Show HN: Formally verified polygon intersection – Opus 4.8 oneshots, prev failed (github.com)

A groundbreaking advancement in computational geometry has been announced with the release of a formally verified polygon intersection algorithm, marking the first of its kind. Utilizing the Lean 4 proof assistant, the algorithm guarantees correctness across all configurations of input polygons. Unlike previous models that required multi-step proofs, the latest release, Opus 4.8, enabled a more streamlined and autonomous approach, showcasing AI's evolving capability to manage complex formal verifications in one shot. The implementation allows users to engage with a web demo where multipolygons can be drawn and intersected, a feature typically found in vector graphic editors. This development is significant for the AI/ML community as it demonstrates the potential of AI agents to independently handle and verify intricate geometrical proofs, reducing reliance on human intervention. The formal verification process ensures that the method aligns with rigorous mathematical definitions, addressing challenges presented by infinite configurations and rare special cases that commonly disrupt classical testing methods. The creator noted a shift in the AI's ability to formulate large proof strategies and pivot when faced with difficulties, emphasizing the rise of more sophisticated AI tools that can tackle complex verification tasks previously deemed difficult or unsolvable. This work not only enhances trust in algorithm correctness but also opens avenues for further exploration and implementation of reliable computational geometry algorithms.