{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:4PM7YRPGI6TR7MP4VNPLPOOVHZ","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":"4776ed4995774244e143c9ecf8902debcebf12a1b4edfda0076e872b748f9757","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"1999-03-16T20:08:39Z","title_canon_sha256":"a359d6d98ad8a146c2beb7faaa91b85537e05305516c21f767da2d8df4dbe6ce"},"schema_version":"1.0","source":{"id":"math/9903095","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9903095","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/9903095v2","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9903095","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"pith_short_12","alias_value":"4PM7YRPGI6TR","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"4PM7YRPGI6TR7MP4","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"4PM7YRPG","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:16a5a8e862637f9e11f6008aef68741e548e4c3dd6758a81ddbade224a24e7e6","target":"graph","created_at":"2026-05-18T01:38:22Z","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":"It is well known that, starting with finite mass, the super-Brownian motion dies out in finite time. The goal of this article is to show that with some additional work, one can prove finite time die-out for two types of systems of stochastic differential equations on the lattice Z^d. Our first system involves the heat equation on the lattice Z^d, with a nonlinear noise term u(t,x)^gamma dB_x(t), with 1/2 <= gamma < 1. The B_x are independent Brownian motions. When gamma = 1/2, the measure which puts mass u(t,x) at x is a super-random walk and it is well-known that the process becomes extinct i","authors_text":"C. Mueller, E. Perkins","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"1999-03-16T20:08:39Z","title":"Extinction for two parabolic stochastic PDE's on the lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9903095","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":"sha256:12091f391b7dc1dd4760762d0e2f4fa9e353648d60736d17f5a34bf3774771ce","target":"record","created_at":"2026-05-18T01:38:22Z","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":"4776ed4995774244e143c9ecf8902debcebf12a1b4edfda0076e872b748f9757","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"1999-03-16T20:08:39Z","title_canon_sha256":"a359d6d98ad8a146c2beb7faaa91b85537e05305516c21f767da2d8df4dbe6ce"},"schema_version":"1.0","source":{"id":"math/9903095","kind":"arxiv","version":2}},"canonical_sha256":"e3d9fc45e647a71fb1fcab5eb7b9d53e7ace7128d12daf3b8477d9efa1ea44b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3d9fc45e647a71fb1fcab5eb7b9d53e7ace7128d12daf3b8477d9efa1ea44b5","first_computed_at":"2026-05-18T01:38:22.608432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:22.608432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CoiO9sO2G6FncH7GQjfPIoR2gKuV5fFIO3OjNYf5eMo6cFuWqDfJjGJXnwWmo9ltV4qsxXHbAZ1G2uhwJgVrBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:22.609127Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9903095","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12091f391b7dc1dd4760762d0e2f4fa9e353648d60736d17f5a34bf3774771ce","sha256:16a5a8e862637f9e11f6008aef68741e548e4c3dd6758a81ddbade224a24e7e6"],"state_sha256":"e2618ec8a87a5d8cc01ce8ae839128dcb304eed695a6b29e73d72017fa80867c"}