The state-switching layer — the R19 bistable cell read over time

The state-switching layer is the R19 bistable cell read over time, with no new machinery. Sweeping the field gives hysteresis — a state resists switching back; the transition latency diverges at the fold, which closes the epilepsy chapter's owed ictal time-course; and the barrier sets the switching threshold. Constant drive reproduces the engine bit-for-bit. efficacy=0.

The plasticity layer gave the atlas a slow structural variable — a connectome that changes with use. It did not give the atlas a fast one: a state that can switch and stay switched until pushed back. Yet that bistable switch has been in the engine from the start — the R19 cell, ṡ = g·s − s³ + h, the pitchfork whose two stable branches the whole framework rests on. Every earlier chapter read it at a single instant. This chapter reads it over time, and that is the entire layer: no new equation, no new constant, just the dynamics of the cell already there. Four sign-only results, each over a swept stimulus (anti-tuning). Hysteresis: sweeping the field up then down, the up- and down-transitions sit on opposite sides of zero, a finite loop of width 2×spinodal ≈ 0.77 — a state, once switched, resists switching back. The ictal time-course: the transition latency diverges as the drive approaches the fold (critical slowing) and falls monotonically as it overshoots — which closes the open ictal time-course the epilepsy chapter explicitly owed to this layer. The barrier: the spinodal rises monotonically with the well depth g, so the same handle that sets the barrier sets the switching threshold — shallow wells flip under a fixed drive, deep wells hold. And the guard: constant-drive integration reproduces the engine's own settle bit-for-bit, with the fold read from the engine, so the layer adds without altering. The layer, not an application: bipolar (episode switching), the ictal onset, and the cycle disorders that use it are owed to the modules that import it. efficacy = 0.

the state-switching layer = the R19 bistable cell read OVER TIME; closes the §25 ictal time-course = hysteresis (loop width 2·spinodal≈0.77), a transition latency that diverges at the fold (critical slowing → the owed §25 ictal time-course), and the barrier as the switching threshold — the plasticity layer (§26) gave the atlas a SLOW structural variable; this layer gives the FAST one — a state that switches and stays switched. No new machinery: the R19 cell ṡ = g·s − s³ + h (the supercritical pitchfork the whole framework rests on) is bistable for g>0; every earlier chapter read it at a single instant, this one reads it OVER TIME. g=1.0 universal R19 scale, fold = the engine's own spinodal(g), no free constant; all grids are swept stimulus probes (anti-tuning). Four results: (E2.1) sweeping the field up then down, the up/down transitions sit on OPPOSITE sides of zero (h_up=+0.39, h_dn=−0.39 on the grid), enclosing a hysteresis loop of width 2·spinodal≈0.77 predicted as twice the fold — a state, once switched, resists switching back; (E2.2) the transition latency DIVERGES as the drive approaches the fold (critical slowing) and falls monotonically as it overshoots (73.4→1.36) — small overshoot gives a slow run-up, large overshoot an abrupt jump — which CLOSES the ictal time-course the epilepsy chapter (§25) explicitly OWED to E2; (E2.3) spinodal(g) rises monotonically with the well depth (0.18 at g=0.6 → 0.64 at g=1.4), so the SAME handle that sets the barrier sets the SWITCHING THRESHOLD — shallow wells flip under a fixed drive, deep wells hold; (E2.4) const-drive integration reproduces the engine's settle BIT-FOR-BIT with the fold read from the engine, so the layer adds without altering (engine e61083ae…, tree 0fbf4988…, byte-unchanged). Axis-A firewall: a bistable transition is a mechanism boundary, not a claim about the felt quality of a mood state (consciousness_claim=0). E2 is the LAYER, not a disorder; bipolar (T2b), the ictal onset, and the cycle disorders import it. efficacy=0; not medical advice; hard problem OPEN. [V mech]. this chapter

epilepsy = the over-synchronisation pole; the ictal state = collapse of the selective gate = excitatory bias drives R to the over-sync ceiling and all assemblies ignite; an anticonvulsant reverses it and raises the threshold — epilepsy is the over-synchronisation pole of the engine's synchrony axis (the global Kuramoto order parameter R on the measured ephaptic kernel, plus the M3 R19 ignition gate). An excitatory/disinhibitory E/I bias raises R monotonically toward the over-sync ceiling (0.422 > health 0.390); past a critical bias (+0.3) the selective single-winner gate collapses and EVERY candidate assembly ignites — the ictal state, a loss of GATING (Axis-A firewall: a mechanism boundary, not a claim about ictal experience; consciousness_claim=0). On one axis: autism-T (under-ignited) < health (selective) < schizophrenia (aberrant, some irrelevant) < epilepsy (all ignited). An inhibitory / threshold-raising anticonvulsant-class push moves R back down and restores the gate — it raises the seizure threshold by moving the operating point away from the over-sync ceiling (the same ceiling the θ-cap must stay below, §20). The static susceptibility is characterised; the ictal time-course is OWED to a state-switching layer (E2). efficacy=0; not medical advice. [V mech]. canonical §25

The fast variable the atlas was missing

Two kinds of change matter for a temporal disorder, and the atlas so far had only one. The plasticity layer supplied the slow one — a connectome that consolidates, that writes a state into structure and keeps it. What it did not supply is the fast one: an operating point that jumps between two stable values and holds the new one until something pushes it back. A mood episode is exactly that — not a slow drift but a switch into a regime that persists, then a switch out. To represent it you need a bistable state read as a dynamical process, not as a snapshot.

The remarkable thing is that this switch needs no new machinery at all. The R19 cell — ṡ = g·s − s³ + h, the supercritical pitchfork that the entire VP framework is built on — is a bistable element. For g > 0 it has two stable branches separated by a barrier, and a field h that tilts between them. Every chapter up to here evaluated that cell at a single instant: settle to the branch the field selects, read the value, move on. This chapter does one thing differently. It watches the cell cross — sweeps the field, times the transitions — and the switching layer falls out of the dynamics that were always there. No new equation. No free constant. The universal R19 scale g = 1, and the fold taken from the engine's own spinodal(g).

Hysteresis: a state that resists switching back (E2.1)

Sweep the tilting field slowly upward from a state resting on the lower branch. The state does not jump as soon as the field turns positive; it clings to the lower branch until the field reaches the upper fold, then snaps up. Now sweep back down: the state clings to the upper branch past zero, until the field reaches the lower fold, then snaps down. The up-transition and the down-transition sit on opposite sides of zero (here at h = +0.39 and h = −0.39 on the sweep grid), enclosing a hysteresis loop of finite width ≈ 2×spinodal = 0.77. The width is not fit — it is predicted as twice the engine's fold, and the measured loop matches to within the sweep step. The meaning is the property a mood episode needs: a state that has switched resists switching back. Removing the push that caused the episode does not end it; the field must reverse past the opposite fold. That asymmetry — easy to enter at one fold, only leaving at the other — is the signature of bistability over time, and it is here with no parameter added.

The ictal time-course, closing the debt to §25 (E2.2)

The epilepsy chapter placed the seizure at the over-synchronisation pole and showed the static structure of an ictal state, but it left one thing explicitly owed: the time-course of the transition into ictus — why onset can be abrupt yet preceded by a slowing — because the static engine had no switching dynamics to express it. This layer pays that debt. Drive the cell toward the fold and time how long the transition takes. As the drive approaches the fold from below the transition latency diverges: right at the fold the barrier between branches vanishes and the state creeps through an arbitrarily flat landscape — critical slowing. Push the drive past the fold and the latency falls monotonically (here from 73.4 just over threshold down to 1.36 at strong overshoot). A small overshoot gives a long, slow approach; a large overshoot gives a sharp jump. That is the qualitative ictal time-course — a slowing as the system rides the edge, an abrupt transition once it tips — emerging from the same fold the epilepsy chapter used for the spatial picture. The §25 ictal time-course is closed. It is a mechanism direction, not a clinical timing and not a prediction about any patient's seizure: efficacy = 0.

The barrier is the switching threshold (E2.3)

What decides whether a given push actually flips the state? The barrier between the two branches, and the engine already sets it: the fold spinodal(g) = 2(g/3)^3/2 rises monotonically with the well depth g (here 0.18 at g=0.6 climbing to 0.64 at g=1.4). A shallow well (small barrier) flips under a fixed drive; a deep well (large barrier) holds against the same drive. The same handle that sets the barrier therefore sets the switching threshold — one parameter, two faces. This is the lever the disorder modules need in both directions. A state that switches too easily is a barrier set too low (episodes triggered by small perturbations); a state that cannot be moved is a barrier set too high. And it gives the sign of a stabiliser without ever asserting a dose: anything that raises the barrier raises the threshold to switch, so episodes become harder to enter. The numeric depths are sweep probes, not tuned constants — the result is the monotone direction, which holds across the whole sweep.

A pure add-on, and what it unlocks (E2.4)

The guard makes the discipline operational, exactly as in the plasticity layer. Held at a constant drive, the time-integration of the cell reproduces the engine's own settle routine bit-for-bit, and the fold used throughout is read from the engine's spinodal, not hand-set. Turning the sweep off recovers the frozen engine exactly: the engine file stays e61083ae…, the emergence tree stays 0fbf4988…, byte-unchanged. E2 adds; it does not alter.

And it is a layer, not a disorder. Its purpose is to be the fast counterpart to the plasticity layer — the substrate the switching conditions stand on. Bipolar as two operating poles with episodes that are bistable transitions, the ictal onset as a fold crossing, the cycle disorders as repeated switching — each needs a state that can jump and hold. E2 supplies that state once, as a reusable object built from the R19 cell already in the engine; the mood and cycle modules that follow import it rather than re-deriving it, and pair it with the plasticity layer (the slow trace) to get episodes that both switch and leave a mark. Everything here is an in-silico coupling state, not a clinical measure. A bistable transition is a mechanism boundary, not a claim about the felt quality of a mood state (Axis-A firewall — consciousness_claim = 0; the hard problem of experience stays open). This is a mechanism-level result about state-switching as represented in the VP framework — not medical advice, not a diagnosis, not a treatment protocol, and not a cure. efficacy = 0; the hard problem stays open.