{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GXTMNFEANU2IMSJWCZXYELREDQ","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":"0d7bb795d2ac6428c1c5fe371bedce2c03744e4cfb6c2f11a16087ffa1b026a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-29T08:56:06Z","title_canon_sha256":"c833f67c513398419d349a6b6d30c7a86bbd4dfb9327b1257d5cc2595bdb7c7c"},"schema_version":"1.0","source":{"id":"1409.8031","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8031","created_at":"2026-05-18T02:20:36Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8031v2","created_at":"2026-05-18T02:20:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8031","created_at":"2026-05-18T02:20:36Z"},{"alias_kind":"pith_short_12","alias_value":"GXTMNFEANU2I","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GXTMNFEANU2IMSJW","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GXTMNFEA","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:ecdc0549172a789b7bfe07d9fd6b32c10edfba24f1bd1afd74af4f56dcb34d2d","target":"graph","created_at":"2026-05-18T02:20:36Z","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":"For the class of stochastic partial differential equations studied in [Conus-Dalang,2008], we prove the existence of density of the probability law of the solution at a given point $(t,x)$, and that the density belongs to some Besov space. The proof relies on the method developed in [Debussche-Romito, 2014]. The result can be applied to the solution of the stochastic wave equation with multiplicative noise, Lipschitz coefficients and any spatial dimension $d\\ge 1$, and also to the heat equation. This provides an extension of the results proved in [Sanz-Sol\\'e and S\\\"u\\ss, 2013].","authors_text":"Andr\\'e S\\\"u{\\ss}, Marta Sanz-Sol\\'e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-29T08:56:06Z","title":"Absolute continuity for SPDEs with irregular fundamental solution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8031","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":"sha256:8eac1e498113084fee7cef93ab80ff9ff8b443c004142d480034fb346a038ad0","target":"record","created_at":"2026-05-18T02:20:36Z","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":"0d7bb795d2ac6428c1c5fe371bedce2c03744e4cfb6c2f11a16087ffa1b026a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-29T08:56:06Z","title_canon_sha256":"c833f67c513398419d349a6b6d30c7a86bbd4dfb9327b1257d5cc2595bdb7c7c"},"schema_version":"1.0","source":{"id":"1409.8031","kind":"arxiv","version":2}},"canonical_sha256":"35e6c694806d34864936166f822e241c07dd44bc766e70fe5532e7ab157bb2db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35e6c694806d34864936166f822e241c07dd44bc766e70fe5532e7ab157bb2db","first_computed_at":"2026-05-18T02:20:36.492255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:36.492255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JiBtsDeyRMenFiZulxfFh6tHCPxhkKwatgqfOl8TESDqpARxkisSjwYBdkUm1MohhxzM+YpFnyGstoWNggssDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:36.492886Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8031","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8eac1e498113084fee7cef93ab80ff9ff8b443c004142d480034fb346a038ad0","sha256:ecdc0549172a789b7bfe07d9fd6b32c10edfba24f1bd1afd74af4f56dcb34d2d"],"state_sha256":"fdaae723e116db6c65e624b354efd7efef17fdf5805b7852d0ac68706c1770f5"}