{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:4XODYRZCERXJ5NDTP6YXKHFDIO","short_pith_number":"pith:4XODYRZC","schema_version":"1.0","canonical_sha256":"e5dc3c4722246e9eb4737fb1751ca34392a2bd4234e4907e318273a216b088b8","source":{"kind":"arxiv","id":"2507.05267","version":1},"attestation_state":"computed","paper":{"title":"Strongly Solving $7 \\times 6$ Connect-Four on Consumer Grade Hardware","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Markus B\\\"ock","submitted_at":"2025-07-01T09:33:24Z","abstract_excerpt":"While the game Connect-Four has been solved mathematically and the best move can be effectively computed with search based methods, a strong solution in the form of a look-up table was believed to be infeasible. In this paper, we revisit a symbolic search method based on binary decision diagrams to produce strong solutions. With our efficient implementation we were able to produce a 89.6 GB large look-up table in 47 hours on a single CPU core with 128 GB main memory for the standard $7 \\times 6$ board size. In addition to this win-draw-loss evaluation, we include an alpha-beta search in our op"},"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":"2507.05267","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.AI","submitted_at":"2025-07-01T09:33:24Z","cross_cats_sorted":[],"title_canon_sha256":"c4c1f767cafe6e6d7958ddcf8e7721146c3ff158ab3808e31ba96aefcac13f14","abstract_canon_sha256":"21f4d177d7eae77a09e45eafcc0dedc122c6d5b08a488ac1942d1e0f7e1ffc2c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:33:27.319261Z","signature_b64":"28f9b/PFwTudOS4oSQNg7cPjbSXllXcAmPxZDSLtntcfzRqNYmOdU+E5HgRt0D0IMofWW0O7lQ7S3oFsBYLQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5dc3c4722246e9eb4737fb1751ca34392a2bd4234e4907e318273a216b088b8","last_reissued_at":"2026-07-05T11:33:27.318699Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:33:27.318699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strongly Solving $7 \\times 6$ Connect-Four on Consumer Grade Hardware","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Markus B\\\"ock","submitted_at":"2025-07-01T09:33:24Z","abstract_excerpt":"While the game Connect-Four has been solved mathematically and the best move can be effectively computed with search based methods, a strong solution in the form of a look-up table was believed to be infeasible. In this paper, we revisit a symbolic search method based on binary decision diagrams to produce strong solutions. With our efficient implementation we were able to produce a 89.6 GB large look-up table in 47 hours on a single CPU core with 128 GB main memory for the standard $7 \\times 6$ board size. In addition to this win-draw-loss evaluation, we include an alpha-beta search in our op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05267","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/2507.05267/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":"2507.05267","created_at":"2026-07-05T11:33:27.318767+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.05267v1","created_at":"2026-07-05T11:33:27.318767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.05267","created_at":"2026-07-05T11:33:27.318767+00:00"},{"alias_kind":"pith_short_12","alias_value":"4XODYRZCERXJ","created_at":"2026-07-05T11:33:27.318767+00:00"},{"alias_kind":"pith_short_16","alias_value":"4XODYRZCERXJ5NDT","created_at":"2026-07-05T11:33:27.318767+00:00"},{"alias_kind":"pith_short_8","alias_value":"4XODYRZC","created_at":"2026-07-05T11:33:27.318767+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/4XODYRZCERXJ5NDTP6YXKHFDIO","json":"https://pith.science/pith/4XODYRZCERXJ5NDTP6YXKHFDIO.json","graph_json":"https://pith.science/api/pith-number/4XODYRZCERXJ5NDTP6YXKHFDIO/graph.json","events_json":"https://pith.science/api/pith-number/4XODYRZCERXJ5NDTP6YXKHFDIO/events.json","paper":"https://pith.science/paper/4XODYRZC"},"agent_actions":{"view_html":"https://pith.science/pith/4XODYRZCERXJ5NDTP6YXKHFDIO","download_json":"https://pith.science/pith/4XODYRZCERXJ5NDTP6YXKHFDIO.json","view_paper":"https://pith.science/paper/4XODYRZC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.05267&json=true","fetch_graph":"https://pith.science/api/pith-number/4XODYRZCERXJ5NDTP6YXKHFDIO/graph.json","fetch_events":"https://pith.science/api/pith-number/4XODYRZCERXJ5NDTP6YXKHFDIO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4XODYRZCERXJ5NDTP6YXKHFDIO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4XODYRZCERXJ5NDTP6YXKHFDIO/action/storage_attestation","attest_author":"https://pith.science/pith/4XODYRZCERXJ5NDTP6YXKHFDIO/action/author_attestation","sign_citation":"https://pith.science/pith/4XODYRZCERXJ5NDTP6YXKHFDIO/action/citation_signature","submit_replication":"https://pith.science/pith/4XODYRZCERXJ5NDTP6YXKHFDIO/action/replication_record"}},"created_at":"2026-07-05T11:33:27.318767+00:00","updated_at":"2026-07-05T11:33:27.318767+00:00"}