> Claude, an AI model developed by Anthropic, discovered the algorithm that refutes the 3SUM, APSP, and Exact Triangle hypotheses. The authors then worked to understand, simplify, strengthen, and extend the algorithm, derive additional consequences, and make the presentation accessible. See “Acknowledgments and Methodology” for how the result was found and shared with the authors. The authors take full responsibility for this paper.
> Claude also verified this paper’s main results using the Lean 4 proof assistant with the Mathlib library.
> Claude also verified this paper’s main results using the Lean 4 proof assistant with the Mathlib library.