Scope and the jammed-vacuum substrate: one drive, two failures, one lever

This package derives the human gonadal-endocrine (HPG) axis on a jammed-vacuum substrate, where a single bistable R19 switch and a single FitzHugh-Nagumo relaxation oscillator generate every reproductive rhythm. One sex-hormone drive h yields two failure modes — an oscillator disease and an oncogenic switch — governed by one lever: temporal pattern. Brain-facing HPA stays in the Felt Cognition paper.

The substrate is the R19 tilted double well V(s) = −γs²/2 + s⁴/4 − hs, whose spinodal h_sp = 2(γ/3)^3/2 = 0.3849 at γ=1 makes every fate-flip discontinuous. The same kernel, run as an FHN oscillator, produces the GnRH pulse, the menstrual cycle, and the spermatogenic cycle by changing only the recovery timescale τ_s. No new physics is introduced here; the vendored primitives are used unchanged.

The substrate is a jammed-vacuum lattice, not a new postulate

The VP programme treats the vacuum as a jammed granular medium; this package inherits its bistable switch and oscillator unchanged. A cell or tissue fate is a point in the R19 double-well potential, and a hormone is a tilt h on that well.

V(s) = -\frac{1}{2}\gamma s^{2} + \frac{1}{4}s^{4} - h\,s — R19 tilted double-well potential (the fate landscape).

The stationary states are the roots of the cubic, so for three real roots there are two minima and a saddle. As the tilt h grows the metastable minimum and the saddle approach and annihilate at the spinodal — beyond it the flip is unavoidable and discontinuous.

\dot s = \gamma s - s^{3} + h \;\Rightarrow\; s^{3} - \gamma s - h = 0 — Force balance; its roots are the basins (outer) and the saddle (middle).

Two locked constants set every threshold and barrier

The spinodal fixes where a switch flips, and the barrier fixes how stable a basin is — both are forced functions of the identity constant γ alone. At γ=1 the spinodal is 0.3849 and the barrier is 0.2500.

h_{\mathrm{sp}}(\gamma) = 2\left(\frac{\gamma}{3}\right)^{3/2} — Spinodal: the drive past which the opposite basin disappears.

\Delta V_{0}(\gamma) = \frac{\gamma^{2}}{4} — Inter-basin energy barrier (state stability).

The unifying thesis: one drive, two failure modes, one lever

One sex-hormone drive h, moved two opposite ways, produces the whole disease map. Move it the wrong pattern and the HPG oscillator fails (an endocrine disorder); lower the barrier and the R19 oncogenic switch crosses (a hormone-driven cancer).

The single control axis the framework exposes is therefore temporal pattern — pulsatile versus continuous, cycling versus sustained. This thesis is developed across the discriminant targets (§3–§7), oncology (§8), therapy (§9) and the disease map (§10).

Firewall: this package owns the gonadal axis only

Decomposition is by physical regime, not textbook organ-system labels: this is the jamming (hormonal-cycle / germline) class. The brain-facing hypothalamic-pituitary-adrenal (HPA) stress axis and felt experience belong to the Felt Cognition paper and are cited, never re-derived here.

Sex-hormone levels are this package’s single source of truth (SSOT); sibling packages cite them rather than recomputing them.