The edge of chaos is the throne of time, not of richness: a sealed dissection of the field's favorite slogan

"Complexity is maximal at the edge of chaos" is among the most repeated claims in the dynamics of neural systems, and our own program confirmed its standard form: debiased perturbational complexity (R-dim, the reproducible dimensionality of the evoked response) traces an inverted-U as a network's spectral radius is dialed from order to chaos (doi:10.5281/zenodo.22100826), with mechanics dissected in a companion paper (doi:10.5281/zenodo.22168299). Here we report what happens to the slogan when its confound is controlled, in one model family (echo-state reservoirs of tanh units; §8). In one-knob designs, criticality (measured maximal Lyapunov exponent λ) and saturation depth (how far activity is driven into the nonlinearity's ceiling) rise together; a sealed two-axis campaign had shown that at matched criticality saturation governs R-dim (Spearman −0.62 to −0.88 in every λ stratum, 95% intervals excluding zero; replicated across seven activation families, two network sizes, biological E/I wiring, and two noise levels), while at matched saturation criticality's effect is not resolved at this n (point estimates +0.04 / +0.05 / −0.19; widest 95% interval [−0.45, +0.11]; the sealed "bound" criteria those estimates passed are satisfied by pure noise 89% of the time and are not counted as evidence). The remaining question — does an R-dim peak survive AT the edge once saturation is held fixed? — resisted three sealed attempts (indeterminate in ρ; a "just-inside-stability" hypothesis killed on virgin ground; indeterminate again on a fine λ-grid). The pre-declared, properly powered last word (protocol sealed publicly before any network was generated, run once; 180 virgin networks in three λ-cells of 60 at fixed saturation) returned its no-crown cell: the edge cell's median R-dim was the lowest of the three (6.41 vs 6.65 near-stable and 6.52 near-chaotic; bootstrap probability that the edge is the maximum: 0.20; edge-minus-flank differences −0.23 and −0.11 with 95% intervals [−0.92, +0.71] and [−0.85, +0.86]). At controlled saturation, no richness crown of the edge is detected at this power: a crown of ≥ 0.5 dimensions has bootstrap probability 0.06–0.10, while the one-knob sweep on the same family spans 3.0 to 6.7 dimensions. The classic inverted-U is, on this evidence, the signature of one-knob trajectories through a two-axis (criticality × saturation) plane. A subsequent sealed test of the opposite reading — an edge penalty, sighted twice — also failed (§7). What the edge does own, sealed separately and replicated, is duration: the coherent response lives longest in the edge stratum (median 110.5 samples against 3.0 deep-stable and 18.0 deep-chaotic as sealed; 58.5, i.e. 19.5× and 3.2×, under the pedestal-exclusion criterion of §5), with the relaxation law T_c ~ 1/|λ| on the stable side at +0.94 either way. The edge-maximum criterion is, however, also passed by a pure relaxation model with no chaos physics; the informative fact is that the edge lives about 3× shorter than that model predicts. The sealed dissociation criterion passed (the T_c-maximizing stratum is at least as close to the edge as the R-dim-maximizing one, bootstrap P = 0.987), but the strict statement — T_c peaks at the edge while R-dim does not — has P = 0.83, below the sealed 0.90 bar; that time and richness are maximized in different places is what these data suggest, not what they seal. The edge of chaos is the throne of time; richness, wherever we have measured it, belongs to freedom from saturation. Every claim above followed the program's standing discipline — public preregistration before blind quantities, single runs, failures reported with the successes, including five sealed deaths reported here for the first time — and every number was mechanically verified against the archived results.