{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7L4WYRGMYPW4EJMLT7JJJY3ES3","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":"aa7ac08c153ec7c32869f9f05f16347e23f6cf116037b5b6b828e5fdebc4da62","cross_cats_sorted":["cs.DC","cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-11-21T22:54:59Z","title_canon_sha256":"9dcf1102574e3d1dd86df8c9b071b615ae4fd040be5ffa8845ce64dc65e888f2"},"schema_version":"1.0","source":{"id":"1711.08076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.08076","created_at":"2026-05-18T00:29:50Z"},{"alias_kind":"arxiv_version","alias_value":"1711.08076v1","created_at":"2026-05-18T00:29:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.08076","created_at":"2026-05-18T00:29:50Z"},{"alias_kind":"pith_short_12","alias_value":"7L4WYRGMYPW4","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7L4WYRGMYPW4EJML","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7L4WYRGM","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:43a201abc0545e0606b2caa13c96f4de8ec877d42dd3edcd55002b57625a657c","target":"graph","created_at":"2026-05-18T00:29:50Z","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 present the solution of a century-old problem known as Schur Number Five: What is the largest (natural) number $n$ such that there exists a five-coloring of the positive numbers up to $n$ without a monochromatic solution of the equation $a + b = c$? We obtained the solution, $n = 160$, by encoding the problem into propositional logic and applying massively parallel satisfiability solving techniques on the resulting formula. We constructed and validated a proof of the solution to increase trust in the correctness of the multi-CPU-year computations. The proof is two petabytes in size and was ","authors_text":"Marijn J.H. Heule","cross_cats":["cs.DC","cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-11-21T22:54:59Z","title":"Schur Number Five"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08076","kind":"arxiv","version":1},"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":"sha256:7b472620e4253326fbe3c22a76f36458a5eca843eb4ce8735acf5181038000de","target":"record","created_at":"2026-05-18T00:29:50Z","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":"aa7ac08c153ec7c32869f9f05f16347e23f6cf116037b5b6b828e5fdebc4da62","cross_cats_sorted":["cs.DC","cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-11-21T22:54:59Z","title_canon_sha256":"9dcf1102574e3d1dd86df8c9b071b615ae4fd040be5ffa8845ce64dc65e888f2"},"schema_version":"1.0","source":{"id":"1711.08076","kind":"arxiv","version":1}},"canonical_sha256":"faf96c44ccc3edc2258b9fd294e36496da9b1b09c0a6fb61791a6d39648f9a44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"faf96c44ccc3edc2258b9fd294e36496da9b1b09c0a6fb61791a6d39648f9a44","first_computed_at":"2026-05-18T00:29:50.729925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:50.729925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+nkj0PYZX620OF1bh20BkKTUsp8udGk54ArET+KX5+Zx5okKbs3pCiBu+bZlkaFkt9UaA4w35UrJNwKfhReqCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:50.730597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.08076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b472620e4253326fbe3c22a76f36458a5eca843eb4ce8735acf5181038000de","sha256:43a201abc0545e0606b2caa13c96f4de8ec877d42dd3edcd55002b57625a657c"],"state_sha256":"dd6522d2ba5a543f0989e59baf52adc7eb9b419815990eb712ee958df53580da"}