{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3PFPBMAO6ZNPEYUK4IA3DNQLB6","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":"bed1e8e1a90a29e5f8cbb6394b2d15d9c064ffd9e676e108312a65725ba1c41a","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-09T20:10:58Z","title_canon_sha256":"8a10a6d6491c53c6ed4539062a292c87e4e0cbc1755d6f79b90e308e0f9d1d0f"},"schema_version":"1.0","source":{"id":"1412.3084","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3084","created_at":"2026-05-18T02:31:38Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3084v1","created_at":"2026-05-18T02:31:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3084","created_at":"2026-05-18T02:31:38Z"},{"alias_kind":"pith_short_12","alias_value":"3PFPBMAO6ZNP","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3PFPBMAO6ZNPEYUK","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3PFPBMAO","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:22eb28d9f0ca824a998d9042afe8b821db1f4b434087cb05b80a6aef7fc08b0e","target":"graph","created_at":"2026-05-18T02:31:38Z","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 investigate a variation of the graph coloring game, as studied in [2]. In the original coloring game, two players, Alice and Bob, alternate coloring vertices on a graph with legal colors from a fixed color set, where a color {\\alpha} is legal for a vertex if said vertex has no neighbors colored {\\alpha}. Other variations of the game change this definition of a legal color. For a fixed color set, Alice wins the game if all vertices are colored when the game ends, while Bob wins if there is a point in the game in which a vertex cannot be assigned a legal color. The least number of colors need","authors_text":"Charles Dunn, Davis Shurbert, Jennifer Nordstrom, Michel Alexis","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-09T20:10:58Z","title":"Clique-Relaxed Competitive Graph Coloring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3084","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:a24eacbfac9712ca00d77aa8f59a2f2b5e1fb90c271319c5dee24c8aac7ac2ff","target":"record","created_at":"2026-05-18T02:31:38Z","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":"bed1e8e1a90a29e5f8cbb6394b2d15d9c064ffd9e676e108312a65725ba1c41a","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-09T20:10:58Z","title_canon_sha256":"8a10a6d6491c53c6ed4539062a292c87e4e0cbc1755d6f79b90e308e0f9d1d0f"},"schema_version":"1.0","source":{"id":"1412.3084","kind":"arxiv","version":1}},"canonical_sha256":"dbcaf0b00ef65af2628ae201b1b60b0f8eca39c84e5eea1403fd800d21655670","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbcaf0b00ef65af2628ae201b1b60b0f8eca39c84e5eea1403fd800d21655670","first_computed_at":"2026-05-18T02:31:38.715646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:38.715646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BUjm2XBV0HrbeNIe25AXNIbqZ4fAu3nt0qW1J9IT4+KpZZd0c4soZwm1QTsuzd4t678gbP7I5m+smhewYrYdDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:38.716201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3084","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a24eacbfac9712ca00d77aa8f59a2f2b5e1fb90c271319c5dee24c8aac7ac2ff","sha256:22eb28d9f0ca824a998d9042afe8b821db1f4b434087cb05b80a6aef7fc08b0e"],"state_sha256":"38097da6a8f65c9d59b4a4771c13efc78e8cebc289695e790f2826be746ecc24"}