L(θ) · objective

Before a lab spends a year on a material, know whether to trust the prediction.

Machine-learned potentials now screen batteries, catalysts, and frameworks faster than any lab can test them. The gap is not speed. It is verification: a model can be confident and wrong, and the cost of finding out is measured in years and missed targets.

Characterize prediction error as a physical field, correct it at runtime, and machine-check every claim.

figures on this page are recomputed in-browser from the committed benchmark — see the data ↗

∫_M · error manifold

Prediction errors collapse onto a low-dimensional ribbon.

range recomputed in-browser from the committed benchmark — see the data ↗

Across classic and machine-learned potentials, atomic-force errors do not scatter randomly. They line up. That geometry makes failure predictable, and predictable failure is correctable failure.

∇_γE · error vectors

Shared error directions make failure predictable across models.

overlap recomputed in-browser from the committed benchmark — see the data ↗

The same local environments — surfaces, vacancies, under-coordinated sites — bias different potentials in similar directions. Where raw alignment can flatter (coupling-aware nulls reach 0.98), what survives blind tests is stronger: rankings hold (r = 0.906 across 36 model–material cells) and the error follows a smooth, coordination-keyed field. Read the live evidence →

Ω(Ξ) · public ledger

Claims are checked by machine, in public.

ribbon check recomputed in-browser from the committed benchmark — see the data ↗

Core claims are sealed as Lean 4 theorems with hash-locked provenance. The proof layer refuses as readily as it accepts — it once caught a rounded success count and changed 27 improvements to 26. The ledger is the public record of every claim, refutation, and correction.