Field-level perturbational complexity is not a proxy for neuronal reproducible dimensionality; its within-brain state changes co-vary in direction

Perturbational complexity is measured from field potentials, yet the quantity of interest lives in neuronal populations. Whether the field-level measurement reflects the reproducible richness of the underlying spiking activity — or a field-specific shadow — has never been tested, because it requires both signals in the same brain during the same perturbations across arousal states. The open Allen Institute dataset provides exactly that: 30-channel epidural EEG and hundreds of Neuropixels single units, recorded simultaneously in head-fixed mice during cortical electrical stimulation, awake and under isoflurane. We computed debiased reproducible dimensionality (R-dim; our companion estimator, doi:10.5281/zenodo.22103044) from sorted spiking populations (338–995 units per session, 10 ms bins) on exactly the trial sets of our published EEG analysis (doi:10.5281/zenodo.22133404; state- and current-matched, same frozen pipeline and seeds), under a preregistration sealed before any spike time was read, with three hypotheses and a four-cell interpretation matrix. Results (n = 15 animals): levels do not correspond across animals (awake R-dim, spikes vs EEG: Spearman ρ = +0.25, p = 0.18) — the sealed cell reads "the field is not a proxy for population dimensionality in level," consistent with both quantities scaling with their own, independent coverage. But the state contrast has a genuine neuronal counterpart (spiking R-dim 8.48 awake vs 4.69 under isoflurane; 11/15 animals; p = 0.0027), spiking dimensionality runs ≈ 3.0× the simultaneous field value, and within-animal state effects co-vary across levels (Δspikes vs ΔEEG: ρ = +0.64, p = 0.0054) — (v2) a preregistered test that passed its own bar, but whose coupling is carried by three sign-reversing animals and does not survive their removal (ρ = +0.301, p = 0.171). The full pattern survives both preregistered bin sizes (5 and 25 ms). Notably, the minority of animals in which anesthesia increased field dimensionality showed the same reversal in their neurons (3/3): the estimator reported the same direction of change at both levels, including in the three animals where that direction was the unexpected one. (v2) We no longer describe this as the estimator faithfully reporting biology at both levels: the level comparison between modalities fails (Q1), and it is the direction of within-animal change that agrees. Labeled exploratory analyses locate these "rebels" on a continuum: spontaneous firing was suppressed uniformly across all animals (isoflurane/awake rate ratio 0.29 vs 0.27 in the rest; p = 0.63; no population silences), while the anesthetic's attenuation of the evoked response varied enormously (1.1–7.9×) and the state effect followed that attenuation (ρ ≈ +0.6 at both levels). Anesthesia suppressed ongoing activity everywhere; where it failed to suppress responsiveness, dimensionality persisted — the founding distinction of the perturbational program, emerging from its own data. A sealed follow-up on the recovery blocks resolves our previous reversibility puzzle: neuronal dimensionality does partially recover (7/8, p = 0.012), but by the same fraction as the field (0.24 vs 0.21) — the incomplete recovery was biology, not measurement — and spontaneous firing recovers about twice the fraction dimensionality does (0.40 vs 0.23, p = 0.008): arousal returns before reproducible dimensionality. A further sealed analysis finds no detectable ceiling in spiking R-dim up to the usable 480 trials (growth at top p = 0.042, deceleration absent), with levels brushing the range where simulated networks saturate — the biological well is deeper than the in-silico ones at matched reach. (v2) per-animal state effects co-vary across levels (Spearman ρ = +0.636, p = 0.0054, n = 15). That coupling is carried by the three animals whose state effect reversed sign: among the twelve animals with the ordinary effect it is ρ = +0.301, p = 0.171, and among the eleven with both effects positive, ρ = +0.182. The field therefore tracks the direction of within-brain change, reversals included — which is the striking part of §3.4 — while graded magnitude tracking is not established here, and graded tracking is what the clinical use we invoked would require.