFT predicts cross-domain universality.

FALSIFICATION

What would refute each claim.

Every candidate science owes an answer to one question: what observation, in principle, would compel an honest investigator to abandon the claim? Four answers follow.

If the continuum hypothesis fails: Learning systems do not admit a useful continuum description at any scale, their behaviour is essentially discrete in a way no continuous field on a manifold can approximate. Current status: finite-element and spectral discretisations of the TDGL equation reproduce qualitative and quantitative features of large networks (see the solver chapter and the energy-based-learning paper).
If no free energy exists: The dynamics of learning systems are not derivable from any free energy functional, no F[φ] whose gradient flow reproduces observed training trajectories. Current status: energy-stable schemes derived from explicit free-energy functionals reproduce training dynamics quantitatively (the mass-robustness paper and the solver chapter's validation suite).
If the signatures don't appear: Correlation lengths fail to diverge near concept-formation transitions, temporal spectra fail to exhibit 1/f^β, mass gap fails to correlate with robustness, or information propagates at infinite effective speed in trained systems. Current status: the signatures are observed (the empirical-signatures chapter, the universal-critical-phenomena paper, and the empirical-validation chapter). The disciplinary question, see the audit, is which universality class.
If external replication fails: Independent groups, using their own architectures, datasets, and measurement protocols, report exponents inconsistent with the corpus values. The corpus currently has four-source internal replication of ν ≈ 0.71; the operative test is external, and we do not yet have it.