{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VDNWRTFOZUUNAADUWPRZYIRTPE","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":"7791d47c525a72a398be51fda934abcce683b450adc7864e954a789b7a71c437","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-31T13:01:19Z","title_canon_sha256":"d68e84e849610c81bd25bba6b2de7635647038ce4b887cc558542b2e36a2f6a2"},"schema_version":"1.0","source":{"id":"1401.0138","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0138","created_at":"2026-05-18T01:29:21Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0138v4","created_at":"2026-05-18T01:29:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0138","created_at":"2026-05-18T01:29:21Z"},{"alias_kind":"pith_short_12","alias_value":"VDNWRTFOZUUN","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VDNWRTFOZUUNAADU","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VDNWRTFO","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:2cec110d8396bed436243a66cf0e2b80c398fbe11e6f484c6b92d5397e9e3cf8","target":"graph","created_at":"2026-05-18T01:29:21Z","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":"A Kneser representation KG(H) for a graph G is a bijective assignment of hyperedges of a hypergraph H to the vertices of G such that two vertices of G are adjacent if and only if the corresponding hyperedges are disjoint. In this paper, we introduce a colored version of the Turan number and use that to determine the chromatic number of some families of graphs in terms of the generalized Turan number of graphs. In particular, we determine the chromatic number of every Kneser multigraph KG(H), where the vertex set of H is the edge set of a multigraph G such that the multiplicity of each edge is ","authors_text":"Hossein Hajiabolhassan, Meysam Alishahi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-31T13:01:19Z","title":"Chromatic Number Via Turan Number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0138","kind":"arxiv","version":4},"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:aa6ac7f5d1deb21ab39e3a77c370f6de9cb8da7bd27e7349c33b148009291bd3","target":"record","created_at":"2026-05-18T01:29:21Z","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":"7791d47c525a72a398be51fda934abcce683b450adc7864e954a789b7a71c437","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-31T13:01:19Z","title_canon_sha256":"d68e84e849610c81bd25bba6b2de7635647038ce4b887cc558542b2e36a2f6a2"},"schema_version":"1.0","source":{"id":"1401.0138","kind":"arxiv","version":4}},"canonical_sha256":"a8db68ccaecd28d00074b3e39c223379183f340160035ce81e4a21b9f40be7ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8db68ccaecd28d00074b3e39c223379183f340160035ce81e4a21b9f40be7ce","first_computed_at":"2026-05-18T01:29:21.931236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:21.931236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kQ+PFEmDQowVNwO15z59swtffN+s4tUtUBFzYajedYwHavo+0muwIv5MqAnCWoug4t1PgwArWKl19B4hqLGODQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:21.931878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0138","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa6ac7f5d1deb21ab39e3a77c370f6de9cb8da7bd27e7349c33b148009291bd3","sha256:2cec110d8396bed436243a66cf0e2b80c398fbe11e6f484c6b92d5397e9e3cf8"],"state_sha256":"6b18f2e3bfb4263b7d00a36dc76cfdb034c74c16ef1a2a9505786cdb099f4c2e"}