{"data":{"event":{"id":"76befd10-ae85-4ff7-833b-d594cdb0459d","slug":"funsearch-cap-set-constructions","title":"FunSearch finds larger cap-set constructions via LLM program search","short_summary":"DeepMind’s FunSearch, pairing a language model with an automated evaluator, discovered new cap-set constructions including a 512-point cap in eight dimensions, published in Nature.","full_description":"On 14 December 2023, Nature published FunSearch, which evolves Python functions using a pretrained LLM and a verifier. Applied to the cap-set problem, it produced constructions larger than the previous n=8 record (512 versus 496) and improved some asymptotic lower-bound constructions. Programs were released for independent checking. The LLM used was in the PaLM 2/Codey family. The mathematical objects are verified; broader “LLM discovery” claims remain specific to these problems.","ledger_type":"benefit","primary_domain_id":"23d935bb-b857-4b2b-9471-d568bb848a66","event_status":"verified","event_date":"2023-12-14T00:00:00.000Z","discovery_date":"2023-12-14T00:00:00.000Z","first_published_date":"2023-12-14T00:00:00.000Z","last_reviewed_date":"2023-12-14T00:00:00.000Z","geographic_scope":"Global mathematics research","affected_population":"Researchers in extremal combinatorics and program synthesis","base_impact_tier":3,"base_score":"10.00","attribution_multiplier":"0.8500","evidence_multiplier":"0.7000","realization_multiplier":"0.7000","durability_multiplier":"1.0000","current_event_score":"3.540200","confidence_level":"high","score_explanation":"New verified constructions are a major combinatorial result (tier 3), not a resolved century problem (tier 4). Attribution is high but not exclusive of the evaluator and human skeleton. Peer review plus checkable programs. Realization is a demonstrated, inspectable construction. Mathematical durability is permanent.","methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","original_methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","published_at":"2023-12-14T00:00:00.000Z","created_at":"2026-09-13T20:47:20.075Z","updated_at":"2026-09-13T20:47:20.075Z","flags":[],"domain_name":"Mathematics","domain_slug":"mathematics","methodology_version":"0.1"},"contributions":[{"id":"ba029411-720b-42e9-a826-2b8b81ce037c","event_id":"76befd10-ae85-4ff7-833b-d594cdb0459d","model_id":"63cd3825-353f-488b-bdd1-94946c7ca52a","role_description":"Provided candidate programs that FunSearch’s evaluator selected and evolved.","attribution_multiplier":"0.8500","credit_share":"0.8500","contribution_score":"3.540200","attribution_rationale":"The LLM generated the evolving functions; humans supplied the skeleton and evaluation.","attribution_confidence":"medium","first_used_date":"2023-12-14T00:00:00.000Z","model_version_if_known":null,"review_status":"approved","created_at":"2026-09-13T20:47:20.075Z","model_slug":"palm-2","model_name":"PaLM 2","identity_class":"named_release","is_internal":false,"family_name":"PaLM","family_slug":"google-deepmind-palm","organization_name":"Google DeepMind","organization_slug":"google-deepmind"}],"sources":[{"id":"7f2e97b8-3b35-4ca1-a5bc-bae0763fbea2","event_id":"76befd10-ae85-4ff7-833b-d594cdb0459d","url":"https://www.nature.com/articles/s41586-023-06924-6","canonical_url":"https://www.nature.com/articles/s41586-023-06924-6","source_type":"peer_reviewed","publisher":"Nature","author":null,"publication_date":"2023-12-14T00:00:00.000Z","retrieved_at":"2026-09-13T20:47:20.075Z","title":"Mathematical discoveries from program search with large language models","excerpt":null,"content_hash":null,"source_reliability_class":"high","is_primary_source":true,"is_independent":true,"is_peer_reviewed":true,"archived_url":null,"created_at":"2026-09-13T20:47:20.075Z"},{"id":"1e4f20c0-9555-443e-b69f-95a041d654a1","event_id":"76befd10-ae85-4ff7-833b-d594cdb0459d","url":"https://deepmind.google/discover/blog/funsearch-making-new-discoveries-in-mathematical-sciences-using-large-language-models/","canonical_url":"https://deepmind.google/discover/blog/funsearch-making-new-discoveries-in-mathematical-sciences-using-large-language-models/","source_type":"developer_announcement","publisher":"Google DeepMind","author":null,"publication_date":"2023-12-14T00:00:00.000Z","retrieved_at":"2026-09-13T20:47:20.075Z","title":"FunSearch: Making new discoveries in mathematical sciences using Large Language Models","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":"2026-09-13T20:47:20.075Z"}],"claims":[{"id":"b12aa389-8cdf-40ba-a8f6-52150ced0a9e","event_id":"76befd10-ae85-4ff7-833b-d594cdb0459d","claim_text":"FunSearch produced a 512-point cap set in dimension 8, improving the prior 496-point construction.","claim_type":"outcome","claim_status":"supported","confidence_score":null,"created_at":"2026-09-13T20:47:20.075Z","updated_at":"2026-09-13T20:47:20.075Z"},{"id":"8dc6d859-ff35-484e-8278-2c58314aa71c","event_id":"76befd10-ae85-4ff7-833b-d594cdb0459d","claim_text":"FunSearch was the first LLM system to produce a new piece of verifiable mathematical knowledge on a longstanding open problem.","claim_type":"significance","claim_status":"supported","confidence_score":null,"created_at":"2026-09-13T20:47:20.075Z","updated_at":"2026-09-13T20:47:20.075Z"}],"revisions":[{"id":"23f56e9f-54c0-48c4-9a05-5ba7849df8d2","event_id":"76befd10-ae85-4ff7-833b-d594cdb0459d","model_id":null,"previous_score":"0.000000","new_score":"3.540200","previous_factors":{},"new_factors":{"evidence":0.7,"base_score":10,"durability":1,"attribution":0.85,"realization":0.7},"change_reason":"Initial adjudicated seed score under methodology 0.1.","trigger_type":"seed","trigger_source_ids":null,"reviewer_id":null,"review_status":"published","created_at":"2026-09-13T20:47:20.075Z"}],"secondary":[{"name":"Computer Science","slug":"computer-science"}]},"methodology_version":"0.1"}