{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KJY37BQPWDZAXAO6YNPH5ADZAY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2b9012d0e1a286c3965b133b28d3be11fdb3a9b9a655fa6c0aa7043332bfdf3c","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-04-05T16:14:31Z","title_canon_sha256":"8a41799bd9543731915e84e40776f69a5cef479ca144ae21429adae421a2ffd2"},"schema_version":"1.0","source":{"id":"1004.0653","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0653","created_at":"2026-05-18T04:19:22Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0653v2","created_at":"2026-05-18T04:19:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0653","created_at":"2026-05-18T04:19:22Z"},{"alias_kind":"pith_short_12","alias_value":"KJY37BQPWDZA","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KJY37BQPWDZAXAO6","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KJY37BQP","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:84ff57103ad43e10672a0640691e07269d2894a062b5a1f47cf5312bdcfd1e99","target":"graph","created_at":"2026-05-18T04:19:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the links between Ramsey theory in the integers, based on van der Waerden's theorem, and (boolean, CNF) SAT solving. We aim at using the problems from exact Ramsey theory, concerned with computing Ramsey-type numbers, as a rich source of test problems, where especially methods for solving hard problems can be developed. In order to control the growth of the problem instances, we introduce \"transversal extensions\" as a natural way of constructing mixed parameter tuples (k_1, ..., k_m) for van-der-Waerden-like numbers N(k_1, ..., k_m), such that the growth of these numbers is guarant","authors_text":"Oliver Kullmann","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-04-05T16:14:31Z","title":"Exact Ramsey Theory: Green-Tao numbers and SAT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0653","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c755295dffd6b9a24cc3a76a6cbe7b9d3b77e59dc366b2b7f7fdc8402c9bf00a","target":"record","created_at":"2026-05-18T04:19:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2b9012d0e1a286c3965b133b28d3be11fdb3a9b9a655fa6c0aa7043332bfdf3c","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-04-05T16:14:31Z","title_canon_sha256":"8a41799bd9543731915e84e40776f69a5cef479ca144ae21429adae421a2ffd2"},"schema_version":"1.0","source":{"id":"1004.0653","kind":"arxiv","version":2}},"canonical_sha256":"5271bf860fb0f20b81dec35e7e8079061f8f2c18387dfb5fe1b8ba9fdcc8ae7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5271bf860fb0f20b81dec35e7e8079061f8f2c18387dfb5fe1b8ba9fdcc8ae7f","first_computed_at":"2026-05-18T04:19:22.320331Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:22.320331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lr5hqdH7NPrhI0Ztof5jdXI5C6cSdDqrEf4QoHIp8bE1QQae4aHKiWoDmkhZDCzqPISVXsEB48ivFAZNqW+0Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:22.320879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0653","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c755295dffd6b9a24cc3a76a6cbe7b9d3b77e59dc366b2b7f7fdc8402c9bf00a","sha256:84ff57103ad43e10672a0640691e07269d2894a062b5a1f47cf5312bdcfd1e99"],"state_sha256":"31461db92875a57861c101e91ccbbcc80e587e9b8b967e0d6f39d030df27a7c7"}