{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:BLKKEL6UQNV5AYCJQM5CWNZPJX","short_pith_number":"pith:BLKKEL6U","schema_version":"1.0","canonical_sha256":"0ad4a22fd4836bd06049833a2b372f4dc52c75154a2593294b1cbbd1f8b38812","source":{"kind":"arxiv","id":"2411.00566","version":1},"attestation_state":"computed","paper":{"title":"PatternBoost: Constructions in Mathematics with a Little Help from AI","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.CO","authors_text":"Adam Zsolt Wagner, Fran\\c{c}ois Charton, Geordie Williamson, Jordan S. Ellenberg","submitted_at":"2024-11-01T13:23:58Z","abstract_excerpt":"We introduce PatternBoost, a flexible method for finding interesting constructions in mathematics. Our algorithm alternates between two phases. In the first ``local'' phase, a classical search algorithm is used to produce many desirable constructions. In the second ``global'' phase, a transformer neural network is trained on the best such constructions. Samples from the trained transformer are then used as seeds for the first phase, and the process is repeated. We give a detailed introduction to this technique, and discuss the results of its application to several problems in extremal combinat"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2411.00566","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-01T13:23:58Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"09a939aa8ab50a06a023ae384bb56116179f12e264bf353c18fdb1cdaad5c4c7","abstract_canon_sha256":"f4c5e18d4e288cb597579a95d48ad69b96522a146612d24caa8a2eb102799f87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:29:44.693369Z","signature_b64":"S8spnMLMycenyvudHP0SLTCid7+pmIdh9deDE6i+beRi7OSRsB8rilAN7o/o0NFZXC2ORtD+5P/Od05XzvHzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ad4a22fd4836bd06049833a2b372f4dc52c75154a2593294b1cbbd1f8b38812","last_reissued_at":"2026-07-05T09:29:44.692738Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:29:44.692738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"PatternBoost: Constructions in Mathematics with a Little Help from AI","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.CO","authors_text":"Adam Zsolt Wagner, Fran\\c{c}ois Charton, Geordie Williamson, Jordan S. Ellenberg","submitted_at":"2024-11-01T13:23:58Z","abstract_excerpt":"We introduce PatternBoost, a flexible method for finding interesting constructions in mathematics. Our algorithm alternates between two phases. In the first ``local'' phase, a classical search algorithm is used to produce many desirable constructions. In the second ``global'' phase, a transformer neural network is trained on the best such constructions. Samples from the trained transformer are then used as seeds for the first phase, and the process is repeated. We give a detailed introduction to this technique, and discuss the results of its application to several problems in extremal combinat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.00566","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.00566/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2411.00566","created_at":"2026-07-05T09:29:44.692817+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.00566v1","created_at":"2026-07-05T09:29:44.692817+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.00566","created_at":"2026-07-05T09:29:44.692817+00:00"},{"alias_kind":"pith_short_12","alias_value":"BLKKEL6UQNV5","created_at":"2026-07-05T09:29:44.692817+00:00"},{"alias_kind":"pith_short_16","alias_value":"BLKKEL6UQNV5AYCJ","created_at":"2026-07-05T09:29:44.692817+00:00"},{"alias_kind":"pith_short_8","alias_value":"BLKKEL6U","created_at":"2026-07-05T09:29:44.692817+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":24,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.05374","citing_title":"The Minkowski grid has robustly many repeated distances","ref_index":4,"is_internal_anchor":true},{"citing_arxiv_id":"2606.26399","citing_title":"Geometry-Aware MCTS for Extremal Problems in Combinatorial Geometry","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2606.26660","citing_title":"Generating Special Triangulations with Transformers","ref_index":39,"is_internal_anchor":false},{"citing_arxiv_id":"2606.17487","citing_title":"A combinatorial large sieve for Sidon sets, distances, and norm forms","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2606.12279","citing_title":"Mathematical perspective on genetic algorithms with optimization guided operators","ref_index":21,"is_internal_anchor":false},{"citing_arxiv_id":"2606.05841","citing_title":"Geometric Sidon Problems","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2606.05629","citing_title":"An automated proof that R(B_8,B_10)=37","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2604.26102","citing_title":"SWE-Edit: Rethinking Code Editing for Efficient SWE-Agent","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2604.26102","citing_title":"SWE-Edit: Rethinking Code Editing for Efficient SWE-Agent","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2606.13619","citing_title":"Split primes and the Elekes-R\\'onyai problem","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2502.12717","citing_title":"Learning the symmetric group: large from small","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2511.02864","citing_title":"Mathematical exploration and discovery at scale","ref_index":56,"is_internal_anchor":false},{"citing_arxiv_id":"2601.13209","citing_title":"AI for Mathematics: Progress, Challenges, and Prospects","ref_index":23,"is_internal_anchor":false},{"citing_arxiv_id":"2604.11101","citing_title":"Generating Hadamard matrices with transformers","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2604.26101","citing_title":"Counterexamples to an Extremal Conjecture for Random Cycle-Factors","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2604.26101","citing_title":"Counterexamples to an Extremal Conjecture for Random Cycle-Factors","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2605.01072","citing_title":"Reconstructing conformal field theoretical compositions with Transformers","ref_index":21,"is_internal_anchor":false},{"citing_arxiv_id":"2605.01120","citing_title":"New Bounds for Zarankiewicz Numbers via Reinforced LLM Evolutionary Search","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2604.11101","citing_title":"Generating Hadamard matrices with transformers","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2604.07240","citing_title":"$k$-server-bench: Automating Potential Discovery for the $k$-Server Conjecture","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2604.15534","citing_title":"Optimal and Near-Optimal Constructions for Bootstrap Percolation in Hypercubes","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2605.02193","citing_title":"Trees and Graphs with Non Log-concave Dominating Set Sequence via AI Tools","ref_index":10,"is_internal_anchor":false},{"citing_arxiv_id":"2604.26101","citing_title":"Counterexamples to an Extremal Conjecture for Random Cycle-Factors","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2604.26101","citing_title":"Counterexamples to an Extremal Conjecture for Random Cycle-Factors","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BLKKEL6UQNV5AYCJQM5CWNZPJX","json":"https://pith.science/pith/BLKKEL6UQNV5AYCJQM5CWNZPJX.json","graph_json":"https://pith.science/api/pith-number/BLKKEL6UQNV5AYCJQM5CWNZPJX/graph.json","events_json":"https://pith.science/api/pith-number/BLKKEL6UQNV5AYCJQM5CWNZPJX/events.json","paper":"https://pith.science/paper/BLKKEL6U"},"agent_actions":{"view_html":"https://pith.science/pith/BLKKEL6UQNV5AYCJQM5CWNZPJX","download_json":"https://pith.science/pith/BLKKEL6UQNV5AYCJQM5CWNZPJX.json","view_paper":"https://pith.science/paper/BLKKEL6U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.00566&json=true","fetch_graph":"https://pith.science/api/pith-number/BLKKEL6UQNV5AYCJQM5CWNZPJX/graph.json","fetch_events":"https://pith.science/api/pith-number/BLKKEL6UQNV5AYCJQM5CWNZPJX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BLKKEL6UQNV5AYCJQM5CWNZPJX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BLKKEL6UQNV5AYCJQM5CWNZPJX/action/storage_attestation","attest_author":"https://pith.science/pith/BLKKEL6UQNV5AYCJQM5CWNZPJX/action/author_attestation","sign_citation":"https://pith.science/pith/BLKKEL6UQNV5AYCJQM5CWNZPJX/action/citation_signature","submit_replication":"https://pith.science/pith/BLKKEL6UQNV5AYCJQM5CWNZPJX/action/replication_record"}},"created_at":"2026-07-05T09:29:44.692817+00:00","updated_at":"2026-07-05T09:29:44.692817+00:00"}