The θ-cap — an external pacemaker for the wiring axis
A wearable theta carrier is the only handle on the wiring axis no chemical reaches, but only as an external pacemaker: it forces long-range coordination inside a narrow window, the benign extra-lane reading is refuted, it is cleanly removable with no dependence, and it is molecularly safe below the spinodal fold. efficacy=0.
The wiring fault needs the long-range coordination supplied directly. A reviewer proposed reading that supply as a wearable θ-cap (a θ-band tACS device) and asked three fair questions, answered here one experiment at a time: is its coupling a benign extra lane or a coherence-forcing pacemaker; is the function it supplies removable; and does years of carrier cause molecular fatigue? The verdicts: it is a pacemaker, not a lane (the keystone negative); it is cleanly removable because it paces rather than repairs; and it is molecularly safe — the binding danger is circuit over-synchronisation, not molecular wear. efficacy = 0 throughout.
The keystone: a pacemaker, not a benign lane
The tempting reframing is that the cap is a harmless additive lane — you simply add a carrier channel on top of the broken substrate and it supplies an extra routing path. The model forks the cap’s coupling four ways on the wiring-faulted cohort and asks which one actually routes. An external clock (a forced carrier, inj·Ω0·sin(ωt−θ)) is the only coupling that lifts synchrony toward health — and only inside a narrow window, inj ≈ 0.08–0.10, tipping into over-synchronisation by inj ≈ 0.15. Every passive coupling is inert: a broadcast relay of the network’s own mean phase never lifts R (Rmax 0.346); a far-pair relay never lifts R (0.345), because the far-pair phases are near-random and there is nothing coherent to relay; a pure superposition cancels exactly.
This is the decisive result of the whole θ-cap analysis: no passive lane routes on a broken substrate. A lane can only carry coherence that already exists, and the wiring fault is the loss of that coherence. The cap can work only by forcing coherence as an external pacemaker — which is why everything downstream is framed as a pacemaker crutch, never a repaired highway. The benign-lane reframing is refuted; refutations are findings.
Removable: the function is supplied only while the cap is on
Using the winning external-clock coupling at the window amplitude, the model measures the long-range coordination the wiring fault destroys (far-pair coherence: health 0.170, deficit 0.050). With the cap on, far-coherence is restored to 0.213 (at or above health) while global synchrony sits at the healthy metastable 0.393 — function restored without over-synchronisation. Cycled through OFF/ON/OFF/ON/OFF epochs with the phase carried continuously (so any acquired dependence would show), every ON epoch returns to health and every OFF epoch returns to the deficit: OFF-epoch drift 0.004, ON-epoch drift 0.005, no rebound undershoot, and the first fresh OFF epoch matches the last post-cycling one.
The reason removability holds is the same reason no passive lane routed: the cap is only an additive drive term, and the oscillator substrate carries no plasticity variable — no slow weight, no memory that persists past the drive. Remove the drive and the intrinsic wiring deficit resumes instantly. The “off during sleep, no dependence” intuition is confirmed — but via the pacemaker mechanism, not a benign lane. The cap does not repair the wiring; the geometry is untouched.
Molecularly safe: the substrate is more robust than the circuit
The slow-photodamage worry is tested where the whole framework rests — the R19 bistable switch (ds/dt = g·s − s³ + h) — with the fatigue law derived from the switch’s own dynamics and no new tuned constant. The switch’s relaxation rate is λ = 2g, and the physiological θ carrier sits deep in the quasi-static regime (Ω = ω/λ = 0.018: the switch relaxes about 56× faster than the carrier cycles). Two fatigue observables follow. Irreversibly, below the spinodal fold the bare switch is a memoryless relaxor: cycling at the window amplitude (margin to the fold 0.425, about 8× the amplitude) never flips the basin at any cycle count; the first flip appears only at amplitude 0.70, past the fold — so the boundary on long-term use is an amplitude (the spinodal), not a cycle count. Reversibly, the only molecular cost is the per-cycle hysteresis loop, recovered each cycle, tiny in the quasi-static regime and scaling as amplitude²; duty-cycling (“cap off during sleep”) cuts the time-integrated load to about 4% of continuous strong drive.
The deeper finding inverts the worry: across the entire sub-fold range there are zero irreversible events at any cycle count, so the cap’s real failure mode is network over-synchronisation, not molecular damage. The binding constraint is the circuit, not the molecule. The engine contains no cumulative-damage variable, and inventing one would require a tuned constant that no-tuning forbids — so this is the faithful bound the actual dynamics give. Every fraction and coupling value here is an in-silico coupling state, not a clinical response rate or a dose; efficacy = 0 throughout. This is a mechanism-level result about the fault structure of autism as represented in the VP framework — not medical advice, a diagnosis, a treatment protocol, or a cure.