GPT-6 Astra Solves Liouville Version of Goldbach, Lean Independently Verifies and Passes

Beating AI News Flash: Anonymous math community account Captain Sude has published a new proof found by GPT-6 Astra, solving the Liouville version of the Goldbach problem.

This problem relaxes the "two primes" in the classic Goldbach conjecture to "two integers with an odd total number of prime factors." Previously, Durham University mathematician Alexander P. Mangerel could only prove it under the assumption that the Generalized Riemann Hypothesis holds and that the even number is sufficiently large.

Astra has now removed these two restrictions, proving it holds for all even numbers greater than 2. The core idea is to first assume that some even number cannot be split in this way, then step by step derive mutually contradictory results.

The complete proof has been written in Lean 4. The project compiles successfully, and an independent audit repository has also successfully reproduced it, finding no `sorry` or additional mathematical axioms.

The classic Goldbach conjecture itself remains unsolved, because the two addends here can still be composite numbers.