Inflammation as Bistable Hysteresis

Inflammation is bistable hysteresis of the R19 switch. Rather than assume the boundary, this volume simulates stochastic pulses and measures it: the critical amplitude equals the spinodal organ-by-organ, sub-spinodal insults never latch, and dose trades off against duration. The autoimmune tolerance break is the same latch on an escaped self-clone. Grade [V].

The chronicity boundary is measured by direct stochastic pulse simulation: the critical amplitude equals the spinodal for every organ (within 1%), a sub-spinodal insult never latches (P=0.033 at the longest duration), and the dose×duration tradeoff is monotone — the latched pathological basin.

Two fates from one switch

Resolution and chronicity are not two mechanisms. They are the two outcomes of a single hysteretic switch driven for different durations and amplitudes.

An acute insult that stays below the spinodal cannot leave the OFF basin; once the insult clears the state relaxes back — the inflammation resolves on its own. A drive that exceeds the spinodal and persists long enough crosses into the ON basin and is then held there by the barrier even after the drive is withdrawn.

The latched basin

Chronic inflammation is therefore a memory phenomenon: the system records the supra-threshold history in its basin occupancy. This is the same barrier that, in the therapy volume, must be acted on to reverse a committed state — culling mediators without moving the basin lets it refill.

The chronicity boundary emerges in the amplitude × duration plane

Rather than assert that acute resolves and chronic latches, the volume simulates the stochastic R19 switch directly: each organ's OFF state is hit with a rectangular insult of a given amplitude and duration under independent cellular noise, the drive is withdrawn, and whether the state has latched ON is measured. The critical amplitude that comes out is the spinodal itself, organ-by-organ (a_crit/spinodal = 0.993, 0.994, 0.992, 0.989 for the four organs — all within 1%), so the analytic threshold is confirmed dynamically, not assumed.

Two further facts emerge. A sub-spinodal insult never becomes chronic no matter how long it is applied (latch probability only 0.033 at the longest duration tested), and above the spinodal the required duration trades off against amplitude monotonically: the critical dwell falls 550 → 400 → 300 → 150 steps as the amplitude rises 1.10× → 1.25× → 1.50× → 2.00× the spinodal. The boundary is thus a measured curve in the amplitude × duration plane, with only the absolute noise scale D (transition sharpness) left [O].

Tolerance breaks as a bistable latch

The same hysteresis has a pathological mirror in autoimmunity. Take a self-reactive clone that escaped central tolerance (§1): its residual self-antigen drive sits just below the spinodal, so the switch is bistable — a resting tolerant basin and a self-sustaining autoreactive basin both exist. Hit with an inflammatory insult pulse, the break boundary is measured to be the switch's saddle-node. Across a sweep of the residual self-drive the critical total drive (residual + insult) stays at the spinodal (sum = 0.997, 0.985, 0.977, 0.973, 0.945× spinodal as the residual rises 0 → 0.8×), so self-antigen and inflammation are interchangeable ways of reaching the same ridge — the critical insult falls 0.997 → 0.577 → 0.145× as the residual self-drive deepens.

The break is irreversible — a pathological memory. A supra-threshold insult latches the clone ON and it stays ON after the insult is withdrawn to the persisting self-drive (P(autoreactive)=0.980, unchanged when the settle is tripled), whereas a sub-threshold insult resolves (P=0.024) and a deeply-tolerant clone under a sub-spinodal total never breaks (P=0.000). The dose×duration tradeoff carries over (critical dwell 550 → 300 → 150 steps as the insult strengthens), and — the link back to §1 — because the critical insult shrinks as the residual self-drive nears the deletion threshold, deeper negative selection leaves only smaller-residual survivors and so raises the insult needed to break tolerance. Autoimmune susceptibility is set by deletion depth; only the absolute break rate (residual depth, insult amplitude/duration, noise scale D) is [O].

A tolerance–immunity dose window between ignorance and deletion

Self-antigen dose has two safe regimes and one dangerous one between them, and the volume measures where the edges fall by composing two of its own processes over a swept dose: central deletion (§1) removes a high-dose clone, while the inflammatory break (above) fires an escaped clone whose residual drive is large enough. The net break-risk is single-peaked in dose — 0.036 at low dose (the clone is ignored), peaking at an intermediate dose (here d=0.80), and 0.000 at high dose (the clone is deleted, central tolerance). The honest sign is the dual of the textbook “safe window”: the interior is the danger band, flanked by two safe regimes — ignorance below and central deletion above.

The band's edges are mechanistic and move predictably. The lower (break) edge = spinodal − insult, so it tracks the insult one-for-one: as the insult rises 0.2 → 0.4 → 0.6× the lower edge falls 0.782 → 0.615 → 0.429 (measured slope -0.882 ≈ −1), and d_lo + insult stays at the spinodal (0.982, 1.015, 1.029×) — the §1 commit threshold. The upper (deletion) edge is insult-independent (fixed at 0.824× by central tolerance), so the band width grows one-for-one with the insult (0.042 → 0.395 as the insult widens, slope 0.882 ≈ +1) and collapses when the insult vanishes — no insult, no danger band. The window position tracks each organ's spinodal (the deletion edge is a constant dimensionless fraction across all four organs). Only the absolute edges (thermal lowering of the deletion edge, insult amplitude, noise scale D) are [O]; the slopes are the clean invariants.