{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IQHAEVH6CZVMXTWBWKSMW3YFE3","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":"39d5bf6b1de68aef542cf14c97c45a9808dbb028f8574f3c1c6edac4a63faca7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-19T19:38:52Z","title_canon_sha256":"f7504849fd9d834ac07e517c7eea839cd9473a898c58161a1b1c591b4480654c"},"schema_version":"1.0","source":{"id":"1611.06418","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06418","created_at":"2026-05-17T23:50:07Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06418v1","created_at":"2026-05-17T23:50:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06418","created_at":"2026-05-17T23:50:07Z"},{"alias_kind":"pith_short_12","alias_value":"IQHAEVH6CZVM","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IQHAEVH6CZVMXTWB","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IQHAEVH6","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:55ebf3a66d7791b14bc087dee46d11a2268e3a7bc813f41aa8a3619af0a719c0","target":"graph","created_at":"2026-05-17T23:50:07Z","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":"For a graph $G$ the expression $G \\overset{v}{\\rightarrow} (a_1, ..., a_s)$ means that for every coloring of the vertices of $G$ in $s$ colors there exists $i \\in \\{1, ..., s\\}$ such that there is a monochromatic $a_i$-clique of color $i$. The vertex Folkman number $F_v(a_1, ..., a_s; q)$ is defined as $$F_v(a_1, ..., a_s; q) = \\min\\{\\vert V(G) \\vert : G \\overset{v}{\\rightarrow} (a_1, ..., a_s) \\mbox{ and } K_q \\not\\subseteq G\\}.$$ In this paper we improve the known bounds on the number $F_v(2, 2, 2, 3; 4)$ by proving with the help of a computer that $20 \\leq F_v(2, 2, 2, 3; 4) \\leq 22$.","authors_text":"Aleksandar Bikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-19T19:38:52Z","title":"New bounds on the vertex Folkman number $F_v(2, 2, 2, 3; 4)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06418","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":"sha256:1788bfccc11d6a477298393d680713fea4c02cdd4899b10f67e4db2eb4337c07","target":"record","created_at":"2026-05-17T23:50:07Z","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":"39d5bf6b1de68aef542cf14c97c45a9808dbb028f8574f3c1c6edac4a63faca7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-19T19:38:52Z","title_canon_sha256":"f7504849fd9d834ac07e517c7eea839cd9473a898c58161a1b1c591b4480654c"},"schema_version":"1.0","source":{"id":"1611.06418","kind":"arxiv","version":1}},"canonical_sha256":"440e0254fe166acbcec1b2a4cb6f0526d7218c4fc07decf091e70def915a3b54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"440e0254fe166acbcec1b2a4cb6f0526d7218c4fc07decf091e70def915a3b54","first_computed_at":"2026-05-17T23:50:07.609015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:07.609015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4uzdYZjqaOZ3nacJt2Ug4iIo+/8liFQWaJXkcH+7wvCTMEoagRHTTZEoKbkXvVdBQoS+AAvx63f0s+XX6xw1Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:07.609607Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06418","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1788bfccc11d6a477298393d680713fea4c02cdd4899b10f67e4db2eb4337c07","sha256:55ebf3a66d7791b14bc087dee46d11a2268e3a7bc813f41aa8a3619af0a719c0"],"state_sha256":"fd1e01f0030b1011303c95a845f84fedc98fe7cb7c03a19102a5778879ce04b7"}