SUMMARY The brain has been generating the same rhythms — delta, theta, alpha, beta, gamma — in every subject ever recorded. The boundaries between them are reproducible to within a hertz across species, ages, anesthesia, wakefulness, epilepsy, psychosis, and states of consciousness. Nobody has explained why they are where they are, why the hierarchy is so stable, or why the same frequency architecture repeatedly reappears across fundamentally different biological conditions. This paper reports two independent lines of analysis, applied to distinct datasets, using distinct mathematical tools. They were not designed to agree. They do. The first line is classical signal analysis. Resting-state EEG recordings were processed through an FFT/Hilbert/chirp/Laplace pipeline— no operator, no framework, no theoretical assumptions beyond the signal-analytic definitions. The canonical band centers follow a power law (fn ∝ n1.60, R2 = 0.995): the frequency hierarchy is quantized, not arbitrary. Hilbert analysis of instantaneous event geometry reveals that beta-band events are bilaterally extended and spatially distributed (iso-trapezoid dominant, P = 0.716), while every other band is locally focal. Chirp analysis shows that iso-trapezoid events carry coherent upward cross-band transport; all other geometry classes do not. In continuous eye-movement recordings from a separate dataset (Malta EOG, n = 6), Laplace analysis of the pre-saccadic director returns a dominant decay constant σ ∈ [−0.31,−0.40] Hz, and the temporal manifold is M.bius anti-periodic: P(f0/2)/P(f0) = 3.92°æ0.40 (p < 0.0001), with lag-T autocorrelation r = −0.808. These are the raw signal facts. The theory did not produce them. They were found first. The significance of these findings is that the electrophysiological hierarchy behaves less like a continuum of freely varying oscillations and more like a discrete closure ladder. The canonical bands therefore appear to occupy stable admissible regimes rather than arbitrary spectral intervals. Within this interpretation, the Wallis product, ∞Y n=1 2n 2n − 1 °§ 2n 2n + 1 = π 2 , acts as the closure ratchet by which discrete sign-chain events progressively approximate smooth periodic structure through finite admissible steps. The apparent smoothness of neural rhythms is therefore not fundamental. It emerges from bounded discrete transport repeatedly approaching closure without exact continuity. The second line applies the wake registry operator to separate datasets: resting-state EEG from 18 subjects (controls and psychosis), intracranial EEG from 13 surgical epilepsy patients (HUP), PET metabolic imaging from 18 subjects, diffusion MRI from 20 subjects (IDEAS II), and post-mortem cortical histology. The operator asks, at each neural event, which of 151 ordered states best satisfies a four-term scoring functional whose constants are fixed without fitting. Across all datasets it finds the same organizational signature: non-uniform registry occupancy with extreme-state dominance, sparse structured transitions, and bounded inter-event timing. In PET it completely separates epilepsy from controls (Cohen’s d = 3.59, p = 2.9 °ø 10−7) without smoothing, atlas registration, or parameter tuning. The separation is associated with fragmentation of the support manifold V (∇ρ = 0), reduced occupancy near the conductor-like Z ≈ 54 regime, and increasing transport-to-support mismatch. In dMRI, four independent microstructural factors map one-to-one onto the four operator variables; beta-band dynamics are orthogonal to the sensory-fugal axis (4% variance explained, versus 28–47% for all other bands). Histology maps the synaptic apposition surface hierarchy onto six registry states disjoint from the seven occupied by wake transport nodes, establishing the anatomical substrate of the support/transport separation. This support/transport separation is central to the interpretation of the data. Neural activity does not behave simply as oscillation propagating through passive tissue. Instead, the results indicate that electrophysiological transport evolves across a finite-support substrate with measurable admissibility structure. The canonical EEG hierarchy therefore reflects stable transport regimes coupled to underlying geometric support. The clinical implications become especially important when considered in relation to consciousness. Existing literature in anesthesia, coma, and brain death consistently reports reductions in connectivity, complexity, and spectral diversity during loss of conscious state. The present results suggest that these observations may reflect a deeper failure of closure stability. Under deep anesthesia or severe suppression, transport density falls below the admissibility floor required to sustain persistent twisted return across the support manifold. In epilepsy and related pathological states, the opposite failure mode appears: temporal transport exceeds the capacity of the support structure to dissipate residual mismatch, producing runaway synchronization, instability, fragmentation, and intermittent discharge. Within this framework, consciousness is not reducible to activity magnitude or connectivity alone. Instead, conscious-state stability depends on maintaining a bounded relationship between temporal transport and finite-support geometry. The apparent continuity of conscious experience emerges as an achieved standing-wave condition in which discrete, non-smooth neural events repeatedly organize into stable twisted closure regimes across the cortical manifold. The M.bius anti-periodicity observed in the signal structure is therefore not incidental; it reflects the requirement that neural transport avoid simple circular repetition and instead maintain re-entrant half-twisted return capable of preserving persistent temporal interior. MEG is the bridge. A single MEG dataset (sub-07 POGS) was analyzed with both the operator pipeline and Laplace analysis of the phase-amplitude coupling envelope. The operator recovers the same null-lattice structure, extreme-state dominance, and sparse transitions seen in EEG. The Laplace analysis returns a dominant decay rate σ = −0.310 Hz — placing it squarely within the cluster [−0.31,−0.40] Hz established by the FFT/Laplace pipeline on entirely different data. The two lines of analysis, on independent datasets, by independent methods, recover the same constants, the same geometry, the same anti-periodic transport structure, and the same two-tier separation between spatial support and temporal transport. Across EEG, MEG, PET, dMRI, histology, and EOG, the same closure architecture repeatedly emerges despite fundamentally different acquisition methods and mathematical approaches. That convergence was not engineered. It is the finding.