12 — Phase gradients Retrospective · exploratory

Alpha's phase gradient: mostly the eyes, a little beyond them

Analysis basis 56-recording cohort (19 vs 37) · dataset release 2026.10.10 · last recomputed in analysis release 4.26 · current

Fourteen electrodes give more than fourteen spectra: they give the spatial phase of the oscillation. Fit a plane to it and alpha acquires a phase-gradient vector — a direction and a steepness across the scalp. In psychedelic-labeled sessions that gradient is nearly twice as steep and much better fitted than in ordinary recordings, and earlier versions of this section read that as alpha traveling. The eye-state labels of v4 show what most of it is: the gradient steepens almost four-fold whenever the eyes close, in every recording that has both states, psychedelic or not. What remains once eye state is matched is a modest difference in the same direction.

Which way the gradient points

Non-psychedelic recordings point every which way and weakly. Psychedelic recordings agree: fourteen of nineteen have a posterior-pointing mean gradient, and the median fraction of windows pointing anterior falls from 70% to 44% (p < 0.001). The three sessions added in October (two ayahuasca, one psilocybin) are among the five that point the other way, so the direction agreement is weaker than the sixteen-session version suggested. A note on sign: the phase used here is the Hilbert phase, which advances with time, so a phase gradient points opposite to the direction of travel, and a posterior-pointing gradient corresponds to travel toward the front, the direction whose packets §13 counts. This estimator's sign convention has not been checked against a wave of known direction (see the end of this section), and LSD, the class with the clearest front-going packets in §13, has the lowest posterior-pointing share here (47%). The most consistent gradient with twenty or more windows is Ayahuasca experiment 006 (246 windows, resultant length 0.83, |k| = 1.02), with two DMT sessions and the other ayahuasca night at 0.76–0.78. One eyes-open desk recording, Workday recording 014, has the highest resultant length in the archive (0.89) with a small, poorly fitted gradient: consistency alone is not the signature.

It is alpha's wave, not the scalp's

A conducted artifact — reference geometry, skull blurring, a shared source seen from fourteen angles — would put the same phase gradient on every frequency band. It does not. Fitting the same plane wave to theta and beta gives a different answer:

Theta does nothing — if anything it is slightly less organized under psychedelics. Beta's |k| rises but its fit does not, and beta at 21 Hz under LSD is largely the alpha harmonic of §11 riding along. The gradient is a property of the alpha band specifically — which rules out a purely conducted artifact, and is also exactly what eye closure predicts, since closing the eyes raises alpha and leaves theta and beta nearly alone.

Every window in the archive

The whole archive, minute by minute

By psychedelic class

Ayahuasca no longer tops every wave measure. Revised. With two sessions it led on magnitude, fit, direction consistency and phase locking; with four it leads only on direction consistency (0.76) and the standing score, and sits below DMT and LSD on |k| (0.84 against 0.79 and 0.67). The two October nights were less eyes-closed than the first two (37% and 22% against 46% and 67% by the v4 classifier), which is the direction §12 predicts for every one of these measures, so the September ordering was partly the eye state of two nights. The second psilocybin session, 61% eyes-closed, does not look like an ordinary recording on these measures, where the first, 4% eyes-closed, did; the class median now sits between LSD and DMT on |k| and fit.

What the numbers would mean physically

Every recording page carries its own wave-vector analysis — the minute-by-minute |k| and fit, the phase-gradient portrait, the leading spatial mode, the standing-versus-traveling trace for all six bands, and the original standing-mode dashboard.

If part of the gradient does reflect propagation, the mechanistic reading connects to §06. A standing alpha pattern is what thalamocortical loop models produce when cortex is driven roughly in phase everywhere. A phase gradient with a stable direction is consistent with a phase lag that accumulates across cortex (on fourteen sensors, lagged sources that do not propagate can produce the same pattern), which in the traveling-wave literature (Muller et al. 2018; Zhang et al. 2018)^12,13 is associated with cortico-cortical rather than purely thalamic drive. On this montage that remains a hypothesis: the measurement is a directional phase structure, compatible with propagating-wave dynamics and equally with a lagged standing pattern, and §13 is where the distinction is pushed as far as fourteen sensors allow.

13 — Waves in motion Retrospective · exploratory

Watching a wave cross the scalp

Analysis basis 36 ordinary recordings pooled for the eyes-open and eyes-closed direction indices and 9 psychedelic sessions with an eye-state split (6 LSD, 1 psilocybin, 2 ayahuasca); 9 recordings for the September interaction tests, with the 15 October recordings run through the same chain · dataset release 2026.10.10 · last recomputed in analysis release 4.26 · current

§12 measured alpha's phase gradient one minute at a time. This section slows the recording down twenty-fold and shows single waves as they happen: the field painted across the scalp, the fourteen traces beneath it, and the same moment on the cortex. Every clip is real data from this archive. The color between electrodes is interpolated; the electrodes are not. Then it asks three things of the whole archive: where a direction of travel survives its controls, whether any band other than alpha has one, and what two waves do when they share the head.

The same moment on the cortex

Where the direction survives: eyes closed, under LSD

Count the packets of two or more cycles that head toward the nose, subtract those heading toward the back, divide by their sum. Ordinary recordings lean back-to-front whenever the eyes are open: +0.19 pooled over 2,200 clean minutes, positive in 21 of the 22 recordings with at least three eyes-open minutes analyzed in September and in every one of the twelve ordinary recordings added in October (+0.09 to +0.37), anywhere from −0.05 to +0.49 depending on the day. Close the eyes and the lean disappears: +0.01 ± 0.01 pooled over 132 clean minutes, a median of +0.01 over the recordings with at least three closed minutes (the eyes-closed minutes of the October workdays fell almost entirely inside the photic sweeps, which are masked, so each of those recordings contributes about two minutes). That is what the literature on alpha waves describes — forward waves with visual input, none or backward at rest^61,62.

Every eye-state split in this section carries one caution. Outside the timed blocks, eye state is the estimate of the classifier described in §16, and that classifier reads posterior alpha power, the height of the alpha peak and the posterior-to-frontal alpha ratio. Sorting windows by its label therefore also sorts them partly by alpha strength, and packet direction is measured from alpha. Sessions under protocol P2 and later open with timed eyes-open and eyes-closed blocks, labeled by the clock rather than by alpha, and those blocks are the cleaner test.

The six LSD sessions look like ordinary recordings while the eyes are open (+0.18 to +0.36). They differ with the eyes closed, where the lean stays: +0.25 to +0.35 in six of six. LSD experiment 016 shows it arriving. Before the dose, eyes-closed alpha had no direction (+0.02 ± 0.07, the same as every ordinary recording); by minutes 48–65 it was +0.41, and eyes-open alpha rose alongside it, +0.05 to +0.38. Eyes-closed packets also run far longer under LSD — the longest 1% last 22 to 100 cycles against 16 in ordinary eyes-closed alpha, where the null gives 14.

This is the archive's first state difference that holds with eye state matched, and it has a precedent: with eyes closed, DMT strengthens forward alpha waves and weakens backward ones, reproducing the pattern of eyes-open visual stimulation⁶⁰. The result here is consistent with, but not sufficient to establish, the same reading for LSD — visual cortex behaving behind closed eyelids as though it were being shown something. The limits are plain. Six sessions, one person. Much of the ordinary eyes-closed time was recorded during photic stimulation, though the two flicker-free cases agree (−0.02 ± 0.04 and −0.11 ± 0.04). The index is a lag asymmetry, not a measured wave. And the DMT, ayahuasca and psilocybin sessions have not yet been split by eye state.

Psilocybin and ayahuasca show the same thing. The three psychedelic sessions recorded after this section was written were run through the same packet chain. With the eyes closed the anterior-going excess is +0.34 ± 0.02 after the psilocybin dose (2,776 packets) against −0.02 ± 0.08 before it in the same session and the same posture (172 packets, about three minutes), and +0.27 ± 0.02 and +0.31 ± 0.03 in the two ayahuasca sessions; the longest 1% of eyes-closed packets reach 88, 50 and 75 cycles against 14 before the psilocybin dose. The within-session pre-dose contrast of the psilocybin session is the cleanest form of this comparison the archive has, because the eyes-closed baseline comes from the same evening; its pre-dose sample is small. Packet rates stay at or below the lag-free null in all three, as under LSD. Three compounds now show the eyes-closed forward lean; none of the twelve ordinary recordings added in October does (ten of eleven at or below +0.04 with the eyes closed).

Ordinary recordings have the same waves

The second group of clips comes from a search of all 24 ordinary recordings under the same rule. Their packets are as frequent, as long in the typical case (median 2.2 cycles) and as well fitted (ρ 0.87) as the LSD ones, and the best single examples — 4.6 cycles at ρ 0.96 in Workday recording 010, 7.9 cycles at ρ 0.94 in Resting baseline 002 — match or beat the LSD exemplars. They run sideways and obliquely as often as front to back; on a montage with eight frontal and four posterior contacts that is partly geometry. No clip separates one state from another. The direction statistics do that.

Beyond alpha: one slow mode, and it is probably the eyes

A direction of travel exists in one place: 9 to 12 Hz, back to front, in 14 of 16 acute sessions and all eight ordinary ones, with a direction consistency of 0.05–0.10 against a null of 0.007. Theta, beta, the alpha harmonic and gamma make packets as often and as long as their nulls and point nowhere (consistency under 0.05 throughout). Rotating patterns occur in 57–64% of samples in every band — and in the null. Only acute sessions have packets longer than lag-free noise allows, and only at 10–11 Hz (the longest 1% reach 20–22 cycles against 17; nine of 16 sessions exceed their null by a quarter, none of the ordinary eight).

The scan was repeated on the fifteen October recordings. In the alpha band the anterior-going index of the first 60 clean minutes is 0.08 to 0.31 for the twelve ordinary recordings (null −0.03 to +0.03) and 0.25, 0.25 and 0.30 for the two ayahuasca sessions and the psilocybin session; the 99th-percentile packet length is 7 to 10 cycles in the ordinary recordings (null 7 to 12) and 13, 21 and 48 cycles in the three psychedelic sessions (null 12, 15 and 17). Theta, beta and gamma again point nowhere.

Two modes stand outside alpha. At 2–3 Hz packets run front to back: index −0.30 in the acute sessions (13 of 16 negative, the DMT sessions lowest at −0.42 to −0.53), −0.09 in ordinary recordings. The frontal contacts of this headset sit above the eyes, so a slow frontal-first pattern is what eye movements look like; it is reported as a mode and read as ocular until shown otherwise. And on the plateau of LSD experiment 016 the 5–6 Hz band acquires a steady left-to-right direction (consistency 0.14–0.19 against 0.01; at the null level before the dose) — in exactly the minutes when §11 finds that line coherent with head motion. Beta and the harmonic do lean weakly toward alpha's direction of the moment (28.6% of samples within 45° against 25.9% by chance; 14 of 16 acute sessions, all eight ordinary), and keep doing so when alpha's waveform shape is removed. No band's direction predicts another's at any lag.

Two waves at once

Any alpha field on fourteen sensors can be written as a sum of plane waves, so finding two is not the question; whether they behave as two is. At every sample the field was fitted with the strongest plane wave, then the strongest second one at least 45° away, then both amplitudes jointly. A pair is a run of three or more cycles in which both directions hold, the second wave is at least half the size of the first, and adding it explains more than it does in 95% of lag-free noise. The first two clips under "Two waves at once" in the player show such pairs, each as the total field beside its two component waves.

Stable pairs are rare — 0.2 to 1.3 a minute in the six LSD sessions, 0.1 to 0.2 in ordinary recordings — and in the four longest LSD sessions four in five are head-on. The commonest is not front-against-back, which lag-free noise produces just as often, but left against right: 44 such pairs in LSD experiment 016 against 9 in its null, 84 against 3 in LSD experiment 008, more than the null in five of the six LSD sessions. Within a pair the two waves share a frequency (0.1–0.2 Hz apart) and wax and wane together (r = +0.70 to +0.92), but less tightly than in the null (+0.84 to +0.99) in every recording. In about 30% of pairs — 28 to 32% in all six LSD sessions — the lead changes hands before the pair breaks up. Afterwards the wave that began stronger carries on alone in 38–40% of cases in the four longest sessions, the weaker one in 21–28%, and something else takes over in the rest. Neither wave's amplitude leads the other's at any lag up to half a second.

Fitting all four axis-aligned waves at once shows how they relate over whole recordings. Forward and backward are strongly phase-locked (0.72–0.95 in the LSD sessions), which is what a standing pattern is — but in all nine recordings they are less locked than the lag-free null (0.90–0.98), where the front–back pattern is perfectly rigid. The real pair slips: two waves, tied but not welded. Across axes the result runs the other way. A front–back wave and a sideways wave have no reason to keep a fixed phase, and in ordinary recordings they do not (0.18–0.30, the null's 0.19–0.26). In the four LSD sessions with the most clean data they do: 0.46 to 0.73 against 0.14 to 0.31, at the same relative phases from session to session (a backward wave within 25° of a sideways one; a forward wave roughly half a cycle from it), with their frequencies pulled together in three of the four (0.26–0.35 Hz apart against 0.33–0.46). In LSD experiment 016 the locking was absent before the dose (0.17, below its null of 0.32) and present after it (0.53 against 0.31). The two shortest LSD sessions, with 26 and 44 clean minutes, do not show it.

That is an interaction in the plain sense: two waves holding a phase relation that instantaneous correlation cannot produce, appearing with the dose. What it is physically cannot be settled here. Two waves that entrain each other would give it; so would a single wave whose front is bent — alpha spreading outward from an occipital source runs forward along the midline and sideways at the flanks, and on fourteen sensors that is a forward wave locked to two sideways ones. Either reading makes the alpha field under LSD more than a standing pattern plus noise.

Waves in different bands

Two waves at different frequencies cannot hold a fixed phase, so they have other ways to interact. A nonlinearity can mix them, putting new lines at the sum and difference of their frequencies. The slow one can nest the fast one, gating its size with its phase — and if the slow wave travels, the fast wave's bursts should travel with it. They can lock n:m, one slow cycle to two fast ones. Or the slow wave can steer the fast one, biasing which way it runs. All four were tested across delta, theta, alpha, beta and gamma in the same nine recordings.

Mixing: none outside alpha's own family. The map has one bright region, alpha with itself (0.42–0.65 in the LSD sessions and eyes-closed rest), and a fainter one where alpha meets its harmonic (0.08–0.22) — the waveform of §11. Nothing sits where a slow wave would mix with alpha: the strip of slow-frequency × alpha cells peaks only at its edge, against alpha's own skirt. The one other feature, delta with delta (0.14–0.26), is in most recordings and strongest over the forehead with eyes open, which is the shape of a blink.

Nesting: the slow waves do not gate alpha. Delta and theta phase leave alpha's amplitude alone (theta: z below 1 in all nine recordings; delta: never above 2.2). They do gate beta, weakly (modulation 0.01–0.02; z up to 22), in eight of nine recordings and most of all at the desk with eyes open — again where eye movements are, since a sharp transient is a slow deflection with fast edges. Alpha gates beta in five of the six LSD sessions, and there the beta bursts travel with the alpha wave: same direction to within 13° in LSD experiments 008, 011, 015 and 016 (z 3.4 to 7.1), not in ordinary recordings. Since "beta" under LSD is largely alpha's harmonic, this is the waveform traveling with its wave rather than a second oscillation riding it. No other envelope travels with its carrier.

Steering and locking. The phase of delta or theta does not bias alpha's direction (the forward-minus-backward balance swings by under 0.005 across a slow cycle; z −1.7 to 2.9). Alpha locks 2:1 to the band at half its frequency only faintly (0.02–0.06), clearing its null in LSD experiments 015, 011 and 016 — and in LSD experiment 015 without any accelerometer coherence at that frequency (0.02, against 0.26 in experiment 016), so the faint half-frequency partner of §11 is not always a head movement.

Across bands, then, the waves largely ignore one another. What looks like cross-band interaction is one non-sinusoidal alpha wave occupying several bands at once, and the eyes occupying the rest.

Four further tests, one oscillation

Alpha and its harmonic. A second wave at twice the frequency would have its own direction. The harmonic's fitted direction agrees with alpha's slightly more often than chance in every LSD session (28–34% within 45°, z 4 to 9.5), and it is phase-locked 2:1 to alpha at all fourteen sites. The locking phase is not uniform across the head: it sits near 0° over the front and near 160° over the back. That is what the average reference does to a front–back alpha pattern whose waveform is not a sine — flip the polarity and the harmonic's phase shifts by half a cycle while twice the alpha phase does not. One waveform, seen from both sides.

Coupling across the head. The bicoherence that ties α to 2α (§11) is as strong between sites as within one: 0.37–0.54 for a frontal pair feeding a posterior harmonic against 0.21–0.38 at a single site in the LSD sessions, the same in eyes-closed ordinary recordings, absent with eyes open. If every site carries the same alpha, every triplet of sites carries the same nonlinearity; this is not distant regions interacting.

Forward against backward. If opposite-going waves competed, one would fall as the other rose. They rise and fall together (r = +0.84 to +0.88 in the LSD sessions; +0.41 to +0.65 in lag-free noise), and once total alpha amplitude is removed the remaining anticorrelation (−0.05 to −0.23) is weaker than the null's (−0.34 to −0.48). At "collisions" — both components strong and balanced — the amplitude minimum sits at F3/F4 or T7/T8, exactly where it sits at random moments of matched amplitude: the montage, not a node.

The October sessions, through the same tests. Two of the LSD signatures reappear in all three new psychedelic sessions: when an alpha packet and its harmonic coincide, the alpha packet is forward-going 0.53 to 0.71 of the time under ayahuasca and psilocybin (0.24 to 0.31 in the twelve ordinary October recordings; 0.40 to 0.67 under LSD and 0.20 to 0.36 in the ordinary recordings of September), and in the forward-against-backward competition the backward fraction is 0.04 to 0.09 (ordinary 0.13 to 0.15). Posterior alpha-with-alpha bicoherence is 0.36 to 0.44 in the three sessions and 0.21 to 0.43 in the ordinary recordings whose alpha sits at 10 Hz (0.06 to 0.11 in the two 9 Hz recordings), and the alpha-with-harmonic term 0.09 to 0.12 against 0.03 to 0.13: the mixing picture of §11 holds, with no new cell lit outside alpha's own family.

The 10.9 : 5.4 : 2.7 Hz chain. On the plateau of LSD experiment 016 the (5.4, 5.4 → 10.9) bicoherence is significant at eight of fourteen sites — and in the accelerometer's own signal (z 3.6). The chain is the head movement of §11, locked to alpha.

14 — Hemispheric asymmetry Retrospective · exploratory

A right-leaning brain — and how much of it is the headset

Analysis basis 56-recording cohort (19 vs 37 for the state contrast) · dataset release 2026.10.10 · last recomputed in analysis release 4.26 · current

Right-hemisphere periodic power exceeds left in most bands and most recordings. All asymmetry here is computed on periodic power: each channel's own 1/f background is fitted and subtracted first, so a difference in background offset between hemispheres cannot masquerade as an oscillatory difference.

The lateralization is an alpha–beta–theta phenomenon. Delta shows none at all, which is itself informative: a pure electrode-gain imbalance would lateralize every band equally, and it does not.

It lives at the back of the head

Frontal-polar lands at -4% and is right-dominant in only 43% of recordings. Parietal is right-dominant in 56 of 56 and occipital in 86%.

The state effect, which is the part worth believing

Treat absolute right-over-left numbers as provisional until the headset is tested with matched impedances and a left–right flip of the cap. The state dependence argues against a simple fixed-gain explanation, but an instrumental contribution to the difference between states remains unresolved until that test is run.

15 — The office state Retrospective · exploratory

An office state with restricted dynamics

Analysis basis 28 workday recordings (27 of at least twenty minutes) against 4 resting and 19 psychedelic recordings; 12 for the September time-on-task analysis; 55 for the performance-score correlations · dataset release 2026.10.10 · last recomputed in analysis release 4.26 · current

The most personally useful result in the archive came from the least exotic recordings. Twenty-eight recordings of ordinary office work describe a state that is quieter and — most strikingly — dynamically frozen; the slowing reported in September did not survive the thirteen office recordings added since. (Every workday recording is pooled here, with its rest blocks and light stimulation masked; the fifteen original office recordings are the basis of the time-on-task and switching-by-task analyses below.)

Low alpha at a screen is normal reactivity. A spatial field that holds one configuration for an entire hour is a different thing — a narrow, low-vigilance regime rather than an actively cycling one. It also degrades across a session (the September analysis of the twelve original office recordings long enough for it): posterior alpha falls with time-on-task in 9 of the 12, and the slow/alpha ratio rises in 10 of 12, losing roughly 13% of alpha between the first and last quarter.