Collapse Phenomena
16 Latin terms naming the structural phenomena discovered across 146 experiments and 20 closure domains. These are not metaphors — each names a measurable pattern in the kernel invariants, verifiable through computation.
Ruptura est fons constantiae. — Rupture is the source of constancy.
Structural Insights
Geometric Slaughter Is Universal
Every domain exhibits geometric slaughter when a single channel approaches ε. In particle physics: quark color → 0 at confinement. In finance: subprime → 0 in 2008. In consciousness: sleep stages → variable channel death. The mechanism is always the same: one near-zero channel in the geometric mean (IC) drags the product toward zero while the arithmetic mean (F) remains healthy. This is the integrity bound IC ≤ F in action.
Scale Inversion Heals Damage
After geometric slaughter at one scale, new degrees of freedom at the next scale can restore IC. Quarks (IC/F ≈ 0.80) → hadrons (IC/F ≈ 0.03) → atoms (IC/F ≈ 0.96). The scale ladder is not monotonic — it oscillates between slaughter and recovery. Each recovery introduces new channels that re-cohere what the previous boundary destroyed. Ruina fecunda — fruitful ruin.
The First Weld Requires Homogeneity
Near the generative threshold (c ≈ 0.318), the first seam closes only when all channels are equal. Heterogeneity at this boundary prevents the budget from reconciling because even small channel variance creates enough gap (Δ = F − IC) to exceed the residual tolerance. Excitatio homogenea — the homogeneous lift.
∞_rec Is a First-Class Verdict
Permanent detention (τ_R = ∞_rec) is not an error — it is a legitimate outcome. A gestus sine receptu (gesture without receipt) is an epistemic emission that cannot close a seam. It may carry insight but it cannot carry credit. The system distinguishes between "not yet returned" and "cannot return" — both are meaningful, both are measured.
Live Demonstration: Geometric Slaughter
Drag the slider to kill one channel. Watch IC collapse while F stays healthy. This is Trucidatio Geometrica — the defining phenomenon of GCD.