{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6KDK5YVU6PPKZQJ2N2X3UMODU2","short_pith_number":"pith:6KDK5YVU","schema_version":"1.0","canonical_sha256":"f286aee2b4f3deacc13a6eafba31c3a6a8547843945931f056829a5fbf017a10","source":{"kind":"arxiv","id":"1509.06964","version":1},"attestation_state":"computed","paper":{"title":"The initial configuration is irrelevant for the possibility of mutual unbounded growth in the two-type Richardson model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Maria Deijfen, Olle H\\\"aggstr\\\"om","submitted_at":"2015-09-23T13:21:47Z","abstract_excerpt":"The two-type Richardson model describes the growth of two competing infections on $\\mathbb{Z}^d$. At time 0 two disjoint finite sets $\\xi_1,\\xi_2\\subset \\mathbb{Z}^d$ are infected with type 1 and type 2 infection respectively. An uninfected site then becomes type 1 (2) infected at a rate proportional to the number of type 1 (2) infected nearest neighbors and once infected it remains so forever. The main result in this paper is, loosely speaking, that the choice of the initial sets $\\xi_1$ and $\\xi_2$ is irrelevant in deciding whether the event of mutual unbounded growth for the two infection t"},"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":"1509.06964","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T13:21:47Z","cross_cats_sorted":[],"title_canon_sha256":"06ea0543ae625c7b72154037fc5613cd9347263dc9e17f652575e580e37d8ca4","abstract_canon_sha256":"a971f01f4a2731cd8e3b65c1587e876d54eba21f31a24474ba439ef06b0b3eea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:17.391035Z","signature_b64":"LsXWOgKa/R1XQpfIAADOVqNx5/8qEqMIKclhGvhq22uBe6wSpvpTZ8cs/kkYi/HnARHOwh4CFsFXQNzumIbUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f286aee2b4f3deacc13a6eafba31c3a6a8547843945931f056829a5fbf017a10","last_reissued_at":"2026-05-18T01:32:17.390287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:17.390287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The initial configuration is irrelevant for the possibility of mutual unbounded growth in the two-type Richardson model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Maria Deijfen, Olle H\\\"aggstr\\\"om","submitted_at":"2015-09-23T13:21:47Z","abstract_excerpt":"The two-type Richardson model describes the growth of two competing infections on $\\mathbb{Z}^d$. At time 0 two disjoint finite sets $\\xi_1,\\xi_2\\subset \\mathbb{Z}^d$ are infected with type 1 and type 2 infection respectively. An uninfected site then becomes type 1 (2) infected at a rate proportional to the number of type 1 (2) infected nearest neighbors and once infected it remains so forever. The main result in this paper is, loosely speaking, that the choice of the initial sets $\\xi_1$ and $\\xi_2$ is irrelevant in deciding whether the event of mutual unbounded growth for the two infection t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06964","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":"1509.06964","created_at":"2026-05-18T01:32:17.390399+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.06964v1","created_at":"2026-05-18T01:32:17.390399+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06964","created_at":"2026-05-18T01:32:17.390399+00:00"},{"alias_kind":"pith_short_12","alias_value":"6KDK5YVU6PPK","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6KDK5YVU6PPKZQJ2","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6KDK5YVU","created_at":"2026-05-18T12:29:07.941421+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/6KDK5YVU6PPKZQJ2N2X3UMODU2","json":"https://pith.science/pith/6KDK5YVU6PPKZQJ2N2X3UMODU2.json","graph_json":"https://pith.science/api/pith-number/6KDK5YVU6PPKZQJ2N2X3UMODU2/graph.json","events_json":"https://pith.science/api/pith-number/6KDK5YVU6PPKZQJ2N2X3UMODU2/events.json","paper":"https://pith.science/paper/6KDK5YVU"},"agent_actions":{"view_html":"https://pith.science/pith/6KDK5YVU6PPKZQJ2N2X3UMODU2","download_json":"https://pith.science/pith/6KDK5YVU6PPKZQJ2N2X3UMODU2.json","view_paper":"https://pith.science/paper/6KDK5YVU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.06964&json=true","fetch_graph":"https://pith.science/api/pith-number/6KDK5YVU6PPKZQJ2N2X3UMODU2/graph.json","fetch_events":"https://pith.science/api/pith-number/6KDK5YVU6PPKZQJ2N2X3UMODU2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6KDK5YVU6PPKZQJ2N2X3UMODU2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6KDK5YVU6PPKZQJ2N2X3UMODU2/action/storage_attestation","attest_author":"https://pith.science/pith/6KDK5YVU6PPKZQJ2N2X3UMODU2/action/author_attestation","sign_citation":"https://pith.science/pith/6KDK5YVU6PPKZQJ2N2X3UMODU2/action/citation_signature","submit_replication":"https://pith.science/pith/6KDK5YVU6PPKZQJ2N2X3UMODU2/action/replication_record"}},"created_at":"2026-05-18T01:32:17.390399+00:00","updated_at":"2026-05-18T01:32:17.390399+00:00"}