{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:GR4IZD3ICP6YS5X6EKXUJUOXZB","short_pith_number":"pith:GR4IZD3I","schema_version":"1.0","canonical_sha256":"34788c8f6813fd8976fe22af44d1d7c8744dfc7e9599df4fdd5075639ba17fd3","source":{"kind":"arxiv","id":"1211.5694","version":2},"attestation_state":"computed","paper":{"title":"The Williams Bjerknes Model on Regular Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Alexander Vandenberg-Rodes, Oren Louidor, Ran J. Tessler","submitted_at":"2012-11-24T18:56:39Z","abstract_excerpt":"We consider the Williams Bjerknes model, also known as the biased voter model on the $d$-regular tree $\\bbT^d$, where $d \\geq 3$. Starting from an initial configuration of \"healthy\" and \"infected\" vertices, infected vertices infect their neighbors at Poisson rate $\\lambda \\geq 1$, while healthy vertices heal their neighbors at Poisson rate 1. All vertices act independently. It is well known that starting from a configuration with a positive but finite number of infected vertices, infected vertices will continue to exist at all time with positive probability iff $\\lambda > 1$. We show that ther"},"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":"1211.5694","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-24T18:56:39Z","cross_cats_sorted":["cs.SI","math-ph","math.MP"],"title_canon_sha256":"b449c27c9f14ee231c1ba39881bd60254ddd17af94fb481ca17261e007889125","abstract_canon_sha256":"eb549b8982b80843db0af2e030d4b4a08bbd23c0a50c1067088f0d8a7d7d3560"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:52.257095Z","signature_b64":"5Q2te4pAwu2nYCV+5BG8ROwcqHHkJl2+ruKiKJ3YEXRlWtP4Y4h0RuHi8BJhWuII4ANyND83wXj519UIGEwyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34788c8f6813fd8976fe22af44d1d7c8744dfc7e9599df4fdd5075639ba17fd3","last_reissued_at":"2026-05-18T03:37:52.256301Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:52.256301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Williams Bjerknes Model on Regular Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Alexander Vandenberg-Rodes, Oren Louidor, Ran J. Tessler","submitted_at":"2012-11-24T18:56:39Z","abstract_excerpt":"We consider the Williams Bjerknes model, also known as the biased voter model on the $d$-regular tree $\\bbT^d$, where $d \\geq 3$. Starting from an initial configuration of \"healthy\" and \"infected\" vertices, infected vertices infect their neighbors at Poisson rate $\\lambda \\geq 1$, while healthy vertices heal their neighbors at Poisson rate 1. All vertices act independently. It is well known that starting from a configuration with a positive but finite number of infected vertices, infected vertices will continue to exist at all time with positive probability iff $\\lambda > 1$. We show that ther"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5694","kind":"arxiv","version":2},"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":"1211.5694","created_at":"2026-05-18T03:37:52.256445+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.5694v2","created_at":"2026-05-18T03:37:52.256445+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5694","created_at":"2026-05-18T03:37:52.256445+00:00"},{"alias_kind":"pith_short_12","alias_value":"GR4IZD3ICP6Y","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"GR4IZD3ICP6YS5X6","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"GR4IZD3I","created_at":"2026-05-18T12:27:06.952714+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/GR4IZD3ICP6YS5X6EKXUJUOXZB","json":"https://pith.science/pith/GR4IZD3ICP6YS5X6EKXUJUOXZB.json","graph_json":"https://pith.science/api/pith-number/GR4IZD3ICP6YS5X6EKXUJUOXZB/graph.json","events_json":"https://pith.science/api/pith-number/GR4IZD3ICP6YS5X6EKXUJUOXZB/events.json","paper":"https://pith.science/paper/GR4IZD3I"},"agent_actions":{"view_html":"https://pith.science/pith/GR4IZD3ICP6YS5X6EKXUJUOXZB","download_json":"https://pith.science/pith/GR4IZD3ICP6YS5X6EKXUJUOXZB.json","view_paper":"https://pith.science/paper/GR4IZD3I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.5694&json=true","fetch_graph":"https://pith.science/api/pith-number/GR4IZD3ICP6YS5X6EKXUJUOXZB/graph.json","fetch_events":"https://pith.science/api/pith-number/GR4IZD3ICP6YS5X6EKXUJUOXZB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GR4IZD3ICP6YS5X6EKXUJUOXZB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GR4IZD3ICP6YS5X6EKXUJUOXZB/action/storage_attestation","attest_author":"https://pith.science/pith/GR4IZD3ICP6YS5X6EKXUJUOXZB/action/author_attestation","sign_citation":"https://pith.science/pith/GR4IZD3ICP6YS5X6EKXUJUOXZB/action/citation_signature","submit_replication":"https://pith.science/pith/GR4IZD3ICP6YS5X6EKXUJUOXZB/action/replication_record"}},"created_at":"2026-05-18T03:37:52.256445+00:00","updated_at":"2026-05-18T03:37:52.256445+00:00"}