{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:B4TTNHDMPI2F5HUG3T56DOVVES","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":"b3eb5250d77d8a680e3b8e5147e24ad746748cadb0a920555119da49e1a2c2d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-02T22:54:02Z","title_canon_sha256":"ff82a7aa076247fa173bb56f2f90a3be7ba1643087c228363c76f0af36dddfb6"},"schema_version":"1.0","source":{"id":"1509.00897","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00897","created_at":"2026-05-18T01:18:52Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00897v3","created_at":"2026-05-18T01:18:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00897","created_at":"2026-05-18T01:18:52Z"},{"alias_kind":"pith_short_12","alias_value":"B4TTNHDMPI2F","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"B4TTNHDMPI2F5HUG","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"B4TTNHDM","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:232fde31497d42e6437bd115c0230440a9c8c2dd98478a53ef60a01922bed780","target":"graph","created_at":"2026-05-18T01:18:52Z","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":"In this paper we study the linear stochastic heat equation, also known as parabolic Anderson model, in multidimension driven by a Gaussian noise which is white in time and it has a correlated spatial covariance. Examples of such covariance include the Riesz kernel in any dimension and the covariance of the fractional Brownian motion with Hurst parameter $H\\in (\\frac 14, \\frac 12]$ in dimension one. First we establish the existence of a unique mild solution and we derive a Feynman-Kac formula for its moments using a family of independent Brownian bridges and assuming a general integrability con","authors_text":"David Nualart, Jingyu Huang, Khoa L\\^e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-02T22:54:02Z","title":"Large time asymptotics for the parabolic Anderson model driven by spatially correlated noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00897","kind":"arxiv","version":3},"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":"sha256:3edcc25c2ff9bcfd8a291c085f9e69717777345b2ab22313ea3610fb0a0dffcb","target":"record","created_at":"2026-05-18T01:18:52Z","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":"b3eb5250d77d8a680e3b8e5147e24ad746748cadb0a920555119da49e1a2c2d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-02T22:54:02Z","title_canon_sha256":"ff82a7aa076247fa173bb56f2f90a3be7ba1643087c228363c76f0af36dddfb6"},"schema_version":"1.0","source":{"id":"1509.00897","kind":"arxiv","version":3}},"canonical_sha256":"0f27369c6c7a345e9e86dcfbe1bab524aaaa0f60134cfb57260c200937684b74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f27369c6c7a345e9e86dcfbe1bab524aaaa0f60134cfb57260c200937684b74","first_computed_at":"2026-05-18T01:18:52.492361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:52.492361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oYoQOlP5hNiG3UMcmyTIV7D9DESvrXZz3AhnpL1kkYSxercimowUdlJ62Rr+0b5LPh3X3x2HtutvVSgRKpDZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:52.492888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00897","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3edcc25c2ff9bcfd8a291c085f9e69717777345b2ab22313ea3610fb0a0dffcb","sha256:232fde31497d42e6437bd115c0230440a9c8c2dd98478a53ef60a01922bed780"],"state_sha256":"466c4bbd8d9b19f2570d4e782e4831e7d10db96012e38bac922aff262a28357f"}