{"slug": "gpt-5-6-pro-finds-counterexample-to-dinitz-garg-goemans-conjecture", "title": "GPT 5.6 Pro finds counterexample to Dinitz-Garg-Goemans conjecture", "summary": "GPT 5.6 Pro has found a counterexample to the Dinitz-Garg-Goemans conjecture, a graph theory problem open for approximately 30 years. The graph exhibits a fractional flow cost of 58, while any unsplittable flow with capacity violation ≤15 has cost at least 60, disproving the conjecture. The user who discovered the counterexample stated they spent many weeks thinking about the problem.", "body_md": "Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years.\nThe graph below has fractional flow cost 58. Any unsplittable flow (with capacity violation <=15) has cost at least 60.\nChat with GPT 5.6 Pro where this was found:\n\n[chatgpt.com/share/6a60b2eb-0…](https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de063)Jul 22, 2026 · 12:18 PM UTC\n\n186\n\n662\n\n7,566\n\n2,566,273\n\nI know counterexamples to old conjectures are becoming a meme at this point. But I really cared about this problem and spent many weeks thinking about it a while ago (in both directions, proof and disproof).\nI think almost all graph flows experts thought about this problem.\n\n12\n\n11\n\n1,536\n\n107,200", "url": "https://wpnews.pro/news/gpt-5-6-pro-finds-counterexample-to-dinitz-garg-goemans-conjecture", "canonical_source": "https://xcancel.com/DmitryRybin1/status/2079904005652893709", "published_at": "2026-07-23 04:01:53+00:00", "updated_at": "2026-07-23 04:22:29.350745+00:00", "lang": "en", "topics": ["artificial-intelligence", "ai-research"], "entities": ["GPT 5.6 Pro", "Dinitz-Garg-Goemans conjecture"], "alternates": {"html": "https://wpnews.pro/news/gpt-5-6-pro-finds-counterexample-to-dinitz-garg-goemans-conjecture", "markdown": "https://wpnews.pro/news/gpt-5-6-pro-finds-counterexample-to-dinitz-garg-goemans-conjecture.md", "text": "https://wpnews.pro/news/gpt-5-6-pro-finds-counterexample-to-dinitz-garg-goemans-conjecture.txt", "jsonld": "https://wpnews.pro/news/gpt-5-6-pro-finds-counterexample-to-dinitz-garg-goemans-conjecture.jsonld"}}