{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:OKYV6D5FRHOEI3RDFNTZ4XNR3W","short_pith_number":"pith:OKYV6D5F","schema_version":"1.0","canonical_sha256":"72b15f0fa589dc446e232b679e5db1dd8ee940c21bea885cadb6766a160fb898","source":{"kind":"arxiv","id":"1103.1676","version":1},"attestation_state":"computed","paper":{"title":"Voter Model Perturbations and Reaction Diffusion Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Edwin Perkins, J. Theodore Cox, Richard Durrett","submitted_at":"2011-03-09T00:48:30Z","abstract_excerpt":"We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \\ge 3$. Combining this result with properties of the PDE, some methods arising from a low density super-Brownian limit theorem, and a block construction, we give general, and often asymptotically sharp, conditions for the existence of non-trivial stationary distributions, and for extinction of one type. As applications, we describe the phase diagrams of three systems when the parameters are clo"},"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":"1103.1676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-09T00:48:30Z","cross_cats_sorted":[],"title_canon_sha256":"28bd49732eb1083c8aad7d27bbf7724fcda1292e0cdc45690b24bbc0f2b97d9c","abstract_canon_sha256":"9e2d2cce5869a4a3466fa8f1a93cc069cf6dde489c6a4d981b7a8f9b230c0784"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:06.005517Z","signature_b64":"k2sREgjVu+24rrf+kEoGZ/0uVB/9A/mrSZmTxN+fT+gii3E4ZwhdUH/Tsn5BdOqPa6RSMKgQ1Bv020u8D1REBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72b15f0fa589dc446e232b679e5db1dd8ee940c21bea885cadb6766a160fb898","last_reissued_at":"2026-05-18T04:27:06.004905Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:06.004905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Voter Model Perturbations and Reaction Diffusion Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Edwin Perkins, J. Theodore Cox, Richard Durrett","submitted_at":"2011-03-09T00:48:30Z","abstract_excerpt":"We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \\ge 3$. Combining this result with properties of the PDE, some methods arising from a low density super-Brownian limit theorem, and a block construction, we give general, and often asymptotically sharp, conditions for the existence of non-trivial stationary distributions, and for extinction of one type. As applications, we describe the phase diagrams of three systems when the parameters are clo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1676","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":"1103.1676","created_at":"2026-05-18T04:27:06.004987+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.1676v1","created_at":"2026-05-18T04:27:06.004987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1676","created_at":"2026-05-18T04:27:06.004987+00:00"},{"alias_kind":"pith_short_12","alias_value":"OKYV6D5FRHOE","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"OKYV6D5FRHOEI3RD","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"OKYV6D5F","created_at":"2026-05-18T12:26:37.096874+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/OKYV6D5FRHOEI3RDFNTZ4XNR3W","json":"https://pith.science/pith/OKYV6D5FRHOEI3RDFNTZ4XNR3W.json","graph_json":"https://pith.science/api/pith-number/OKYV6D5FRHOEI3RDFNTZ4XNR3W/graph.json","events_json":"https://pith.science/api/pith-number/OKYV6D5FRHOEI3RDFNTZ4XNR3W/events.json","paper":"https://pith.science/paper/OKYV6D5F"},"agent_actions":{"view_html":"https://pith.science/pith/OKYV6D5FRHOEI3RDFNTZ4XNR3W","download_json":"https://pith.science/pith/OKYV6D5FRHOEI3RDFNTZ4XNR3W.json","view_paper":"https://pith.science/paper/OKYV6D5F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.1676&json=true","fetch_graph":"https://pith.science/api/pith-number/OKYV6D5FRHOEI3RDFNTZ4XNR3W/graph.json","fetch_events":"https://pith.science/api/pith-number/OKYV6D5FRHOEI3RDFNTZ4XNR3W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OKYV6D5FRHOEI3RDFNTZ4XNR3W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OKYV6D5FRHOEI3RDFNTZ4XNR3W/action/storage_attestation","attest_author":"https://pith.science/pith/OKYV6D5FRHOEI3RDFNTZ4XNR3W/action/author_attestation","sign_citation":"https://pith.science/pith/OKYV6D5FRHOEI3RDFNTZ4XNR3W/action/citation_signature","submit_replication":"https://pith.science/pith/OKYV6D5FRHOEI3RDFNTZ4XNR3W/action/replication_record"}},"created_at":"2026-05-18T04:27:06.004987+00:00","updated_at":"2026-05-18T04:27:06.004987+00:00"}