{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KAH4U6K4N63DCROHCM32IBZTVK","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":"c39058cd69f7e82c5b78decb770e125370b1b4b4c81663281639d55afacc08f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-23T07:05:59Z","title_canon_sha256":"90d42cd0785d95fe3d9ed59816769aff3f11adb96bde6fb158b8dbd9268774a1"},"schema_version":"1.0","source":{"id":"1707.07254","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07254","created_at":"2026-05-17T23:40:56Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07254v4","created_at":"2026-05-17T23:40:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07254","created_at":"2026-05-17T23:40:56Z"},{"alias_kind":"pith_short_12","alias_value":"KAH4U6K4N63D","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KAH4U6K4N63DCROH","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KAH4U6K4","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:bbc0ceff3ddd1e7291d07f85e29d855d799a5d01c5fb56b608f51b7a5773de82","target":"graph","created_at":"2026-05-17T23:40:56Z","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 prove existence of solutions to continuity equations in a separable Hilbert space. We look for solutions which are absolutely continuous with respect to a reference measure \\gamma which is Fomin-differentiable with exponentially integrable partial logarithmic derivatives. We describe a class of examples to which our result applies and for which we can prove also uniqueness. Finally, we consider the case where \\gamma is the invariant measure of a reaction-diffusion equation and prove uniqueness of solutions in this case. We exploit that the gradient operator D_x is closable with respect to L","authors_text":"Franco Flandoli, Giuseppe Da Prato, Michael Roeckner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-23T07:05:59Z","title":"Absolutely continuous solutions for continuity equations in Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07254","kind":"arxiv","version":4},"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":"sha256:65d0a7225afaba9bff42a2e1ef181d4f1400765678f06c4f758a741b39771ab8","target":"record","created_at":"2026-05-17T23:40:56Z","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":"c39058cd69f7e82c5b78decb770e125370b1b4b4c81663281639d55afacc08f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-23T07:05:59Z","title_canon_sha256":"90d42cd0785d95fe3d9ed59816769aff3f11adb96bde6fb158b8dbd9268774a1"},"schema_version":"1.0","source":{"id":"1707.07254","kind":"arxiv","version":4}},"canonical_sha256":"500fca795c6fb63145c71337a40733aab42cb828769c97d65db5e07d20a6a64e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"500fca795c6fb63145c71337a40733aab42cb828769c97d65db5e07d20a6a64e","first_computed_at":"2026-05-17T23:40:56.264291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:56.264291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IOK1wqdwSyYfEVrAFTybUbha9g2UDlclaHbonoU1oLAr/JyFqCAuN5Jy+gpXlrM3YCITuOoaxplwNVSvWW7wCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:56.265102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.07254","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65d0a7225afaba9bff42a2e1ef181d4f1400765678f06c4f758a741b39771ab8","sha256:bbc0ceff3ddd1e7291d07f85e29d855d799a5d01c5fb56b608f51b7a5773de82"],"state_sha256":"10041046a1c000ad59b9e44d070bf797987342d55cf673455a0415707e28051d"}