{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:3FN6LFSSNIOIDD7CBLYOP7JROK","short_pith_number":"pith:3FN6LFSS","schema_version":"1.0","canonical_sha256":"d95be596526a1c818fe20af0e7fd3172b33d21669490b58d929d17b991fc7240","source":{"kind":"arxiv","id":"1509.07006","version":1},"attestation_state":"computed","paper":{"title":"The pleasures and pains of studying 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":"2015-09-23T14:26:00Z","abstract_excerpt":"This paper provides a survey of known results and open problems for the two-type Richardson model, which is a stochastic model for competition on $\\mathbb{Z}^d$. In its simplest formulation, the Richardson model describes the evolution of a single infectious entity on $\\mathbb{Z}^d$, but more recently the dynamics have been extended to comprise two competing growing entities. For this version of the model, the main question is whether there is a positive probability for both entities to simultaneously grow to occupy infinite parts of the lattice, the conjecture being that the answer is yes if "},"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":"1509.07006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T14:26:00Z","cross_cats_sorted":[],"title_canon_sha256":"ec90c7397a21ddb4ee3fa9815d68c960a242bc9205be9a59a3833d3a4ba89dbb","abstract_canon_sha256":"5de0b7ad710c5ed10b3aad5426a64d548f6aa61ba7dce10eb3213a17a83cc693"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:17.225269Z","signature_b64":"IHXZDl9xVu1JfqEihPrRVS6BYPZLJezxfV/i6zZ4pNHcRm+2d5R/IMVw0zt9BVUo+r/FTz63Ix/QqdZd+sOADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d95be596526a1c818fe20af0e7fd3172b33d21669490b58d929d17b991fc7240","last_reissued_at":"2026-05-18T01:32:17.224542Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:17.224542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The pleasures and pains of studying 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":"2015-09-23T14:26:00Z","abstract_excerpt":"This paper provides a survey of known results and open problems for the two-type Richardson model, which is a stochastic model for competition on $\\mathbb{Z}^d$. In its simplest formulation, the Richardson model describes the evolution of a single infectious entity on $\\mathbb{Z}^d$, but more recently the dynamics have been extended to comprise two competing growing entities. For this version of the model, the main question is whether there is a positive probability for both entities to simultaneously grow to occupy infinite parts of the lattice, the conjecture being that the answer is yes if "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07006","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":"1509.07006","created_at":"2026-05-18T01:32:17.224629+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.07006v1","created_at":"2026-05-18T01:32:17.224629+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07006","created_at":"2026-05-18T01:32:17.224629+00:00"},{"alias_kind":"pith_short_12","alias_value":"3FN6LFSSNIOI","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"3FN6LFSSNIOIDD7C","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"3FN6LFSS","created_at":"2026-05-18T12:29:02.477457+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/3FN6LFSSNIOIDD7CBLYOP7JROK","json":"https://pith.science/pith/3FN6LFSSNIOIDD7CBLYOP7JROK.json","graph_json":"https://pith.science/api/pith-number/3FN6LFSSNIOIDD7CBLYOP7JROK/graph.json","events_json":"https://pith.science/api/pith-number/3FN6LFSSNIOIDD7CBLYOP7JROK/events.json","paper":"https://pith.science/paper/3FN6LFSS"},"agent_actions":{"view_html":"https://pith.science/pith/3FN6LFSSNIOIDD7CBLYOP7JROK","download_json":"https://pith.science/pith/3FN6LFSSNIOIDD7CBLYOP7JROK.json","view_paper":"https://pith.science/paper/3FN6LFSS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.07006&json=true","fetch_graph":"https://pith.science/api/pith-number/3FN6LFSSNIOIDD7CBLYOP7JROK/graph.json","fetch_events":"https://pith.science/api/pith-number/3FN6LFSSNIOIDD7CBLYOP7JROK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3FN6LFSSNIOIDD7CBLYOP7JROK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3FN6LFSSNIOIDD7CBLYOP7JROK/action/storage_attestation","attest_author":"https://pith.science/pith/3FN6LFSSNIOIDD7CBLYOP7JROK/action/author_attestation","sign_citation":"https://pith.science/pith/3FN6LFSSNIOIDD7CBLYOP7JROK/action/citation_signature","submit_replication":"https://pith.science/pith/3FN6LFSSNIOIDD7CBLYOP7JROK/action/replication_record"}},"created_at":"2026-05-18T01:32:17.224629+00:00","updated_at":"2026-05-18T01:32:17.224629+00:00"}