The formal verification arrived alongside a community effort that raised the algorithm's conditional exponent saving parameter κ from OpenAI's initial 2⁻¹⁸² to 0.0017137844912361143, up 2.6% since Oct. 13. The latest gains followed an "anticipatory dirty borrowing" technique from contributor 1337isnot1337 that reuses idle registers to cut helper registers per call from 480 to 400 in a test word, prompting 19 record pull requests from six contributors that lifted the unverified κ by 1.4% in about 13 hours.
Tuesday, October 20, 2026
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Open Source Contributors Verify OpenAI's Sub-n log n Integer Multiplication Proof in Lean in Six Days
AI5 days ago
Open source contributors Platypii, identified as Kenny, and jdb1729 formally proved OpenAI's sub-n log n integer multiplication result in the Lean theorem prover in six days. Project coordinator Doug Colkitt noted that comparable formalization efforts previously required person years of work because Lean lacked existing library coverage for the underlying multitape Turing machine model, requiring Kenny to build new libraries across a broad area of mathematics and computer science.
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