{"data":{"event":{"id":"3dd2eaae-17b5-4d7d-a4bc-056b74c54f5f","slug":"anthropic-internal-claude-zeta-zero-bound","title":"An unreleased Claude raises the critical-line zero bound for zeta from 41.6% to 67.2%","short_summary":"On 10 August 2026 Anthropic reported that an unreleased research Claude, prompted to attempt the Riemann hypothesis, instead improved the proven lower bound on zeros on the critical line from 41.6% to 67.2%. Anthropic mathematicians and two outside experts examined the argument. The Riemann hypothesis remains open.","full_description":"A staff member asked Claude to take a real stab at the Riemann hypothesis. The unreleased research model did not prove RH. Over two Claude Code sessions (~31 million output tokens, ~60 subagents) it combined work of Aryan, Baluyot–Goldston–Suriajaya–Turnage-Butterbaugh, Montgomery, and Bombieri to raise the classical proportion of zeros known to lie on the critical line. Levent Alpöge and Ralph Furman wrote an informal expert note; Brian Conrey and Dan Goldston examined the paper on short notice; a Lean formalization is reported to pass Comparator. Anthropic says it does not expect the method to prove RH. This is an unreleased Claude, not the version-unspecified Claude row and not a Millennium solution.","ledger_type":"benefit","primary_domain_id":"23d935bb-b857-4b2b-9471-d568bb848a66","event_status":"provisional","event_date":"2026-08-10T00:00:00.000Z","discovery_date":"2026-08-10T00:00:00.000Z","first_published_date":"2026-08-10T00:00:00.000Z","last_reviewed_date":"2026-10-28T00:00:00.000Z","geographic_scope":"International","affected_population":"Analytic number theory research community","base_impact_tier":3,"base_score":"10.00","attribution_multiplier":"0.8500","evidence_multiplier":"0.7000","realization_multiplier":"0.8500","durability_multiplier":"1.0000","current_event_score":"5.057500","confidence_level":"medium","score_explanation":"A large improvement to a classical zeta-zero proportion is major analytic number theory (tier 3), not a Riemann Hypothesis solution. Attribution is to the unreleased Claude (0.85). Evidence is a lab paper, named expert readers, and a reported Lean formalization (0.70). Realization is a public argument plus machine-checkable artifact (0.85). A correct bound is permanent (1.00).","methodology_version_id":"8745541b-0f8e-4d5a-9b47-5291d3813a8d","original_methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","published_at":"2026-08-10T00:00:00.000Z","created_at":"2026-09-13T22:56:05.431Z","updated_at":"2026-10-28T20:22:47.621Z","flags":[],"domain_name":"Mathematics","domain_slug":"mathematics","methodology_version":"0.2"},"contributions":[{"id":"14bea73c-16a9-4ab2-9555-1bb84156fcba","event_id":"3dd2eaae-17b5-4d7d-a4bc-056b74c54f5f","model_id":"a2587c5d-4454-4d1b-809e-9242031d0c77","role_description":"Unreleased research Claude that produced the 67.2% bound while attempting RH; humans validated and wrote an informal note.","attribution_multiplier":"0.8500","credit_share":"1.0000","contribution_score":"5.057500","attribution_rationale":"Anthropic attributes the proof search to an unreleased research version of Claude, not to a named Opus/Sonnet/Fable release.","attribution_confidence":"medium","first_used_date":"2026-08-10T00:00:00.000Z","model_version_if_known":null,"review_status":"approved","created_at":"2026-09-13T22:56:05.431Z","model_slug":"anthropic-internal-research-model-2026-08","model_name":"Anthropic Internal Research Model — 2026-08","identity_class":"internal_unreleased","is_internal":true,"family_name":"Claude","family_slug":"anthropic-claude","organization_name":"Anthropic","organization_slug":"anthropic"}],"sources":[{"id":"fa4fafe4-b519-402c-929b-a479f09dd243","event_id":"3dd2eaae-17b5-4d7d-a4bc-056b74c54f5f","url":"https://www.anthropic.com/research/riemann-zeta","canonical_url":"https://www.anthropic.com/research/riemann-zeta","source_type":"developer_announcement","publisher":"Anthropic","author":null,"publication_date":"2026-08-10T00:00:00.000Z","retrieved_at":"2026-09-13T22:56:05.431Z","title":"Claude's progress on the Riemann hypothesis","excerpt":null,"content_hash":null,"source_reliability_class":"low","is_primary_source":true,"is_independent":false,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T22:56:05.431Z"}],"claims":[{"id":"8775aba1-5341-4dc5-ae4d-0c881f4b8aac","event_id":"3dd2eaae-17b5-4d7d-a4bc-056b74c54f5f","claim_text":"An unreleased Claude improved the proven lower bound on zeta zeros on the critical line from 41.6% to 67.2%.","claim_type":"outcome","claim_status":"supported","confidence_score":null,"created_at":"2026-10-28T20:22:47.621Z","updated_at":"2026-10-28T20:22:47.621Z"},{"id":"acf6e932-e8f3-4cd9-9b6f-94ee851dbe97","event_id":"3dd2eaae-17b5-4d7d-a4bc-056b74c54f5f","claim_text":"This proves the Riemann hypothesis.","claim_type":"significance","claim_status":"disputed","confidence_score":null,"created_at":"2026-10-28T20:22:47.621Z","updated_at":"2026-10-28T20:22:47.621Z"}],"revisions":[{"id":"594e777f-d96f-44ee-9132-4a5667ef0f10","event_id":"3dd2eaae-17b5-4d7d-a4bc-056b74c54f5f","model_id":null,"previous_score":"0.000000","new_score":"1.487500","previous_factors":{},"new_factors":{"evidence":0.5,"base_score":10,"durability":0.7,"attribution":0.85,"realization":0.5},"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"},{"id":"e0e6a89c-24ff-40c2-84ca-99c8213f6845","event_id":"3dd2eaae-17b5-4d7d-a4bc-056b74c54f5f","model_id":null,"previous_score":"1.487500","new_score":"5.057500","previous_factors":{},"new_factors":{"flags":[],"evidence":0.7,"base_score":10,"durability":1,"attribution":0.85,"realization":0.85},"change_reason":"Methodology 0.2: keep Major / not RH; 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