{"data":{"event":{"id":"1e3e52cf-f7f8-4714-b437-e150a9b55366","slug":"claude-fable-5-q2-absolute-galois","title":"Claude Fable 5 produces a presentation of Gal(Q̄₂/Q₂)","short_summary":"On 9 June 2026 David Roe elicited a Claude Fable 5 solution to Epoch’s open problem asking for a presentation of the absolute Galois group of the 2-adics. Epoch later accepted verifier output and noted a second, independent GPT-5.5 Pro solution. Epoch warns the verifier is short of a full proof on this problem.","full_description":"Presentations of Gal(Q̄_p/Q_p) are classical for odd p; p=2 was a documented gap. Epoch lists Fable 5 as first solver, with a later GPT-5.5 Pro writeup by David Turturean. Because Epoch says verifier evidence here is short of a full proof, the event is provisional Notable rather than Major, and Fable 5 keeps first-solver credit rather than splitting equally.\n\nUpdate (2026-06-26): Summary of METR's predeployment evaluation of GPT-5.6 Sol June 26, 2026 A summary of METR's independent, predeployment evaluation of GPT-5.6 Sol Read more. Summary of METR's predeployment evaluation of GPT-5.6 Sol June 26, 2026 A summary of METR's independent, predeployment evaluation of GPT-5.6 Sol Read more\n\nUpdate (2026-09-21): Advisory Group on Mathematics and Artificial Intelligence. OpenAI is working with an independent Advisory Group on Mathematics and Artificial Intelligence to guide the review and communication of emerging AI results.","ledger_type":"benefit","primary_domain_id":"23d935bb-b857-4b2b-9471-d568bb848a66","event_status":"provisional","event_date":"2026-06-09T00:00:00.000Z","discovery_date":"2026-06-09T00:00:00.000Z","first_published_date":"2026-06-09T00:00:00.000Z","last_reviewed_date":"2026-09-21T00:00:00.000Z","geographic_scope":"International","affected_population":"Algebraic number theory research community","base_impact_tier":2,"base_score":"3.00","attribution_multiplier":"0.7500","evidence_multiplier":"0.5000","realization_multiplier":"0.4500","durability_multiplier":"0.6500","current_event_score":"0.329100","confidence_level":"medium","score_explanation":"An explicit Q₂ Galois presentation is notable (tier 2) until a complete proof is written. Fable 5 was first (0.75). Evidence is Epoch’s verifier plus a later writeup (0.40). Realization is a candidate presentation, not a textbook theorem (0.45). Follow-up ingest: independent source raised evidence; added a follow-up source. Follow-up ingest: added a follow-up source.","methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","original_methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","published_at":"2026-06-09T00:00:00.000Z","created_at":"2026-09-13T22:56:05.431Z","updated_at":"2026-09-21T18:01:08.493Z","flags":[],"domain_name":"Mathematics","domain_slug":"mathematics","methodology_version":"0.1"},"contributions":[{"id":"98ccd1cb-ab3e-4dee-9d80-f8a5db8d5aa2","event_id":"1e3e52cf-f7f8-4714-b437-e150a9b55366","model_id":"19e2b5dd-4f37-446a-8344-48196c5acf5a","role_description":"First system Epoch records as solving the Q₂ absolute Galois presentation problem, elicited by David Roe.","attribution_multiplier":"0.7500","credit_share":"1.0000","contribution_score":"0.329100","attribution_rationale":"Epoch names Claude Fable 5 as first solved; a later GPT-5.5 Pro solution is independent confirmation, not a co-search on the original run.","attribution_confidence":"medium","first_used_date":"2026-06-09T00:00:00.000Z","model_version_if_known":null,"review_status":"approved","created_at":"2026-09-13T22:56:05.431Z","model_slug":"claude-fable-5","model_name":"Claude Fable 5","identity_class":"named_release","is_internal":false,"family_name":"Claude","family_slug":"anthropic-claude","organization_name":"Anthropic","organization_slug":"anthropic"}],"sources":[{"id":"3880bde3-8721-4eeb-a21f-3de3db0553ba","event_id":"1e3e52cf-f7f8-4714-b437-e150a9b55366","url":"https://epoch.ai/frontiermath/open-problems/q2-absolute-galois","canonical_url":"https://epoch.ai/frontiermath/open-problems/q2-absolute-galois","source_type":"other","publisher":"Epoch AI","author":null,"publication_date":"2026-06-09T00:00:00.000Z","retrieved_at":"2026-09-13T22:56:05.431Z","title":"A Presentation of the Absolute Galois Group of Q₂","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":"dc648adb-4444-4221-95be-5ae6cd04ef8b","event_id":"1e3e52cf-f7f8-4714-b437-e150a9b55366","url":"https://metr.org/blog/2026-06-26-gpt-5-6-sol/","canonical_url":"https://metr.org/blog/2026-06-26-gpt-5-6-sol/","source_type":"other","publisher":"METR Blog","author":null,"publication_date":"2026-06-26T00:00:00.000Z","retrieved_at":"2026-09-17T03:00:52.338Z","title":"Summary of METR's predeployment evaluation of GPT-5.6 Sol June 26, 2026 A summary of METR's independent, predeployment evaluation of GPT-5.6 Sol Read more","excerpt":"Summary of METR's predeployment evaluation of GPT-5.6 Sol June 26, 2026 A summary of METR's independent, predeployment evaluation of GPT-5.6 Sol Read more","content_hash":null,"source_reliability_class":"medium","is_primary_source":false,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-17T03:00:52.338Z"},{"id":"ba08b6fa-2a4a-44be-adb7-bb86066ad1be","event_id":"1e3e52cf-f7f8-4714-b437-e150a9b55366","url":"https://openai.com/index/advisory-group-on-mathematics-and-ai","canonical_url":"https://openai.com/index/advisory-group-on-mathematics-and-ai","source_type":"developer_announcement","publisher":"OpenAI News","author":null,"publication_date":"2026-09-21T00:00:00.000Z","retrieved_at":"2026-09-21T18:01:08.452Z","title":"Advisory Group on Mathematics and Artificial Intelligence","excerpt":"OpenAI is working with an independent Advisory Group on Mathematics and Artificial Intelligence to guide the review and communication of emerging AI results.","content_hash":null,"source_reliability_class":"medium","is_primary_source":false,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-21T18:01:08.452Z"}],"claims":[{"id":"1ddc965a-ea11-4e60-b1d2-e0235f6bf60a","event_id":"1e3e52cf-f7f8-4714-b437-e150a9b55366","claim_text":"Epoch records a Claude Fable 5 solution, elicited 9 June 2026, to a presentation of the absolute Galois group of Q₂.","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"},{"id":"7919fa00-6cf0-4653-9e5c-b64bf24e9e5b","event_id":"1e3e52cf-f7f8-4714-b437-e150a9b55366","claim_text":"Epoch’s verifier constitutes a complete proof of the 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