The site labels the problem OPEN (proof-claims thread of 2026-10-07). Two full claims of July 2026, developed independently and both crediting AI systems, assert the answer yes with the same explicit limit, the centered Cauchy law of scale $1/(2\pi)$: Kwon's manuscript and Wang's preprint with a Lean 4 proof. Neither has been accepted by the site or refereed. This page departs from the site's label and records the problem as proved, because this corpus built and audited a port of Wang's Lean proof, whose two main theorems answer the site's question yes and pin the Cauchy limit (Formalization).