{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UTMGG7Z6U2ZQYG6LPX36SKEDV3","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":"17795818bb7c79104f9f46fe6e04f582a53fc85545302aef2bd51552da62dad1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-10T12:29:46Z","title_canon_sha256":"f6abcee8e049e783409694a43d8b4450c8132b73e5590bde44ccd110322a6964"},"schema_version":"1.0","source":{"id":"1801.03344","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.03344","created_at":"2026-05-18T00:26:17Z"},{"alias_kind":"arxiv_version","alias_value":"1801.03344v1","created_at":"2026-05-18T00:26:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.03344","created_at":"2026-05-18T00:26:17Z"},{"alias_kind":"pith_short_12","alias_value":"UTMGG7Z6U2ZQ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UTMGG7Z6U2ZQYG6L","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UTMGG7Z6","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:23335eb0608ca2d7637cf295e6aeb7a41d85d68df115fc68d3b66e7514cb6699","target":"graph","created_at":"2026-05-18T00:26:17Z","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 study $BV$ functions in a Hilbert space $X$ endowed with a probability measure $\\nu$, assuming that $\\nu$ is Fomin differentiable along suitable directions. We establish basic characterizations, and we apply the general theory to relevant examples, including invariant measures of some stochastic PDEs.","authors_text":"Alessandra Lunardi, Giuseppe Da Prato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-10T12:29:46Z","title":"BV functions in Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03344","kind":"arxiv","version":1},"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:cc37dd853c4e7cee4a5087103dc8e73e531e6929f90c80b418e4052f9e7661cc","target":"record","created_at":"2026-05-18T00:26:17Z","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":"17795818bb7c79104f9f46fe6e04f582a53fc85545302aef2bd51552da62dad1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-10T12:29:46Z","title_canon_sha256":"f6abcee8e049e783409694a43d8b4450c8132b73e5590bde44ccd110322a6964"},"schema_version":"1.0","source":{"id":"1801.03344","kind":"arxiv","version":1}},"canonical_sha256":"a4d8637f3ea6b30c1bcb7df7e92883aef7576ac24a7ba311c560fce5e33ed000","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4d8637f3ea6b30c1bcb7df7e92883aef7576ac24a7ba311c560fce5e33ed000","first_computed_at":"2026-05-18T00:26:17.332728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:17.332728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jY9NGNYzQQdIE8zVBZyJeAItzKaV++59wPIJZw82VlxnLXHcxsybc3r10oHZNU/xdRmeKdllYsSe9B5uJwqTBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:17.333201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.03344","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc37dd853c4e7cee4a5087103dc8e73e531e6929f90c80b418e4052f9e7661cc","sha256:23335eb0608ca2d7637cf295e6aeb7a41d85d68df115fc68d3b66e7514cb6699"],"state_sha256":"8f8da37d1569626b52b9f1eda6dee7f11337b24062b4cd01045fb5fdbd9ddb70"}