{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:LBJXLSBJLQZFZ4N7HE6P3OBNJZ","short_pith_number":"pith:LBJXLSBJ","schema_version":"1.0","canonical_sha256":"585375c8295c325cf1bf393cfdb82d4e485dc58e7632ff610a59b37fd7561bcf","source":{"kind":"arxiv","id":"2606.05629","version":1},"attestation_state":"computed","paper":{"title":"An automated proof that R(B_8,B_10)=37","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bernard Lidick\\'y, Jeremy Kalfus","submitted_at":"2026-06-04T02:57:28Z","abstract_excerpt":"We present a short proof that the book Ramsey number $R(B_8,B_{10})$ equals 37. The lower bound $R(B_8,B_{10}) \\ge 37$ is already available in the literature, so it is enough to rule out a 37-vertex graph containing neither a copy of $B_8$ nor a copy of $B_{10}$ in its complement. The problem as well as the proof were found with AutoMath, an AI-assisted mathematical discovery workflow developed by the first author. A Lean formalization of the upper-bound argument is available in the accompanying repository."},"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":"2606.05629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-04T02:57:28Z","cross_cats_sorted":[],"title_canon_sha256":"55e292a3c90b7f13fa1ac8e557ed2d3a3bca3a29305fdf8a5eb9b112fa8e3c40","abstract_canon_sha256":"2e26168a4b593f37c4c17557542de0ee80f84ac7604c5af2adbfe719deaf2321"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:14:57.119749Z","signature_b64":"Kl9Pnx2y6LOFwIlA1tfmqUtd8BGgRJf7ZF2Mg8GSoE725oTSCog+jH8vcBV1KfpPx9h9NUjtTzT7m+NHWXsBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"585375c8295c325cf1bf393cfdb82d4e485dc58e7632ff610a59b37fd7561bcf","last_reissued_at":"2026-06-05T01:14:57.119230Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:14:57.119230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An automated proof that R(B_8,B_10)=37","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bernard Lidick\\'y, Jeremy Kalfus","submitted_at":"2026-06-04T02:57:28Z","abstract_excerpt":"We present a short proof that the book Ramsey number $R(B_8,B_{10})$ equals 37. The lower bound $R(B_8,B_{10}) \\ge 37$ is already available in the literature, so it is enough to rule out a 37-vertex graph containing neither a copy of $B_8$ nor a copy of $B_{10}$ in its complement. The problem as well as the proof were found with AutoMath, an AI-assisted mathematical discovery workflow developed by the first author. A Lean formalization of the upper-bound argument is available in the accompanying repository."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05629","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/2606.05629/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":"2606.05629","created_at":"2026-06-05T01:14:57.119308+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.05629v1","created_at":"2026-06-05T01:14:57.119308+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.05629","created_at":"2026-06-05T01:14:57.119308+00:00"},{"alias_kind":"pith_short_12","alias_value":"LBJXLSBJLQZF","created_at":"2026-06-05T01:14:57.119308+00:00"},{"alias_kind":"pith_short_16","alias_value":"LBJXLSBJLQZFZ4N7","created_at":"2026-06-05T01:14:57.119308+00:00"},{"alias_kind":"pith_short_8","alias_value":"LBJXLSBJ","created_at":"2026-06-05T01:14:57.119308+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LBJXLSBJLQZFZ4N7HE6P3OBNJZ","json":"https://pith.science/pith/LBJXLSBJLQZFZ4N7HE6P3OBNJZ.json","graph_json":"https://pith.science/api/pith-number/LBJXLSBJLQZFZ4N7HE6P3OBNJZ/graph.json","events_json":"https://pith.science/api/pith-number/LBJXLSBJLQZFZ4N7HE6P3OBNJZ/events.json","paper":"https://pith.science/paper/LBJXLSBJ"},"agent_actions":{"view_html":"https://pith.science/pith/LBJXLSBJLQZFZ4N7HE6P3OBNJZ","download_json":"https://pith.science/pith/LBJXLSBJLQZFZ4N7HE6P3OBNJZ.json","view_paper":"https://pith.science/paper/LBJXLSBJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.05629&json=true","fetch_graph":"https://pith.science/api/pith-number/LBJXLSBJLQZFZ4N7HE6P3OBNJZ/graph.json","fetch_events":"https://pith.science/api/pith-number/LBJXLSBJLQZFZ4N7HE6P3OBNJZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LBJXLSBJLQZFZ4N7HE6P3OBNJZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LBJXLSBJLQZFZ4N7HE6P3OBNJZ/action/storage_attestation","attest_author":"https://pith.science/pith/LBJXLSBJLQZFZ4N7HE6P3OBNJZ/action/author_attestation","sign_citation":"https://pith.science/pith/LBJXLSBJLQZFZ4N7HE6P3OBNJZ/action/citation_signature","submit_replication":"https://pith.science/pith/LBJXLSBJLQZFZ4N7HE6P3OBNJZ/action/replication_record"}},"created_at":"2026-06-05T01:14:57.119308+00:00","updated_at":"2026-06-05T01:14:57.119308+00:00"}