{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OKYV6D5FRHOEI3RDFNTZ4XNR3W","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9e2d2cce5869a4a3466fa8f1a93cc069cf6dde489c6a4d981b7a8f9b230c0784","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-09T00:48:30Z","title_canon_sha256":"28bd49732eb1083c8aad7d27bbf7724fcda1292e0cdc45690b24bbc0f2b97d9c"},"schema_version":"1.0","source":{"id":"1103.1676","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1676","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1676v1","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1676","created_at":"2026-05-18T04:27:06Z"},{"alias_kind":"pith_short_12","alias_value":"OKYV6D5FRHOE","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OKYV6D5FRHOEI3RD","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OKYV6D5F","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:abadaba151ad96746c341968f893bd11663d6b40cf925145144b139fb4ecbd39","target":"graph","created_at":"2026-05-18T04:27:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Edwin Perkins, J. Theodore Cox, Richard Durrett","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-09T00:48:30Z","title":"Voter Model Perturbations and Reaction Diffusion Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1676","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c37bdc2f6bb2043fd3cfacb5a076fedb8bc9ceaad6267ef9e252118870c5efde","target":"record","created_at":"2026-05-18T04:27:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9e2d2cce5869a4a3466fa8f1a93cc069cf6dde489c6a4d981b7a8f9b230c0784","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-09T00:48:30Z","title_canon_sha256":"28bd49732eb1083c8aad7d27bbf7724fcda1292e0cdc45690b24bbc0f2b97d9c"},"schema_version":"1.0","source":{"id":"1103.1676","kind":"arxiv","version":1}},"canonical_sha256":"72b15f0fa589dc446e232b679e5db1dd8ee940c21bea885cadb6766a160fb898","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72b15f0fa589dc446e232b679e5db1dd8ee940c21bea885cadb6766a160fb898","first_computed_at":"2026-05-18T04:27:06.004905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:06.004905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k2sREgjVu+24rrf+kEoGZ/0uVB/9A/mrSZmTxN+fT+gii3E4ZwhdUH/Tsn5BdOqPa6RSMKgQ1Bv020u8D1REBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:06.005517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1676","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c37bdc2f6bb2043fd3cfacb5a076fedb8bc9ceaad6267ef9e252118870c5efde","sha256:abadaba151ad96746c341968f893bd11663d6b40cf925145144b139fb4ecbd39"],"state_sha256":"72838300250786a3482a2fc4ff26bd51ee7d7d6aef0a2e71e6d01ec2ec9bf73b"}