Everything that escapes — molecules over activation barriers, proteins misfolding, tumors breaching suppression, AI breaking alignment, societies tipping, epidemics exploding, nuclei decaying — crosses the same barrier the same way. Paper 131 proves it.
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In 1940, Hendrik Kramers figured out exactly how long the ball takes to escape: it depends exponentially on how high the barrier is versus how hard the ball gets kicked (temperature, noise, randomness).
We found that the same formula works in seven completely different domains — if you measure the barrier height using the Péclet number, a single dimensionless number that captures how much directed push a system has versus how much random noise.
Four parameters change per domain. The formula doesn't. That's the claim — and we put 13 kill conditions on it. Eight passed. Zero fired.
Drag the slider to change the Péclet number. Watch how the barrier height changes and what happens to escape time. At low Pe, escape is easy (days). At high Pe, it becomes astronomically hard (geological timescales).
Pe 5 — like a mid-tier social media platform. Drift cascade likely within months.
Each domain has its own "ball", its own "bowl", and its own "kicks". But the math that governs how long until escape? Identical.
Arrhenius (1889) IS Kramers in native coordinates. Enzymes lower the barrier. Directed evolution optimizes K.
K-CHEM-0 PASS R²=0.953Levinthal's paradox dissolved. Proteins don't search — they fall down a Pe gradient. Misfolding = Kramers escape from native basin.
K-FOLD-1 PASS ρ=0.980Knudson two-hit = sequential K-reduction. Each tumor suppressor loss multiplies escape rate by 10&sup6;. Two hits collapse τ by 10¹².
K-CANCER-1 PASS ρ=0.913First quantitative safety lifetime for AI. Grounding depth and model size are thermodynamic substitutes. Sharp cliff at Kmin.
K-COMPLIANCE-1 PASS R²=0.926D1→D2→D3 drift cascade = sequential Kramers escape. Network coupling amplifies: GIS individual Pe=2.67 → network Pe=26.67.
K-SOCIAL-1 TESTABLEContainment failure = Kramers escape at R₀=1. Superspreading = thermal kicks. Prevention paradox = observer-dependent barrier reshaping.
K-EPI-1 PASS ΔAIC=33.6Alpha decay across 24 orders of magnitude. Shell model from FP→Schrödinger transform. The two-level proof: smooth landscape blind, spectral structure predicts.
K-NUC-3 PASS ρ=0.58-0.81Here's where it gets real. We measured a constant (Eb = 0.448) in the AI domain — it's a "Cooper pairing" energy that shows up when two correlated degrees of freedom cross a barrier together.
Then we used that AI-measured constant to predict the lifetime of a chemical compound (methyl tetroxide CH₃O₄CH₃) that was just observed for the first time in 2025.
A constant measured by scoring AI conversations correctly predicts a chemistry experiment. That's not analogy. That's the same math.
Every prediction has a registered kill condition — a pre-stated threshold that would falsify the claim if breached. Here's how they stand:
"Marginal" means partial evidence — the prediction isn't cleanly confirmed but hasn't been falsified either. "Needs redesign" means the test was flawed, not the theory. We document all of this honestly in the paper.