{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6G7IJCPCZAHF3BDELD77VHYDER","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":"04e8089089f5c752f93657e03b485fc28c97b54631b1afe2d7cf82a92c2cb7f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-20T21:11:34Z","title_canon_sha256":"7ae5340ec3b22bb9c6412e74e0f67825a5f04a977ffcdb68d8ebb4df43edd731"},"schema_version":"1.0","source":{"id":"1511.06774","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06774","created_at":"2026-05-18T01:26:19Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06774v1","created_at":"2026-05-18T01:26:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06774","created_at":"2026-05-18T01:26:19Z"},{"alias_kind":"pith_short_12","alias_value":"6G7IJCPCZAHF","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6G7IJCPCZAHF3BDE","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6G7IJCPC","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:4743b8761bbee2fab23f52e01c75ee0d7f77b1720b096371685fe5a4ae7ca1ae","target":"graph","created_at":"2026-05-18T01:26:19Z","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":"Graph burning is a model for the spread of social contagion. The burning number is a graph parameter associated with graph burning that measures the speed of the spread of contagion in a graph; the lower the burning number, the faster the contagion spreads. We prove that the corresponding graph decision problem is \\textbf{NP}-complete when restricted to acyclic graphs with maximum degree three, spider graphs and path-forests. We provide polynomial time algorithms for finding the burning number of spider graphs and path-forests if the number of arms and components, respectively, are fixed.","authors_text":"Anthony Bonato, Elham Roshanbin, Jeannette Janssen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-20T21:11:34Z","title":"Burning a Graph is Hard"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06774","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:aab14ba10d8241eba1398156c5f7ece2493a894ef37bd899f1f23426280a7c31","target":"record","created_at":"2026-05-18T01:26:19Z","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":"04e8089089f5c752f93657e03b485fc28c97b54631b1afe2d7cf82a92c2cb7f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-20T21:11:34Z","title_canon_sha256":"7ae5340ec3b22bb9c6412e74e0f67825a5f04a977ffcdb68d8ebb4df43edd731"},"schema_version":"1.0","source":{"id":"1511.06774","kind":"arxiv","version":1}},"canonical_sha256":"f1be8489e2c80e5d846458fffa9f03244eee17066277ea9511d3cb5103f4575c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1be8489e2c80e5d846458fffa9f03244eee17066277ea9511d3cb5103f4575c","first_computed_at":"2026-05-18T01:26:19.495351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:19.495351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rKXTAPRaDMd+2MlBawcf3Eer1vrTjr60SM4C/KDfVDFKhMV10FcvcMOyrIRe/d60ldyRbdZqtSlWx0d1JDHEBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:19.495913Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.06774","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aab14ba10d8241eba1398156c5f7ece2493a894ef37bd899f1f23426280a7c31","sha256:4743b8761bbee2fab23f52e01c75ee0d7f77b1720b096371685fe5a4ae7ca1ae"],"state_sha256":"bc6fb853b51b60572c664d7af318af0d89ccad1e19e73d9e6dbd1f098614abaf"}