Immune Memory as Barrier Persistence

Immune memory is barrier-protected persistence of the ON state. This volume does not just assert stability — it removes the drive and simulates the stochastic ON→OFF escape, and the measured mean lifetime ranks in ascending γ order while the Kramers law (log-rate linear in barrier) emerges. Higher-γ organs remember longest. Grade [V].

With the drive removed the ON state persists; the measured mean lifetime (MFPT) ranks in the same ascending order as γ (bone_marrow_hematopoiesis → spleen → thymus → lymphoid_adaptive), and log(escape-rate) is linear in the barrier (R²=0.998) — the Kramers law emerging from a direct stochastic escape simulation, with absolute lifetime [O].

Persistence without a drive

Memory is the ON basin surviving the removal of antigen. The barrier γ²/4 is what keeps the clone in the ON basin once the affinity drive falls to zero, so no ongoing antigen is required to remember.

Forgetting is not passive decay here: erasing the memory takes a reverse drive of at least the spinodal, the mirror of activation. Below that, the memory is stable.

Stability ranking

Because the barrier grows with γ, the organs rank in durability exactly as they rank in γ. The adaptive lymphoid compartment has the largest barrier and so is the most stable long-term store — consistent with durable adaptive immunity outliving innate responses.

The durability ordering emerges from a stochastic escape simulation

Rather than infer stability from the barrier height alone, the volume simulates forgetting directly: each organ's clone is initialised in the ON basin, the antigen drive is removed (h=0), and an ensemble of cells evolves under overdamped Langevin noise until they escape back to OFF. The mean ON-state lifetime is measured as the inverse escape rate, and it ranks bone-marrow 37.5 < spleen 55.8 < thymus 64.0 < lymphoid 76.9 — exactly the ascending-γ order, so the durability ranking is confirmed dynamically rather than read off the barrier.

The Kramers law itself emerges: the logarithm of the measured escape rate is linear in the independently computed γ²/4 barrier (R²=0.998) with an Arrhenius slope of -6.1, recovering the expected −1/D=-6.7. The stability ordering and the exponential law are therefore [V] (simulation-measured); only the absolute lifetime, which depends on the uncalibrated cellular-noise scale D, is left [O].