{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YTNXBAFJZRTFHWORUU5GZJ7FB6","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":"f8058598c48ce5021b3eec1af18aa50f52c7c69aebcb7d4a1ceaad8d857e233d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-15T09:55:38Z","title_canon_sha256":"50d4e0f386945c347e5f9ac81fe5cc0cb793d8c1af09ae907638f9f39b82abc0"},"schema_version":"1.0","source":{"id":"1102.3016","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3016","created_at":"2026-05-18T03:25:35Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3016v4","created_at":"2026-05-18T03:25:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3016","created_at":"2026-05-18T03:25:35Z"},{"alias_kind":"pith_short_12","alias_value":"YTNXBAFJZRTF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YTNXBAFJZRTFHWOR","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YTNXBAFJ","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:d48f766785ce96af06a3666ff78025a62a8bfb19f37f2f7116e447937d59cbb0","target":"graph","created_at":"2026-05-18T03:25:35Z","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 a graph $G$, a fire starts at some vertex. At every time step, firefighters can protect up to $k$ vertices, and then the fire spreads to all unprotected neighbours. The $k$-surviving rate $\\rho_k(G)$ of $G$ is the expectation of the proportion of vertices that can be saved from the fire, if the starting vertex of the fire is chosen uniformly at random. For a given class of graphs $\\cG$ we are interested in the minimum value $k$ such that $\\rho_k(G)\\ge\\epsilon$ for some constant $\\epsilon>0$ and all $G\\in\\cG$ i.e., such that linearly many vertices are expected to be saved in every graph from","authors_text":"F\\'elix Sipma, Fr\\'ed\\'eric Maffray, Jan van den Heuvel, Louis Esperet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-15T09:55:38Z","title":"Fire Containment in Planar Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3016","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":"sha256:1a90e796104e81146a5c12ac723a3cc1994b88883271248a43a6a57afbd59c2b","target":"record","created_at":"2026-05-18T03:25:35Z","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":"f8058598c48ce5021b3eec1af18aa50f52c7c69aebcb7d4a1ceaad8d857e233d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-15T09:55:38Z","title_canon_sha256":"50d4e0f386945c347e5f9ac81fe5cc0cb793d8c1af09ae907638f9f39b82abc0"},"schema_version":"1.0","source":{"id":"1102.3016","kind":"arxiv","version":4}},"canonical_sha256":"c4db7080a9cc6653d9d1a53a6ca7e50f8eeea9e96db88f8cdc3f1b5e7a011376","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4db7080a9cc6653d9d1a53a6ca7e50f8eeea9e96db88f8cdc3f1b5e7a011376","first_computed_at":"2026-05-18T03:25:35.333000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:35.333000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vx3sN8qagEJ9KrSDvM4TWENAR4DASB0bb9524rrRFzhFgGxjA3QYt/hIZhwXbiTgU8vx4Tga/+DwLoJuaWD7Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:35.333797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3016","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a90e796104e81146a5c12ac723a3cc1994b88883271248a43a6a57afbd59c2b","sha256:d48f766785ce96af06a3666ff78025a62a8bfb19f37f2f7116e447937d59cbb0"],"state_sha256":"099fde219cb9f9f1be06008ab9c261a2e6bad1b5a2a6a47d7424d622e7df056e"}