{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:YTNXBAFJZRTFHWORUU5GZJ7FB6","short_pith_number":"pith:YTNXBAFJ","schema_version":"1.0","canonical_sha256":"c4db7080a9cc6653d9d1a53a6ca7e50f8eeea9e96db88f8cdc3f1b5e7a011376","source":{"kind":"arxiv","id":"1102.3016","version":4},"attestation_state":"computed","paper":{"title":"Fire Containment in Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"F\\'elix Sipma, Fr\\'ed\\'eric Maffray, Jan van den Heuvel, Louis Esperet","submitted_at":"2011-02-15T09:55:38Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1102.3016","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-15T09:55:38Z","cross_cats_sorted":[],"title_canon_sha256":"50d4e0f386945c347e5f9ac81fe5cc0cb793d8c1af09ae907638f9f39b82abc0","abstract_canon_sha256":"f8058598c48ce5021b3eec1af18aa50f52c7c69aebcb7d4a1ceaad8d857e233d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:35.333797Z","signature_b64":"Vx3sN8qagEJ9KrSDvM4TWENAR4DASB0bb9524rrRFzhFgGxjA3QYt/hIZhwXbiTgU8vx4Tga/+DwLoJuaWD7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4db7080a9cc6653d9d1a53a6ca7e50f8eeea9e96db88f8cdc3f1b5e7a011376","last_reissued_at":"2026-05-18T03:25:35.333000Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:35.333000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fire Containment in Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"F\\'elix Sipma, Fr\\'ed\\'eric Maffray, Jan van den Heuvel, Louis Esperet","submitted_at":"2011-02-15T09:55:38Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3016","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1102.3016","created_at":"2026-05-18T03:25:35.333132+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.3016v4","created_at":"2026-05-18T03:25:35.333132+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3016","created_at":"2026-05-18T03:25:35.333132+00:00"},{"alias_kind":"pith_short_12","alias_value":"YTNXBAFJZRTF","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YTNXBAFJZRTFHWOR","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YTNXBAFJ","created_at":"2026-05-18T12:26:47.523578+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YTNXBAFJZRTFHWORUU5GZJ7FB6","json":"https://pith.science/pith/YTNXBAFJZRTFHWORUU5GZJ7FB6.json","graph_json":"https://pith.science/api/pith-number/YTNXBAFJZRTFHWORUU5GZJ7FB6/graph.json","events_json":"https://pith.science/api/pith-number/YTNXBAFJZRTFHWORUU5GZJ7FB6/events.json","paper":"https://pith.science/paper/YTNXBAFJ"},"agent_actions":{"view_html":"https://pith.science/pith/YTNXBAFJZRTFHWORUU5GZJ7FB6","download_json":"https://pith.science/pith/YTNXBAFJZRTFHWORUU5GZJ7FB6.json","view_paper":"https://pith.science/paper/YTNXBAFJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.3016&json=true","fetch_graph":"https://pith.science/api/pith-number/YTNXBAFJZRTFHWORUU5GZJ7FB6/graph.json","fetch_events":"https://pith.science/api/pith-number/YTNXBAFJZRTFHWORUU5GZJ7FB6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YTNXBAFJZRTFHWORUU5GZJ7FB6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YTNXBAFJZRTFHWORUU5GZJ7FB6/action/storage_attestation","attest_author":"https://pith.science/pith/YTNXBAFJZRTFHWORUU5GZJ7FB6/action/author_attestation","sign_citation":"https://pith.science/pith/YTNXBAFJZRTFHWORUU5GZJ7FB6/action/citation_signature","submit_replication":"https://pith.science/pith/YTNXBAFJZRTFHWORUU5GZJ7FB6/action/replication_record"}},"created_at":"2026-05-18T03:25:35.333132+00:00","updated_at":"2026-05-18T03:25:35.333132+00:00"}