Status: validation record. The value here is a falsifiable instrument, not an out-prediction claim. Closes no open problem.
TNFR's canonical magnitudes (the structural tetrad |∇φ|, K_φ, Φ_s, ξ_C;
the pulse ω_k = √λ_k; the coherence C; the structural frequency νf) are
meant to be confronted with real data — tests that can fail. The engine
ships the data-agnostic instrument; it does not bundle datasets.
confront_signal
maps any real multichannel signal → the emergent phase-locking graph
(build_coupling_graph,
U3/PLV) → the canonical read-outs (tetrad, pulse, ξ_C via the emergent
spectral gap, coherence C) → the emergent two-face diagnosis
(emergent_wave_fraction:
project the signal onto the emergent L_sym eigenmodes and read the damping
from each modal coordinate's own AR(2) dynamics — oscillate ⇒ conservative-
wave face, relax ⇒ diffusive face — so the verdict is set by the emergent
dynamics, not by a fixed γ or the raw input spectrum).
Demo: example 159
(python examples/10_applications/159_empirical_confrontation_pipeline.py path/to/signal.npy).| Confrontation | Result | Reading |
|---|---|---|
| Local phase tetrad ` | ∇φ | , |
Global Kuramoto R vs seizure | AUC ≈ 0.49 (chance) | global hypersynchrony does not rise under the bipolar montage / focal onset — the state is local, not mean-field |
νf (single structural frequency) | tracks the measured dominant EEG frequency (Spearman ρ ≈ 0.86); fingerprints subjects | νf is canonical and provably meaningful (a robust rhythm meter) |
Single-νf conservative-wave forecaster (few-shot, leave-one-patient-out) | ties a strong Gaussian process and a stabilised DMD/Koopman model (within ~1%); beats a parameter-matched neural net | strong-baseline accuracy from 1–3 physical constants on emergent geometry, ~20× cheaper than the neural TNFR |
Face diagnosis (verify_overdamped_projection at the data-fitted γ) | real EEG sits on the under-damped (conservative / oscillatory) face | the engine's own certificate locates real data on the correct face |
| Pre-ictal (5 min before onset) tetrad | every magnitude at chance | the tetrad is a detection marker (concurrent), not a prediction marker |
A second, independent confrontation run through the shipped instrument
(confront_signal, data-fitted face) on the PhysioNet eegmmidb eyes-open
(R01) vs eyes-closed (R02) baselines — 10 subjects, 64-channel, drift removed
(fft_bandpass 1–40 Hz), paired across subjects with a two-sided binomial sign
test. Data are not bundled (fetched to a scratch dir); the run is
reproducible from the engine alone.
| Confrontation (open→closed) | Result | Reading |
|---|---|---|
Emergent face (modal AR(2) on L_sym) | WAVE / under-damped in 18/20 conditions | the emergent two-face verdict: real EEG is on the conservative (wave) face; a real thermal field (heat diffusion) lands on the diffusive face (97–99% of 2-day windows), so the certificate discriminates two real systems |
K_φ (phase curvature, local) | rises in 10/10 subjects (paired dz ≈ +1.1, sign-test p ≈ 0.002) | the phase-curvature field — a canonical TNFR magnitude with no standard analogue — is the most consistent cross-subject state marker |
| **` | ∇φ | `** (phase gradient, local) |
C (coherence) / Q (quality factor) | both rise (8/10 each) | a sharper, more coherent rhythm; C is a trend (p ≈ 0.11) |
Global Kuramoto R | falls in 9/10 (dz ≈ −0.9) | mean-field synchrony moves opposite to the local fields — the local tetrad and R dissociate |
Collective pulse ω₀=√λ₂ | structural ω₀ ∈ [0.12, 0.27] vs measured 1–11 Hz (Spearman ≈ −0.3); flat open↔closed (dz ≈ −0.2, p = 1.0) | the pulse ω_k=√λ_k is the coupling graph's spatial / topological standing-wave spectrum — not the temporal Hz spectrum, and not a state marker here (the k-NN PLV topology is state-insensitive by construction); the local tetrad carries the state |
Falsification and correction. The naive single-subject reading (eyes-closed
⇒ |∇φ| down) did not generalise: cross-subject, |∇φ| and K_φ rise
while R falls. Measured first, then reported — the cross-subject test
corrected a premature single-subject conclusion. The consistent structural fact
is a local↔global dissociation: eyes-closed alpha is a spatially-structured
rhythm (local phase curvature up, global in-phase order down), an established
phenomenon (alpha as a spatial / travelling wave) that the canonical local
tetrad reads correctly where the mean-field order parameter mis-signs it.
Recovers a known phenomenon structurally; closes nothing, beats nothing, is not
new physics.
Beyond the static read-outs, the evolution law itself is confrontable
in-engine (nodal_prediction_skill):
the EPI channel of ∂EPI/∂t = ν_f·ΔNFR is graph diffusion, so its one-step
predictor x̂(t+1) = x(t) − c·L_rw·x(t) (a single fitted diffusion step
c = ν_f·dt) is scored by the one-step increment variance it explains beyond
persistence, against a per-channel AR-1 baseline.
| Signal | nodal 1-step skill | AR-1 | Reading |
|---|---|---|---|
| synthetic graph diffusion | +0.16–+0.21 (recovers c) | +0.03 | validated: the predictor recovers a genuine diffusion law |
| real EEG (eyes-closed) | +0.02 | +0.05 | oscillatory — the EPI diffusion channel is weak; AR-1 wins |
| real thermal field (60–120 min steps) | +0.015–+0.029 | +0.013–+0.025 | diffusive — the nodal diffusion matches/edges AR-1 at diffusive timescales |
Diffusion-selective, internally consistent with the two faces. The nodal EPI channel is a diffusion law, so its one-step skill tracks how diffusive the system is: positive and AR-1-matching for the thermal (diffusive-face) field, weak for oscillatory EEG (wave-face, where AR-1 wins). Absolute skills are small (~0.02–0.03 on real data) — a structural-fidelity result, not superior forecasting. This anchors the paradigm's core evolution law on real data, not just its static observables.
νf, the local tetrad), stability by construction.K_φ
p ≈ 0.002) but C is only a trend. It recovers a known phenomenon (spatial
alpha) rather than out-predicting a baseline.L_sym mode), not from
the input spectrum. It certifies both faces on real data — EEG on the
wave face (18/20) and a real thermal field on the diffusive face (97–99%),
completing the discrimination the input-spectrum Q could not — but the per-mode
fit is under-powered for very short windows (EEG converges to wave only for
windows of roughly a thousand samples or more).See also docs/STRUCTURAL_INTERFACE_THEORY.md
(the tetrad vs the Kuramoto order parameter on real EEG) and
theory/EMERGENT_ONTOLOGY.md §0 (the empirical
caveat this record nuances).