{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:QFQ5E2NQTY5GBM7SGY4N5SPTC2","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":"8d84f7d3a3d6cc2f76d45f3820d6f8e6c9dc48acc6b27c9c67c76a68f539e652","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-07-21T10:39:56Z","title_canon_sha256":"21e22d08b5a2e5f8863c0ac1f394985d58e039d208182e89dba03ecd2270d007"},"schema_version":"1.0","source":{"id":"0807.3233","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.3233","created_at":"2026-05-18T00:44:34Z"},{"alias_kind":"arxiv_version","alias_value":"0807.3233v2","created_at":"2026-05-18T00:44:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.3233","created_at":"2026-05-18T00:44:34Z"},{"alias_kind":"pith_short_12","alias_value":"QFQ5E2NQTY5G","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"QFQ5E2NQTY5GBM7S","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"QFQ5E2NQ","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:1b13ab6e75a307fe823fbe73cf7f9e0ce648c8b758b05f5543b76ec2fb860cc3","target":"graph","created_at":"2026-05-18T00:44:34Z","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":"In 1977, Wegner conjectured that the chromatic number of the square of every planar graph $G$ with maximum degree $\\Delta\\ge8$ is at most $\\bigl\\lfloor\\frac32\\Delta\\bigr\\rfloor+1$. We show that it is at most $\\frac32 \\Delta (1+o(1))$ (where the $o(1)$ is as $\\Delta\\to+\\infty$), and indeed that this is true for the list chromatic number and for more general classes of graphs.","authors_text":"Bruce Reed, Colin McDiarmid, Fr\\'ed\\'eric Havet, Jan van den Heuvel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-07-21T10:39:56Z","title":"List Colouring Squares of Planar Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.3233","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:bcbc5033c2bf6f178d62d866e00a8e7c75223fe0f180ee0152db42676d3a9b38","target":"record","created_at":"2026-05-18T00:44:34Z","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":"8d84f7d3a3d6cc2f76d45f3820d6f8e6c9dc48acc6b27c9c67c76a68f539e652","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-07-21T10:39:56Z","title_canon_sha256":"21e22d08b5a2e5f8863c0ac1f394985d58e039d208182e89dba03ecd2270d007"},"schema_version":"1.0","source":{"id":"0807.3233","kind":"arxiv","version":2}},"canonical_sha256":"8161d269b09e3a60b3f23638dec9f3169a3ce1de9cae7808e9abefc9f451815a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8161d269b09e3a60b3f23638dec9f3169a3ce1de9cae7808e9abefc9f451815a","first_computed_at":"2026-05-18T00:44:34.080812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:34.080812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s9Fi4ObKX5/SeWXwzFVJFMxsQiY3/7kE3B7riG8xDYAEgfXcpm0izXCUemKoQgNPq8pnv94yxC0Lbex2Cpi/Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:34.081205Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.3233","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcbc5033c2bf6f178d62d866e00a8e7c75223fe0f180ee0152db42676d3a9b38","sha256:1b13ab6e75a307fe823fbe73cf7f9e0ce648c8b758b05f5543b76ec2fb860cc3"],"state_sha256":"ab2a9dfe7d7bbec72c1db0ab578406c0b1a4020f6293d8db028509e54ad4f78d"}