The hair follicle is the one skin structure that cycles autonomously, so it needs an oscillator, not a static switch. Putting the same measured EDAR γ on the same vendored relaxation oscillator yields an anagen-dominant cycle with no new constant; four alopecias then follow as that one cycle driven off its set-point, telogen effluvium shedding exactly one telogen after the stressor.
The hair follicle — the one autonomously cycling integumentary structure — is reproduced as an emergent relaxation oscillator on the same measured EDAR γ that emerged the skin appendage, with no new fitted constant. The cycle is anagen-dominant with a plateau-then-collapse waveform [V] Simulation-verified; the absolute fraction and years-long period stay open [O] Open (obstacle stated). Four alopecias follow as signed perturbations of the one cycle — androgenetic (shortened anagen, reversed by minoxidil), areata (sustained anagen arrest with regrowth hysteresis), telogen effluvium (a delayed self-limited shed exactly one telogen after the stressor), and anagen effluvium (an immediate shed bypassing telogen) — passing an intervention-reversal battery and a three-way opposite-sign/opposite-timing discriminant, the layer adding no constant while the core-battery hash stays fixed.
The hair follicle is the one skin structure that cycles — so it needs an oscillator, not a switch
Every mechanism so far has been a static R19 switch: the barrier sits in one basin, the melanin screen in another. But the core battery itself reports a gap — there is no autonomous oscillator anywhere in the integumentary class, and the one structure that demands one is the hair follicle, which cycles on its own between a long growth phase (anagen), a brief regression (catagen), and a resting phase (telogen), then re-enters growth without any external clock. This page closes that gap with no new organ and no new fitted constant: it puts the same measured EDAR γ = 1.3696 that already emerged the skin appendage onto the same vendored relaxation oscillator the thermoregulation page (T5) already uses, and reads off the cycle.
| Quantity | Value | Meaning |
|---|---|---|
| Master gene (measured) | EDAR γ = 1.3696 | the appendage organ's own γ, read-only — not refitted |
| Spinodal | 0.617 | substrate-derived from γ (sets the regime scale) |
| Growth bias | 0.308 | half the appendage spinodal — a substrate-scaled regime scale [F], not fitted to a hair phenotype |
| Oscillates | yes | the follicle cycles autonomously (limit cycle, not a fixed point) |
| Anagen-dominant | yes | growth occupies the larger share of the cycle |
| Relaxation waveform | yes | a long plateau then a fast collapse, not a smooth sinusoid |
The cycle is anagen-dominant (the growth phase takes a fraction of about 0.59 of the cycle) and has a clear relaxation shape — the plateau occupies about 0.87 of each beat before a rapid collapse, exactly the long-growth/short-rest asymmetry the biology shows. These two facts — that growth dominates and that the waveform is a plateau-then-collapse relaxation cycle — are the simulation-verified core [V] Simulation-verified of this page; they come straight out of the substrate with nothing tuned.
The package is deliberately honest about what it does not claim here. The absolute anagen fraction (the cited 85–90%) and the absolute period (years) are not fitted: a single constant drive strong enough to reach 88% would push the element through its Hopf point and kill the oscillation altogether. So the substrate is graded against those anchors by dominance and direction, not by magnitude — the model reproduces that anagen dominates and that the waveform relaxes, and the absolute fraction and the years-long period remain open [O] Open (obstacle stated), inheriting the appendage target's standing obstacle (a per-follicle calibration). This is the same no-tuning rule the rest of the package runs under, applied to a dynamical regime.
Four alopecias are this one oscillator driven off its cycle
With the oscillator established, the four major patterned hair-loss diseases follow with no new physics — each is the same cycle driven away from its set-point, and each established treatment is the same drive reversed. Four diseases pass a clinical-sign plus intervention-reversal battery and a three-way opposite-sign / opposite-timing discriminant, with no constant introduced.
| Disease | Cycle handle | Covered as |
|---|---|---|
| Androgenetic alopecia | anagen duration | standing anti-growth drive shortens the anagen plateau → progressive miniaturisation |
| Alopecia areata | premature catagen | sustained immune-type drive forces anagen → telogen; regrows on removal (hysteresis) |
| Telogen effluvium | phase synchronisation | a transient stressor synchronises a cohort into telogen; sheds one telogen later, self-limited |
| Anagen effluvium | anagen-matrix arrest | a direct cytotoxic insult sheds anagen hairs immediately, bypassing telogen |
Anagen duration off both poles: androgenetic alopecia versus its therapy
Androgenetic alopecia is a standing anti-growth drive on the cycle: the anagen plateau shortens, so the anagen fraction falls progressively from about 0.59 through 0.54 to 0.49 — the substrate's account of terminal-to-vellus miniaturisation across successive cycles. A pro-growth drive (minoxidil or an anti-androgen) lengthens anagen back to about 0.63: the same knob, reversed, not a new mechanism. Progressive miniaturisation reproduces (yes).
Anagen arrest under a sustained drive: alopecia areata
Alopecia areata is a sustained premature-catagen drive: an immune-type signal forces follicles out of anagen, dropping the anagen fraction to about 0.48 while the drive persists. Because the underlying element is bistable, removing the drive lets anagen resume — the fraction recovers to about 0.59, the regrowth-on-removal hysteresis the clinic sees. Anagen suppression reproduces (yes); it is sustained while driven, which is the pole that contrasts with the self-limited effluvium below.
The decisive timing test: delayed versus immediate shedding
The two effluvia share a cause — a synchronising insult — but differ in when the hair sheds, and the oscillator reproduces both timings from one cycle. Telogen effluvium is a transient systemic stressor that pushes an anagen cohort synchronously into telogen; that cohort then sheds one telogen duration later. In the simulation the shed peak lags the stressor by exactly 365 steps — which is precisely one telogen arc (365 steps = (1 − 0.59) of the cycle) — then the cohort re-enters anagen, so the shed is self-limited. Anagen effluvium, by contrast, is a direct cytotoxic insult to the growing matrix (chemotherapy or radiation): the anagen hair sheds immediately, with a lag of 0 steps, bypassing telogen entirely, and reverses once the insult stops. Same oscillator, opposite timing — the delayed-versus-immediate dichotomy reproduces (yes).
The discriminant: opposite alopecias from opposite drive signs and timings
As with the static diseases, the decisive evidence is that opposite clinical entities fall out of the same oscillator driven in opposite ways, with no constant changed between them.
| Axis | One pole | Opposite pole | Reproduced |
|---|---|---|---|
| Anagen duration | minoxidil / anti-androgen (long) | androgenetic (short) | yes |
| Shed timing | telogen effluvium (delayed, one telogen) | anagen effluvium (immediate) | yes |
| Persistence | alopecia areata (sustained while driven) | telogen effluvium (self-limited) | yes |
All three opposite pairs reproduce (yes). That a single relaxation cycle yields shortened anagen and lengthened anagen, sustained loss and self-limited loss, and delayed shedding and immediate shedding from opposite signs and timings alone — with the same EDAR γ and no new parameter — is the strongest internal evidence that the alopecias are cycle dynamics, not bespoke fits.
Grades and reproducibility
Every mechanism here is a simulation-verified shape, control, or timing [V] Simulation-verified — oscillation, anagen-dominance, the relaxation waveform, the miniaturisation direction, the one-telogen shed lag, the immediate-versus-delayed dichotomy. Every clinical mapping rests on a cited anchor [L] Cited anchor. Every absolute magnitude is open [O] Open (obstacle stated) — the absolute anagen fraction, the years-long period, absolute hair counts and shed fractions — each inheriting the appendage target's obstacle (a per-follicle calibration). No disease introduces a new constant; each is a named perturbation of the one oscillator.
The hair-cycle pipeline is deterministic on its own terms: two independent runs hash to an identical SHA-256, separate from both the core battery and the pathology layer. Crucially, adding this oscillator layer does not touch the core T1–T5+oncology battery, whose result hash is unchanged at 1fb59f556e01….