§9 · maturation
Maturation has an interior optimum, innate/adaptive split by timescale, tolerance mirrors memory
Affinity maturation EMERGES from iterated germinal-centre selection, and its gain peaks at an interior optimum (0.40 survivor fraction): too-weak selection loses ground, too-stringent collapses it. Innate and adaptive immunity split into two well-separated durability timescales ranked by measured γ, and tolerance is the same PAX5 switch driven the opposite way. [V]/[O].
A germinal-centre loop on the substrate (pool 300, 14 rounds) MEASURES the inverted-U: gain runs from -0.040954 under weak selection to a peak of +0.033064 and back toward +0.000132 when over-stringent. Innate (RUNX1) and adaptive (PAX5) separate into a measured MFPT ratio of 2.369×, and the tolerance flip sits at the same spinodal magnitude as memory, both basins held after the drive clears.
Maturation emerges, and its gain has an interior optimum
Iterated selection on the germinal-centre loop is run directly on the substrate: a pool of 300 over 14 rounds. The maturation gain is not asserted — it EMERGES, and it is non-monotone in selection pressure: too-weak selection loses ground (negative gain), an interior survivor fraction is optimal, and over-stringent selection starves the pool back toward zero gain.
| survivor fraction | selection pressure | maturation gain |
|---|---|---|
| 1.000 | 0.000 | -0.040954 |
| 0.600 | 0.400 | +0.032436 |
| 0.400 | 0.600 | +0.033064 |
| 0.250 | 0.750 | +0.033064 |
| 0.150 | 0.850 | +0.033064 |
| 0.100 | 0.900 | +0.033064 |
| 0.060 | 0.940 | +0.033064 |
| 0.033 | 0.967 | +0.033064 |
| 0.020 | 0.980 | +0.000132 |
| 0.010 | 0.990 | +0.000132 |
Innate versus adaptive is a two-timescale durability split
At noise D = 0.12 the innate master (RUNX1, shallower barrier) and the adaptive master (PAX5, deeper barrier) separate into two well-spaced decay timescales. The slower arm is the deeper barrier, and the ordering tracks the measured γ — durability is read from the escape statistic, not assigned.
| arm | master gene | γ | barrier | surviving fraction | MFPT |
|---|---|---|---|---|---|
| innate | RUNX1 | 1.3225 | 0.4373 | 0.3564 | 77.54 |
| adaptive | PAX5 | 1.4892 | 0.5544 | 0.6469 | 183.65 |
The adaptive arm outlasts the innate arm by a measured factor of 2.369×. Absolute lifetimes in days or years are runtime [O].
Tolerance is memory's mirror drive on the same switch
On PAX5 (γ = 1.4892, spinodal 0.6995), a positive drive of 0.7065 settles the switch into memory, while the equal and opposite drive of 0.7065 settles it into tolerance. The two thresholds are symmetric at the spinodal magnitude, and both basins are held after the drive clears — memory and tolerance are the same switch read with opposite sign. The sign law is measured; the absolute desensitisation dose and schedule are [O], and clinical tolerance is handed to clinicians.