{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:F5RERLXBQEFXBNYU2HNR3L4LSO","short_pith_number":"pith:F5RERLXB","schema_version":"1.0","canonical_sha256":"2f6248aee1810b70b714d1db1daf8b93a944a189532f87720f9603daece4686c","source":{"kind":"arxiv","id":"1403.5927","version":1},"attestation_state":"computed","paper":{"title":"The contact process on finite homogeneous trees revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Valesin, Jean-Christophe Mourrat, Michael Cranston, Thomas Mountford","submitted_at":"2014-03-24T12:09:00Z","abstract_excerpt":"We consider the contact process with infection rate $\\lambda$ on $\\mathbb{T}_n^d$, the $d$-ary tree of height $n$. We study the extinction time $\\tau_{\\mathbb{T}_n^d}$, that is, the random time it takes for the infection to disappear when the process is started from full occupancy. We prove two conjectures of Stacey regarding $\\tau_{\\mathbb{T}_n^d}$. Let $\\lambda_2$ denote the upper critical value for the contact process on the infinite $d$-ary tree. First, if $\\lambda < \\lambda_2$, then $\\tau_{\\mathbb{T}_n^d}$ divided by the height of the tree converges in probability, as $n \\to \\infty$, to a"},"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":"1403.5927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-24T12:09:00Z","cross_cats_sorted":[],"title_canon_sha256":"6114b9318c6b2a04e29370e752f05f4a47e2f73890eee927da15e4ef831d9803","abstract_canon_sha256":"440a12fb2b1978d805e894a2fefdcc2720a9185779e2a8a34a72ea1090d2be37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:47.434064Z","signature_b64":"6z+1tVh5JayrHTOO857fUXDeB29p+fnNRQPexpK94Dyflt5/wc1mIKPqdVEO/DnE/rPygl25TuSBaKfR3KQcDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f6248aee1810b70b714d1db1daf8b93a944a189532f87720f9603daece4686c","last_reissued_at":"2026-05-18T02:55:47.433329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:47.433329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The contact process on finite homogeneous trees revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Valesin, Jean-Christophe Mourrat, Michael Cranston, Thomas Mountford","submitted_at":"2014-03-24T12:09:00Z","abstract_excerpt":"We consider the contact process with infection rate $\\lambda$ on $\\mathbb{T}_n^d$, the $d$-ary tree of height $n$. We study the extinction time $\\tau_{\\mathbb{T}_n^d}$, that is, the random time it takes for the infection to disappear when the process is started from full occupancy. We prove two conjectures of Stacey regarding $\\tau_{\\mathbb{T}_n^d}$. Let $\\lambda_2$ denote the upper critical value for the contact process on the infinite $d$-ary tree. First, if $\\lambda < \\lambda_2$, then $\\tau_{\\mathbb{T}_n^d}$ divided by the height of the tree converges in probability, as $n \\to \\infty$, to a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5927","kind":"arxiv","version":1},"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":"1403.5927","created_at":"2026-05-18T02:55:47.433459+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.5927v1","created_at":"2026-05-18T02:55:47.433459+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5927","created_at":"2026-05-18T02:55:47.433459+00:00"},{"alias_kind":"pith_short_12","alias_value":"F5RERLXBQEFX","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"F5RERLXBQEFXBNYU","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"F5RERLXB","created_at":"2026-05-18T12:28:28.263976+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/F5RERLXBQEFXBNYU2HNR3L4LSO","json":"https://pith.science/pith/F5RERLXBQEFXBNYU2HNR3L4LSO.json","graph_json":"https://pith.science/api/pith-number/F5RERLXBQEFXBNYU2HNR3L4LSO/graph.json","events_json":"https://pith.science/api/pith-number/F5RERLXBQEFXBNYU2HNR3L4LSO/events.json","paper":"https://pith.science/paper/F5RERLXB"},"agent_actions":{"view_html":"https://pith.science/pith/F5RERLXBQEFXBNYU2HNR3L4LSO","download_json":"https://pith.science/pith/F5RERLXBQEFXBNYU2HNR3L4LSO.json","view_paper":"https://pith.science/paper/F5RERLXB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.5927&json=true","fetch_graph":"https://pith.science/api/pith-number/F5RERLXBQEFXBNYU2HNR3L4LSO/graph.json","fetch_events":"https://pith.science/api/pith-number/F5RERLXBQEFXBNYU2HNR3L4LSO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F5RERLXBQEFXBNYU2HNR3L4LSO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F5RERLXBQEFXBNYU2HNR3L4LSO/action/storage_attestation","attest_author":"https://pith.science/pith/F5RERLXBQEFXBNYU2HNR3L4LSO/action/author_attestation","sign_citation":"https://pith.science/pith/F5RERLXBQEFXBNYU2HNR3L4LSO/action/citation_signature","submit_replication":"https://pith.science/pith/F5RERLXBQEFXBNYU2HNR3L4LSO/action/replication_record"}},"created_at":"2026-05-18T02:55:47.433459+00:00","updated_at":"2026-05-18T02:55:47.433459+00:00"}