{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4YLAO6RXF7EUWAHID7VH7VFW7U","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":"a8a615382e156a4b1bdf5183df108158600465252ad04701228d24bdbe21287a","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-22T16:08:00Z","title_canon_sha256":"e76cfb4de09df27435e9f706d86562704ce814bca144ddbccf01f1733ec9b439"},"schema_version":"1.0","source":{"id":"2405.13780","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.13780","created_at":"2026-07-05T10:41:46Z"},{"alias_kind":"arxiv_version","alias_value":"2405.13780v2","created_at":"2026-07-05T10:41:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.13780","created_at":"2026-07-05T10:41:46Z"},{"alias_kind":"pith_short_12","alias_value":"4YLAO6RXF7EU","created_at":"2026-07-05T10:41:46Z"},{"alias_kind":"pith_short_16","alias_value":"4YLAO6RXF7EUWAHI","created_at":"2026-07-05T10:41:46Z"},{"alias_kind":"pith_short_8","alias_value":"4YLAO6RX","created_at":"2026-07-05T10:41:46Z"}],"graph_snapshots":[{"event_id":"sha256:38bcec8040287bfb87078a3aca6b8f6fb422468625b3c7395a26492e1ff89e53","target":"graph","created_at":"2026-07-05T10:41:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2405.13780/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We put forward a new method for proving weak uniqueness of stochastic equations with singular drifts driven by a non-Markov or infinite-dimensional noise. We apply our method to study stochastic heat equation (SHE) driven by Gaussian space-time white noise $$ \\frac{\\partial}{\\partial t} u_t(x)=\\frac12 \\frac{\\partial^2}{\\partial x^2}u_t(x)+b(u_t(x))+\\dot{W}_{t}(x), \\quad t>0,\\, x\\in D\\subset\\mathbb{R}, $$ and multidimensional stochastic differential equation (SDE) driven by fractional Brownian motion with the Hurst index $H\\in(0,1/2)$ $$ d X_t=b(X_t) dt +d B_t^H,\\quad t>0. $$ In both cases $b$ ","authors_text":"Leonid Mytnik, Oleg Butkovsky","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-22T16:08:00Z","title":"Weak uniqueness for singular stochastic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.13780","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":"sha256:0be27ace514b679657277cbfd05b9c1ca94c04c22b829d6085d840648ba1e5e6","target":"record","created_at":"2026-07-05T10:41:46Z","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":"a8a615382e156a4b1bdf5183df108158600465252ad04701228d24bdbe21287a","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-22T16:08:00Z","title_canon_sha256":"e76cfb4de09df27435e9f706d86562704ce814bca144ddbccf01f1733ec9b439"},"schema_version":"1.0","source":{"id":"2405.13780","kind":"arxiv","version":2}},"canonical_sha256":"e616077a372fc94b00e81fea7fd4b6fd020736fe6c66a7f6f3031fa53d31271d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e616077a372fc94b00e81fea7fd4b6fd020736fe6c66a7f6f3031fa53d31271d","first_computed_at":"2026-07-05T10:41:46.601994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:41:46.601994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"onh+XdWKTo7cQRr4lwQV4OZd2V9Lzpu9Qh385wjTtT3qioWpkgIJlY6pn7kAAw9SAB9ha7pH8zhteByDBW3YCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:41:46.602504Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.13780","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0be27ace514b679657277cbfd05b9c1ca94c04c22b829d6085d840648ba1e5e6","sha256:38bcec8040287bfb87078a3aca6b8f6fb422468625b3c7395a26492e1ff89e53"],"state_sha256":"107b1c8120f8d8e2bd8560fa88938058fea57c455329ba6cd91756a89eabe0f6"}