{"data":{"event":{"id":"53bb9303-37ab-4e39-97ec-f6e384680e4c","slug":"dinitz-garg-goemans-counterexample","title":"Rybin, using GPT-5.6 Pro, counters the Dinitz–Garg–Goemans unsplittable-flow cost conjecture","short_summary":"On 22 July 2026 Dmitry Rybin announced an explicit 7-vertex graph in which a feasible fractional unsplittable-flow costs 58 while every congestion-legal unsplittable flow costs at least 60, disproving Goemans’ cost-preserving rounding conjecture. He attributes the construction to GPT-5.6 Pro. An Isabelle Archive of Formal Proofs entry later checks the finite instance.","full_description":"Dinitz, Garg, and Goemans proved that a fractional single-source flow can be rounded to an unsplittable flow with congestion at most the largest demand. Goemans conjectured that rounding can also preserve cost. Rybin posted a 7-vertex, 9-arc instance with demands 15, 10, and 15: fractional cost 58 versus unsplittable cost ≥60 under capacity violation ≤15. The 1999 congestion theorem is unaffected. A later AFP development verifies the finite counterexample in Isabelle; that formalization used AI for proof engineering, but the mathematical discovery credit remains GPT-5.6 Pro with Rybin.","ledger_type":"benefit","primary_domain_id":"23d935bb-b857-4b2b-9471-d568bb848a66","event_status":"provisional","event_date":"2026-07-22T00:00:00.000Z","discovery_date":"2026-07-22T00:00:00.000Z","first_published_date":"2026-07-22T00:00:00.000Z","last_reviewed_date":"2026-07-22T00:00:00.000Z","geographic_scope":"International","affected_population":"Combinatorial optimization research community","base_impact_tier":2,"base_score":"3.00","attribution_multiplier":"0.7500","evidence_multiplier":"0.4000","realization_multiplier":"0.5500","durability_multiplier":"0.7000","current_event_score":"0.346500","confidence_level":"medium","score_explanation":"An explicit counterexample to a named 1999 cost conjecture is notable (tier 2). GPT-5.6 Pro found the instance under Rybin’s prompting (0.75). Evidence is a public announcement plus an Isabelle check of the finite graph (0.40). Realization is a reproducible construction (0.55).","methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","original_methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","published_at":"2026-07-22T00:00:00.000Z","created_at":"2026-09-13T22:56:05.431Z","updated_at":"2026-09-13T22:56:05.431Z","flags":[],"domain_name":"Mathematics","domain_slug":"mathematics","methodology_version":"0.1"},"contributions":[{"id":"7833bd2f-0c5c-4b3a-8ddd-a0cc32c9805e","event_id":"53bb9303-37ab-4e39-97ec-f6e384680e4c","model_id":"c56f0731-9e4f-40b1-8887-fa319c5114bf","role_description":"Produced the explicit 7-vertex counterexample in a GPT-5.6 Pro session posted by Dmitry Rybin.","attribution_multiplier":"0.7500","credit_share":"1.0000","contribution_score":"0.346500","attribution_rationale":"Rybin’s announcement and later writeups name GPT-5.6 Pro as the system that found the graph.","attribution_confidence":"medium","first_used_date":"2026-07-22T00:00:00.000Z","model_version_if_known":null,"review_status":"approved","created_at":"2026-09-13T22:56:05.431Z","model_slug":"gpt-5-6-pro","model_name":"GPT-5.6 Pro","identity_class":"named_release","is_internal":false,"family_name":"GPT-5.6","family_slug":"openai-gpt-5-6","organization_name":"OpenAI","organization_slug":"openai"}],"sources":[{"id":"19132112-77ed-4388-8c96-653ec51eeef7","event_id":"53bb9303-37ab-4e39-97ec-f6e384680e4c","url":"https://x.com/DmitryRybin1/status/2079904005652893709","canonical_url":"https://x.com/DmitryRybin1/status/2079904005652893709","source_type":"other","publisher":"X","author":null,"publication_date":"2026-07-22T00:00:00.000Z","retrieved_at":"2026-09-13T22:56:05.431Z","title":"Dinitz–Garg–Goemans conjecture is false","excerpt":null,"content_hash":null,"source_reliability_class":"medium","is_primary_source":true,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T22:56:05.431Z"},{"id":"8de1c609-cf91-41de-a85e-7c886fa9790d","event_id":"53bb9303-37ab-4e39-97ec-f6e384680e4c","url":"https://vibemathed.com/problem/dinitz-garg-goemans-unsplittable-flow","canonical_url":"https://vibemathed.com/problem/dinitz-garg-goemans-unsplittable-flow","source_type":"other","publisher":"VibeMathed","author":null,"publication_date":"2026-07-28T00:00:00.000Z","retrieved_at":"2026-09-13T22:56:05.431Z","title":"Dinitz-Garg-Goemans Conjecture","excerpt":null,"content_hash":null,"source_reliability_class":"medium","is_primary_source":false,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T22:56:05.431Z"},{"id":"4b1f93b0-6fa0-4cd4-b57e-4e82e487147e","event_id":"53bb9303-37ab-4e39-97ec-f6e384680e4c","url":"https://isa-afp.org/entries/Dinitz_Garg_Goemans_Counterexample.html","canonical_url":"https://isa-afp.org/entries/Dinitz_Garg_Goemans_Counterexample.html","source_type":"other","publisher":"Archive of Formal Proofs","author":null,"publication_date":"2026-08-01T00:00:00.000Z","retrieved_at":"2026-09-13T22:56:05.431Z","title":"A Formal Counterexample to the Cost-Preserving Single-Source Unsplittable Flow Conjecture","excerpt":null,"content_hash":null,"source_reliability_class":"medium","is_primary_source":false,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T22:56:05.431Z"}],"claims":[{"id":"e19fb5f5-53db-4941-9b60-919daa80e133","event_id":"53bb9303-37ab-4e39-97ec-f6e384680e4c","claim_text":"An explicit graph has fractional unsplittable-flow cost 58 versus unsplittable cost at least 60, contradicting the Dinitz–Garg–Goemans cost conjecture.","claim_type":"outcome","claim_status":"supported","confidence_score":null,"created_at":"2026-09-13T22:56:05.431Z","updated_at":"2026-09-13T22:56:05.431Z"}],"revisions":[{"id":"7a144a20-6e63-4fe4-8f62-33c04f34c754","event_id":"53bb9303-37ab-4e39-97ec-f6e384680e4c","model_id":null,"previous_score":"0.000000","new_score":"0.346500","previous_factors":{},"new_factors":{"evidence":0.4,"base_score":3,"durability":0.7,"attribution":0.75,"realization":0.55},"change_reason":"Imported events under methodology 0.1.","trigger_type":"editorial_import","trigger_source_ids":null,"reviewer_id":null,"review_status":"published","created_at":"2026-09-13T22:56:05.431Z"}],"secondary":[{"name":"Computer Science","slug":"computer-science"}]},"methodology_version":"0.1"}