{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SS5AT7BTPF6TSIYDK7NXV5OUYF","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":"e5925feb6c9dfb5c0ed13f4eb07a80c53f539ac8ec778247b2d9fdd447318fb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-08T11:01:11Z","title_canon_sha256":"a7e4c01c332d2b894ea0cffd6d2a87a3f86dd76a7e1b384ba9775f2883274b41"},"schema_version":"1.0","source":{"id":"1112.1807","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1807","created_at":"2026-05-18T03:35:02Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1807v3","created_at":"2026-05-18T03:35:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1807","created_at":"2026-05-18T03:35:02Z"},{"alias_kind":"pith_short_12","alias_value":"SS5AT7BTPF6T","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SS5AT7BTPF6TSIYD","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SS5AT7BT","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:5197e82832917d3a6d75524b346da5802230e25eee8b97849595bdccbf11cceb","target":"graph","created_at":"2026-05-18T03:35:02Z","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 analyze the concepts of analytically weak solutions of stochastic differential equations (SDEs) in Hilbert spaces with time-dependent unbounded operators and give conditions for existence and uniqueness of such solutions. Our studies are motivated by a stochastic partial differential equation (SPDE) arising in industrial mathematics.","authors_text":"Benedict Baur, Martin Grothaus, Tan Thanh Mai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-08T11:01:11Z","title":"Analytically weak solutions to SPDEs with unbounded time-dependent differential operators and an application"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1807","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:dfb7fb347a7d25dda91fb636329fe38bc14f8a595cc4302b4b1b896c8405ff43","target":"record","created_at":"2026-05-18T03:35:02Z","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":"e5925feb6c9dfb5c0ed13f4eb07a80c53f539ac8ec778247b2d9fdd447318fb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-08T11:01:11Z","title_canon_sha256":"a7e4c01c332d2b894ea0cffd6d2a87a3f86dd76a7e1b384ba9775f2883274b41"},"schema_version":"1.0","source":{"id":"1112.1807","kind":"arxiv","version":3}},"canonical_sha256":"94ba09fc33797d39230357db7af5d4c14c76654acbd93298b127e3bb0d8e83ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94ba09fc33797d39230357db7af5d4c14c76654acbd93298b127e3bb0d8e83ad","first_computed_at":"2026-05-18T03:35:02.254521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:02.254521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JXhHcXdiX7wBVrEtcC3pXBd2+f6N/MlZ27+FJ3RgT1oXpVrrplmPi8XZGmoTyyaqwnh4O4USqiMkFA9xqODBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:02.255226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1807","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfb7fb347a7d25dda91fb636329fe38bc14f8a595cc4302b4b1b896c8405ff43","sha256:5197e82832917d3a6d75524b346da5802230e25eee8b97849595bdccbf11cceb"],"state_sha256":"b258cd7ba4ebaa75bf3178c13a90fd03e8f45e00a8b68b64e1af2a2487b4acc6"}