What happened
Whether the core of an approval-based multi-winner (ABC) election is always nonempty has been open since Aziz, Brill, Conitzer, Elkind, Freeman, and Walsh (2017). It is the standard group-fairness notion of proportional representation for committee elections. Epoch listed a request for an empty-core counterexample as a Major-advance FrontierMath: Open Problems item; Peters had suggested the problem for the benchmark. The 10 September 2026 preprint (arXiv:2609.11912) proves there is no such counterexample. The argument introduces a voting rule that maximizes an entropy-like “harmonic entropy” objective over committees and payment systems; every local optimum lies in the core, so a core committee can be found in polynomial time. The authors write that the proof was obtained with GPT-6 Astra. Epoch’s 18 September note records a human + AI solution: the authors attribute the primary idea and proof to Astra in a lengthy interactive session; Peters told Epoch he doubts the team would have found the proof without Astra, and also that Astra does not appear to solve it from a simple prompt. Because the theorem shows the stated counterexample task is impossible, Epoch still marks the problem solved under its policy. This is newly created social-choice knowledge, not a FrontierMath exam score, and it is separate from Astra’s August ten-proofs cluster and from FrontierMath Erdős. Update (2026-09-14): Open-Source AI and Open Models Reading List. Article URL: https://www.interconnects.ai/p/open-source-ai-reading-list Comments URL: https://news.ycombinator.com/item?id=49690260 Points: 18 # Comments: 1 Update (2026-09-19): Laya the open source version of Jev. Article URL: https://laya.convaiinnovations.com/ Comments URL: https://news.ycombinator.com/item?id=49765348 Points: 12 # Comments: 2 Update (2026-09-19): Microsoft director: AI scraping 'the largest theft of labor in human history'. Article URL: https://www.tomshardware.com/tech-industry/artificial-intelligence/microsoft-director-called-ai-scraping-the-largest-theft-of-labor-in-human-history-while-openai-head-brands-chatgpt-an-existential-threat-to-publishers-revelations-come-from-legal-briefs-filed-in-nyt-lawsuit Comments URL: https://news.ycombinator.com/item?id=49768921 Points: 79 # Comments: 21 Update (2026-09-22): GPT-6 Sol and Luna. Article URL: https://openai.com/index/introducing-gpt-6-sol-and-luna/ Comments URL: https://news.ycombinator.com/item?id=49805509 Points: 370 # Comments: 176 Update (2026-09-22): The current balance of power in open models. Article URL: https://www.interconnects.ai/p/the-current-balance-of-power-in-open Comments URL: https://news.ycombinator.com/item?id=49808816 Points: 16 # Comments: 3 Update (2026-09-23): GPT-6 Astra has gained the ability to drive a car. Article URL: https://drivingbench.com/ Comments URL: https://news.ycombinator.com/item?id=49817404 Points: 41 # Comments: 26 Update (2026-09-24): Best LLM for every budget, updated daily. Article URL: https://bestmodelforyourbudget.terrydjony.com/ Comments URL: https://news.ycombinator.com/item?id=49830866 Points: 43 # Comments: 20 Update (2026-09-24): Open Source Replication of the Auditing Game Model Organism We release an open source replication of the model organism from our previous auditing game paper.. Open Source Replication of the Auditing Game Model Organism We release an open source replication of the model organism from our previous auditing game paper. Update (2026-09-22): AI Exec: We May Have Pulled Off “The Largest Theft of Labor in Human History” - Mother Jones. AI Exec: We May Have Pulled Off “The Largest Theft of Labor in Human History” Mother Jones