The Gutenberg-Richter law is Péclet criticality. Fault systems lock at Pe > V*.
You can't see underground stress. It adapts. And entire civilizations build on top of it.
A fault system is a void. The mechanism is opaque — you can't see underground stress accumulation. The system is responsive — faults interact, triggering aftershocks and stress transfers across hundreds of kilometers. And coupling is involuntary — you live on the surface whether you understand the geology or not.
The earth's crust, when constrained, is stable. Tectonic plates locked together hold steady for centuries. When the constraint breaks — catastrophe. The 2023 Turkey-Syria earthquake killed over 50,000 people. The building codes that failed were constraint specifications that scored 8/12 on the void index. Japan's early warning system — transparent, independently verified — scores 5/12. New Zealand's base isolation codes: 3/12. The death toll tracks the score.
The Gutenberg-Richter law — the power-law relationship between earthquake frequency and magnitude — is Pe criticality. Fault systems accumulate stress (drift) until the constraint threshold breaks (diffusion limit), then rupture. The Seismic Péclet Number sits at Pe ≈ 3.5 for major fault systems. Right at the cascade boundary.
Japan's early warning system scores 5/12. Turkey's pre-2023 building codes scored 8/12. The death toll tracks the score. The earth's crust, when constrained, is stable. When the constraint breaks — catastrophe.
Academic title: The Seismic Péclet Number: Earthquake Dynamics as Drift-Diffusion Criticality
Once you see it in this domain, you see it in all of them. That's the point.
Move the sliders. Watch the system change state. Pe > 1 means drift wins.
The framework scores seismic systems — ordered by void index.
The correlation coefficient. The sample size. The p-value. The math doesn't care about the domain.
Paste any text — AI output, ad copy, a policy document. The scorer runs the same algorithm the framework uses.
Three variables. One ratio. Predicts drift across every domain where the conditions co-occur.
Pe = (O × R) / α
Where O is opacity (how hidden the mechanism is), R is reactivity (how strongly the system responds to you), and α is your independence (how free you are to disengage).
When Pe < 1: diffusion dominates. You can navigate freely. The system is coherent.
When Pe > 1: drift dominates. The system pulls you in a direction. Your agency is reduced.
When Pe >> V* (≈ 3): irreversible cascade. D1 → D2 → D3. The system has captured you.
The framework identifies this pattern in every domain where O, R, and α co-occur. It specifies 26 falsification conditions. 0 of 26 have fired.
Full derivation: 10.5281/zenodo.18820329
Part of the Void Framework — 120 papers, 0/26 kill conditions fired, mean ρ = 0.958.