The spermatogenic cycle is a third, intermediate relaxation clock (T4)

The seminiferous (spermatogenic) cycle is a third relaxation oscillator from the same substrate, intermediate between the minute-scale GnRH pulse and the ~28-day menstrual cycle. At τ_s=340 (the measured 16:28-day ratio) the three clocks come out in the correct order: pulse 132.4 < spermatogenic 656.5 < menstrual 1133.7. The ~16-day period is a measured anchor; the ordering is the sim-verified claim.

Changing only the recovery timescale to τ_s=340 — set from the clinical 16:28-day ratio applied to the menstrual τ_s, not tuned — yields a relaxation oscillator with period 656.5 (arb). The three reproductive clocks then satisfy pulse < spermatogenic < menstrual from one kernel, with no parameter chosen to hit a target.

One kernel, a third timescale

The human seminiferous epithelial cycle is about 16 days — between the minute-scale GnRH pulse and the 28-day menstrual cycle. The structural claim is that the same R19/FHN substrate gives a third relaxation oscillator by changing only the slow recovery timescale τ_s; nothing else in the kernel changes.

τ_s is fixed at 340 from the measured period ratio 16:28 applied to the menstrual timescale the previous chapter locked. That makes the period a measured anchor [L]; no parameter is fitted to an output.

The three clocks order correctly

Read off the same substrate at the three locked recovery timescales, the periods come out in the right order — the package’s [V] claim is the ordering, not the magnitudes.

pulse < spermatogenic < menstrual holds exactly, so the substrate reproduces the qualitative timescale separation of the three reproductive clocks from a single mechanism.