A replicated association between resting spectral slope and TMS-evoked complexity fails blind preregistered confirmation

Simulation work (companion papers) indicates that perturbational complexity — the quantity behind the clinically validated PCI family of consciousness measures — reflects the reproducible dimensionality of a system's causal response, maximal at the edge of chaos on its stable side, with excitation/inhibition balance controlling the distance to that edge. As a prediction of that model, not as an established fact: across awake humans, individuals whose spontaneous cortical dynamics sit closer to the edge should produce longer-lasting and more complex evoked responses. We tested this in the open TMS-EEG dataset of Biabani et al. (2019) (three samples: n = 29, 94, 12; 62 channels; prefrontal, premotor and parietal stimulation), using the pre-stimulus spectral slope (3–40 Hz, alpha excluded) — a proposed proxy of E/I ratio (Gao et al., 2017) — as the distance-to-edge variable, and standard PCIst of the evoked response as the complexity readout. A flatter resting slope predicted higher evoked PCIst in the discovery sample (Spearman ρ = +0.42, p = 0.024, n = 29) and replicated in the independent large sample (ρ = +0.47, p < 10⁻⁴, n = 94); the third sample (n = 12) was uninformative (ρ = +0.03, wide CI), as expected at that size. Three controls were run, and only one passed in both samples: the slope did not predict a matched pre-stimulus null PCIst (ρ = −0.14/−0.20, n.s. — ruling out generic data-quality coupling); the association survived partialing out baseline RMS, a proxy for trial count, in the replication sample (partial ρ = +0.33, p = 0.0012) but not in the discovery sample (+0.21, p = 0.27) — and baseline RMS is itself strongly coupled to the slope (−0.40 and −0.62), so this control is the weakest link in the chain, not the strongest; and a mechanistic intermediate emerged only in part — flatter slopes predicted longer-persisting evoked responses in the replication sample (ρ = +0.34, p = 0.0008; this first link was null in the discovery sample, +0.15, p = 0.44), and response persistence predicted complexity (ρ = +0.32, p = 0.0017; ρ = +0.71, p < 10⁻⁴ in the discovery sample) — the critical-slowing signature expected if flatter spectra index proximity to instability. Secondarily, in the sample with a realistic (sensory-matched) sham, sham-evoked PCIst did not differ significantly from real TMS (medians 41.4 vs 42.8; one-sided Wilcoxon p = 0.095 over 48 site×subject pairs from 12 subjects × 4 sites; aggregating to subject level leaves the verdict unchanged, p = 0.10). We state this as a failure to reject, not as equivalence: no equivalence test was preregistered, and with 12 subjects the 95% interval on the difference still admits differences of up to roughly a sixth of the index. What the comparison does quantify, at the level of the index itself, is how much of "perturbational" complexity sensory co-stimulation can carry without masking. We then performed the definitive test: a blind, preregistered confirmation on an independent trial-level dataset (OpenNeuro ds008037, same laboratory, CC0; 30 subjects; analysis plan, windows, thresholds and direction frozen before download; pilot subject excluded; trial counts equalized at 60; debiased PCIst-XV as readout). The association did not confirm: Spearman ρ = +0.031, one-sided p = 0.43. The test had power 0.75–0.84 against the exploratory effect sizes (ρ = 0.42–0.47; Fisher-z approximation, one-sided α = 0.05, n = 30), so the result rules out an effect of the exploratory size but not a small one (ρ ≤ 0.2); the trial-rejection confound check was clean (ρ = −0.18). The exploratory association — replicated across two samples, passing one artifact control in both samples and two only in the replication sample, p < 10⁻⁴ in the larger — did not survive the one test that could not flatter it. The confirmatory design changed three things at once (true resting-state slope instead of averaged-baseline slope; debiased instead of standard estimator; new sample), and a labeled post-hoc decomposition measured all four variable combinations in the same 30 subjects to localize the broken link. It did not support the selection bias of the standard estimator (companion paper) as the driver — the debiased estimator gave the same weak association with the averaged-baseline slope as the standard one (ρ = +0.25 vs +0.20, both n.s.) — and located the failure in the predictor: the averaged-baseline slope on which the exploratory finding was built shares only 17% of its variance with the true resting-state slope (ρ = 0.41). We publish the full arc as a case study in why internal controls and replication, without blind preregistered confirmation, are not enough. The realistic-sham observation (sensory-only stimulation reproducing most of the perturbational complexity value without masking) is independent of the failed association and stands as reported, with its stated uncertainty.