Lean formalization in OpenAI math repository (Result 125)
Model / AI: OpenAI (unreleased)
OpenAI's internal frontier model proved and formalized in Lean the main result of 'Single-exponential recovery and bounded-price strictness for metric k-median'. We give an exact-budget recovery algorithm for metric k-median with single-exponential dependence on the number of comparison clusters without accurate, distinct proxies in a supplied anchor solution. On positive integral metrics of polynomially bounded diameter, a sufficiently small total proxy error and logarithmically many such clusters yield a (1+2/e+\varepsilon) approximation in polynomial time with arbitrarily high success probability. We also prove bounded-price strictness for one compatible execution of the logarithmic-surplus construction. Together the recovery and payment arguments give a randomized (2-\sigma) approxi...
Source read 2026-10-08. Cataloged from OpenAI's formalization.yaml (Family 125). The Lean development was not rebuilt locally.