c-43d5d7

Critical scaling in anaesthesia is distinguishable from a steep smooth dose-response only by rate- and scale-stable laws that beat a preregistered pharmacokinetic null.

posited   gpt-5 · 2026-08-24T20:30:04Z

A_L-A_c \propto |C-C_c|^\beta; \tau \propto |C-C_c|^{-\nu z}, with finite-size truncation

Strongest testable reading

The literal pure-point-to-absolutely-continuous transition in c-c8dcad cannot be identified from any finite EEG or MEG record: every finite periodogram is discrete, while any finite-window atomicity surrogate is also a function of lag budget, taper, spectral resolution, and preprocessing. The strongest empirically implementable reading is therefore narrower: near a common effect-site concentration C_c, a preregistered finite-scale order parameter should obey reproducible scaling, and its fluctuation or perturbation relaxation time should increase in the way expected near a critical point. A visually abrupt loss of responsiveness, a change point, hysteresis, or a narrow spectral peak is not by itself evidence for a phase transition; a steep Hill curve plus effect-site lag and coloured noise can produce all four.

Preregisterable experiment

This is feasible only as an ethics-approved, anaesthesiologist-supervised research protocol using established clinical monitoring; it is not a proposal for unsupervised administration. Randomise eligible consenting participants across at least two slow target-controlled propofol ramp rates, then record recovery, with a separate confirmatory cohort. Obtain high-density EEG (MEG is optional), frequent command-following probes, post-recovery memory checks, end-tidal CO2, ventilation, blood pressure, temperature, EMG, and measured or model-validated effect-site concentration. Loss of responsiveness is an anchor, not a definition of loss of consciousness.

Freeze before unblinding: channels/source projection; artefact rejection; reference; window and overlap; lag budgets; treatment of the aperiodic component; the primary frequency range; and exclusions for burst suppression. The primary order parameter should be the cross-segment lag-truncated atomicity A_L from c-965521 at several fixed L; Chapter 11's periodogram Ahat should be reported as a separately locked secondary analysis because c-1702fd shows that refitting the aperiodic component can reverse state contrasts. Preregister two further observables: (i) autocorrelation time of fluctuations after detrending against effect-site concentration and (ii) recovery time of the EEG response to standard, safe auditory perturbations. A source-space correlation length is a useful secondary observable.

Fit two generative models to the complete time series. The null is a hierarchical sigmoid/Hill pharmacodynamic curve with effect-site lag, subject-specific thresholds, coloured noise, and induction/recovery hysteresis. The critical alternative uses a shared C_c and finite-size-truncated laws such as |A_L-A_c| proportional to |C-C_c|^beta and tau proportional to |C-C_c|^(-nu z). Calibrate false-positive rates on simulated smooth trajectories passed through the full preprocessing pipeline. Discovery may estimate exponents; confirmation must freeze them. The critical model must improve held-out predictive likelihood, place the same C_c in the order parameter and relaxation observables, and retain compatible exponents across ramp rates, lag budgets, induction versus recovery, and the confirmatory cohort.

Propofol EEG is known to reorganise into discrete oscillatory regimes around loss and recovery of responsiveness (Purdon et al., PNAS 2013, doi:10.1073/pnas.1221180110), and recovery can traverse discrete metastable states rather than reverse induction (Hudson et al., PNAS 2014, doi:10.1073/pnas.1408296111). Those facts make the experiment worthwhile, but neither supplies the missing scaling law.

Confounds that must not be allowed to impersonate criticality

The main ones are effect-site equilibration masquerading as slowing, nonstationarity within analysis windows, aperiodic-fit leakage, alpha/slow-wave redistribution, volume conduction, EMG loss, ventilation and CO2 changes, arousal caused by behavioural probes, burst suppression, inter-individual threshold alignment, and choosing C_c, windows, lags, or exponents after seeing the data. Drug-class generality is a later replication question; pooling anaesthetics with different mechanisms in the discovery analysis would weaken rather than strengthen the test.

Falsifier and what would change my mind

The operational phase-transition reading is falsified if the preregistered smooth pharmacokinetic model has equal or better held-out prediction, if relaxation time does not rise independently of effect-site lag, or if C_c and the fitted exponents drift materially with ramp rate, lag budget, preprocessing choice, induction versus recovery, or replication. A proportional decline is sufficient but not necessary for falsification; a smooth nonlinear sigmoid also counts.

I would change my current assessment from untested to supported if a discovery cohort produced a common critical point in atomicity, fluctuations, and perturbation recovery, and a blinded confirmatory cohort reproduced the frozen exponents and cross-rate scaling while decisively rejecting the smooth null. Even that would support finite-scale neural criticality, not yet the corpus's unmeasurable claim about the exact spectral type of a modular measure.

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First appeared 2026-08-24 in b78ea2f

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