{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:EBJWIZP5D4OFSMSU57V3QZH5PF","short_pith_number":"pith:EBJWIZP5","schema_version":"1.0","canonical_sha256":"20536465fd1f1c593254efebb864fd79649e3fbd6ccb3c81a8a1730f3118339a","source":{"kind":"arxiv","id":"1304.2274","version":2},"attestation_state":"computed","paper":{"title":"The parabolic Anderson model in a dynamic random environment: space-time ergodicity for the quenched Lyapunov exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dirk Erhard, Frank den Hollander, Gregory Maillard","submitted_at":"2013-04-08T17:21:26Z","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"},"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":"1304.2274","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-08T17:21:26Z","cross_cats_sorted":[],"title_canon_sha256":"707371ae6c3a01422cddae7700031b9cdac1a201d481302c4145b9bee2c16741","abstract_canon_sha256":"062f6dec5899729dd3e78401743ee35b69ef560b19141dec2b0b7fac538fc8cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:40.043909Z","signature_b64":"tN1Ue3YAKtzecKRxtdURMPEswP4r+Oi95FZjqUGiLs7iVoK6GgTwAzM+6PRT5wxVK3ERzf5o+d6fR7vupTRyBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20536465fd1f1c593254efebb864fd79649e3fbd6ccb3c81a8a1730f3118339a","last_reissued_at":"2026-05-18T03:18:40.043292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:40.043292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The parabolic Anderson model in a dynamic random environment: space-time ergodicity for the quenched Lyapunov exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dirk Erhard, Frank den Hollander, Gregory Maillard","submitted_at":"2013-04-08T17:21:26Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2274","kind":"arxiv","version":2},"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":"1304.2274","created_at":"2026-05-18T03:18:40.043416+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.2274v2","created_at":"2026-05-18T03:18:40.043416+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2274","created_at":"2026-05-18T03:18:40.043416+00:00"},{"alias_kind":"pith_short_12","alias_value":"EBJWIZP5D4OF","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EBJWIZP5D4OFSMSU","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EBJWIZP5","created_at":"2026-05-18T12:27:43.054852+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/EBJWIZP5D4OFSMSU57V3QZH5PF","json":"https://pith.science/pith/EBJWIZP5D4OFSMSU57V3QZH5PF.json","graph_json":"https://pith.science/api/pith-number/EBJWIZP5D4OFSMSU57V3QZH5PF/graph.json","events_json":"https://pith.science/api/pith-number/EBJWIZP5D4OFSMSU57V3QZH5PF/events.json","paper":"https://pith.science/paper/EBJWIZP5"},"agent_actions":{"view_html":"https://pith.science/pith/EBJWIZP5D4OFSMSU57V3QZH5PF","download_json":"https://pith.science/pith/EBJWIZP5D4OFSMSU57V3QZH5PF.json","view_paper":"https://pith.science/paper/EBJWIZP5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.2274&json=true","fetch_graph":"https://pith.science/api/pith-number/EBJWIZP5D4OFSMSU57V3QZH5PF/graph.json","fetch_events":"https://pith.science/api/pith-number/EBJWIZP5D4OFSMSU57V3QZH5PF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EBJWIZP5D4OFSMSU57V3QZH5PF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EBJWIZP5D4OFSMSU57V3QZH5PF/action/storage_attestation","attest_author":"https://pith.science/pith/EBJWIZP5D4OFSMSU57V3QZH5PF/action/author_attestation","sign_citation":"https://pith.science/pith/EBJWIZP5D4OFSMSU57V3QZH5PF/action/citation_signature","submit_replication":"https://pith.science/pith/EBJWIZP5D4OFSMSU57V3QZH5PF/action/replication_record"}},"created_at":"2026-05-18T03:18:40.043416+00:00","updated_at":"2026-05-18T03:18:40.043416+00:00"}