GoKawiilLean 4 formalization confirms prime gaps of at most 186, but relies on unproven axioms
A new repository presents a Lean 4 formal proof deriving the bound liminf(p_{n+1}-p_n) ≤ 186 for consecutive primes, building on the Maynard-Tao style DHL[40,2] admissible-tuple framework. The proof chain is conditional on three explicit input axioms covering Kloosterman sum bounds and related estimates, which have not themselves been formalized as Lean proofs despite being backed by established results like Deligne's theorem via Katz's monograph.