math

They just merged my PR for the current tightest bound on the integer multiplication problem: https://github.com/CrocSwap/integer-mult-bounds/pull/37#even... Something interesting happened last night: Researchers started proposing tighter conditional bounds for integer multiplication, submitted by OpenAI yesterday, then a swarm of collaborators online pushed it even further. Its so interesting that human researchers provided the insights to push to the out-of distribution solutions that no one model reached alone. I just submitted the current new best conditional bound, conditional κ = 4.123863984e-5, and I have a very useful system setup for auto-research that requires human intuition to reach out-of-distribution solutions. I have a list of ideas to test so we may not be done yet :) Original paper from OpenAI: https://github.com/openai/m

They just retracted 3 manuscripts: In “Algebraicity of Weil classes on split abelian eightfolds” a sign error invalidates a stabilization-trace cancellation argument and the construction used by two dependent papers. As a result, we have withdrawn the following three manuscripts: - Algebraicity of Weil classes on split abelian eightfolds - Algebraicity of Kuga–Satake Correspondences for K3 Surfaces - The rational Hodge conjecture for products of K3 surfaces These were all related to the Hodge conjecture, one of the Millennium Prize problems. I wonder how many more will be retracted in the coming months. https://github.com/openai/math/pull/1/files/301488868beec11b...