What must a theory of perturbational complexity explain? Nine preregistration-hardened constraints, six dead hypotheses, and a minimal visibility account

Abstract

Across five preprints (doi:10.5281/zenodo.22100546, .22100826, .22101059, .22120069, .22133403), we measured how perturbational complexity behaves once its estimator is debiased, what quantity it tracks — the reproducible dimensionality of the evoked response (R-dim) — and how that quantity depends on dynamics, trial count, species, and arousal state, always under preregistrations sealed before data contact and with failures published. This paper consolidates the empirical residue into nine constraints that any theory of perturbational complexity must satisfy, reports the autopsies of six hypotheses of ours that died against them (including our own formal theory, killed in two sealed prediction cycles), and offers the minimal account we know of that survives: reproducible components with rapidly decaying amplitudes become visible one by one as trial averaging lowers an effective noise floor. With an approximately exponential amplitude spectrum, this account reproduces, with three lines of algebra, five constraints at once: logarithmic growth of R-dim with trial count, absence of a detectable human ceiling at protocol-scale trial counts, finite system-specific ceilings in simulated networks, level scaling with electrode coverage without growth scaling, and — via uniform attenuation of component amplitudes — the downward displacement of the growth curve under anesthesia. (v2) v1 described that displacement as parallel (level, not slope); preprint 6 v2 withdraws the parallel-shift shape, so C9 now constrains the existence of the contrast and the recovery lag rather than the shape. The account is explicitly not a theory of consciousness: it is silent on why rich spectra require edge-of-chaos dynamics, why networks self-organize toward that regime, and why recovery from anesthesia lags the state change. It does, however, make a quantitative, falsifiable prediction — the vertical displacement between two states' curves should equal twice the within-state slope times the log of the evoked-amplitude gain ratio — and we tested it: the test protocol was sealed publicly before the one unpublished quantity it requires (the gain ratio) was computed for any animal, and run once. The prediction held on both sealed criteria at the field level (ordering ρ = +0.41, one-sided p = 0.038, n = 20; median observed/predicted ratio 1.00). It then failed its cross-level replication: sealed identically and run once on spiking populations of the same brains (commit 76f2fea), ordering inverted (ρ = −0.29, p = 0.84) and observed displacements exceeded predictions by a median factor of 3.0 — anesthesia does more to neuronal dimensionality than uniform amplitude gain allows. The visibility account therefore survives as an economical summary of the trial-scaling constraints and of C9's shape, and dies as a mechanistic claim at the neuronal level; we report the refutation of our own model here rather than elsewhere. We then chased the structural change itself with a further sealed protocol: anesthesia rotates the population response subspace to near-orthogonality (median between-state overlap 0.082 against a within-state control of 0.532; lower in 15 of 15 animals, p = 3.1 × 10⁻⁵) — anesthesia does not attenuate a fixed response so much as replace it — yet the extent of rotation does not scale the excess displacement either (ρ = −0.09, p = 0.62), killing the rotation-as-explanation hypothesis in the same run that established the rotation. The last pre-declared candidate, per-component decoherence, is reported as untested for a reason we document in full: our estimator of trial-level coherence at matched amplitude failed its pre-registered known-truth validation bench (three versions, criteria fixed before each run, all archived), and under our rules an uncertified instrument runs no confirmatory test. The theory this field needs must pass through all nine constraints; we mark where every account we tried has failed so others can start further ahead.