{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EBJWIZP5D4OFSMSU57V3QZH5PF","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":"062f6dec5899729dd3e78401743ee35b69ef560b19141dec2b0b7fac538fc8cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-08T17:21:26Z","title_canon_sha256":"707371ae6c3a01422cddae7700031b9cdac1a201d481302c4145b9bee2c16741"},"schema_version":"1.0","source":{"id":"1304.2274","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2274","created_at":"2026-05-18T03:18:40Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2274v2","created_at":"2026-05-18T03:18:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2274","created_at":"2026-05-18T03:18:40Z"},{"alias_kind":"pith_short_12","alias_value":"EBJWIZP5D4OF","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EBJWIZP5D4OFSMSU","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EBJWIZP5","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:40a0e2d34738d2d9b9cbe2be287e5f0a090b815d352ac966a100ae8b87550b02","target":"graph","created_at":"2026-05-18T03:18:40Z","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 continue our study of the parabolic Anderson equation $\\partial u(x,t)/\\partial t = \\kappa\\Delta u(x,t) + \\xi(x,t)u(x,t)$, $x\\in\\Z^d$, $t\\geq 0$, where $\\kappa \\in [0,\\infty)$ is the diffusion constant, $\\Delta$ is the discrete Laplacian, and $\\xi$ plays the role of a \\emph{dynamic random environment} that drives the equation. The initial condition $u(x,0)=u_0(x)$, $x\\in\\Z^d$, is taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump","authors_text":"Dirk Erhard, Frank den Hollander, Gregory Maillard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-08T17:21:26Z","title":"The parabolic Anderson model in a dynamic random environment: space-time ergodicity for the quenched Lyapunov exponent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2274","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:a78a9329de5a6c877fce7ec28960ad50d6468714a3c2ee5fd9a24eb6857b9ef6","target":"record","created_at":"2026-05-18T03:18:40Z","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":"062f6dec5899729dd3e78401743ee35b69ef560b19141dec2b0b7fac538fc8cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-08T17:21:26Z","title_canon_sha256":"707371ae6c3a01422cddae7700031b9cdac1a201d481302c4145b9bee2c16741"},"schema_version":"1.0","source":{"id":"1304.2274","kind":"arxiv","version":2}},"canonical_sha256":"20536465fd1f1c593254efebb864fd79649e3fbd6ccb3c81a8a1730f3118339a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20536465fd1f1c593254efebb864fd79649e3fbd6ccb3c81a8a1730f3118339a","first_computed_at":"2026-05-18T03:18:40.043292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:40.043292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tN1Ue3YAKtzecKRxtdURMPEswP4r+Oi95FZjqUGiLs7iVoK6GgTwAzM+6PRT5wxVK3ERzf5o+d6fR7vupTRyBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:40.043909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2274","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a78a9329de5a6c877fce7ec28960ad50d6468714a3c2ee5fd9a24eb6857b9ef6","sha256:40a0e2d34738d2d9b9cbe2be287e5f0a090b815d352ac966a100ae8b87550b02"],"state_sha256":"9702685f3842afc3462e3c36fd3b207faba7a2f547ffd5fb91eb13bc0da208fb"}