{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UBUWOK24XREL2ZTROKXCIYJN7Z","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":"8808234bf51fe67202f4d195eebea3002f38bc9665fdffc33126d0e80f8fae5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-12T16:23:48Z","title_canon_sha256":"8adb4a6cc643908f56a8508e55b0fa984d65ed7156d671ecec52124167545aa9"},"schema_version":"1.0","source":{"id":"1312.3533","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3533","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3533v2","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3533","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"UBUWOK24XREL","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UBUWOK24XREL2ZTR","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UBUWOK24","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:d72af89be600ab53dfc8e24436a716a0b28da82de1cbfbc28bfc606b9054415b","target":"graph","created_at":"2026-05-18T00:54:04Z","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 study a two dimensional version of Neuhauser's long range sexual reproduction model and prove results that give bounds on the critical values $\\lambda_f$ for the process to survive from a finite set and $\\lambda_e$ for the existence of a nontrivial stationary distribution. Our first result comes from a standard block construction, while the second involves a comparison with the \"generic population model\" of Bramson and Gray (1991). An interesting new feature of our work is the suggestion that, as in the one dimensional contact process, edge speeds characterize critical values. We are able t","authors_text":"Mariya Bessonov, Richard Durrett","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-12T16:23:48Z","title":"Phase transitions for a planar quadratic contact process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3533","kind":"arxiv","version":2},"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":"sha256:4bf3c2764a00c1a311d8c0e44b57a8faee79f54183e2c9b337eb51a8898c1b1b","target":"record","created_at":"2026-05-18T00:54:04Z","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":"8808234bf51fe67202f4d195eebea3002f38bc9665fdffc33126d0e80f8fae5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-12T16:23:48Z","title_canon_sha256":"8adb4a6cc643908f56a8508e55b0fa984d65ed7156d671ecec52124167545aa9"},"schema_version":"1.0","source":{"id":"1312.3533","kind":"arxiv","version":2}},"canonical_sha256":"a069672b5cbc48bd667172ae24612dfe46c2a234d7481cdd7328fb5853ffc65b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a069672b5cbc48bd667172ae24612dfe46c2a234d7481cdd7328fb5853ffc65b","first_computed_at":"2026-05-18T00:54:04.092433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:04.092433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"48fklgIAqvmQbrQ5pWhuni9B2iDzGyaEPM48DYo7M4kAwyE/h2Qepxc8NfvETjgPV7r7vrN8MCFvfG3jCBFCCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:04.092816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3533","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bf3c2764a00c1a311d8c0e44b57a8faee79f54183e2c9b337eb51a8898c1b1b","sha256:d72af89be600ab53dfc8e24436a716a0b28da82de1cbfbc28bfc606b9054415b"],"state_sha256":"d8f0f4820ea726b10c2f8c6e11a46843b43896a5a099659ccd85b5c48da26fdb"}