{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:C7IGKU5MITPAQGL675EYPGXRGH","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":"cf6be2e030616fb8f2b1f3a62ad6054eee025e634060b20c1dcc38d6eec2b623","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-16T17:39:07Z","title_canon_sha256":"1f5642683a51d976fc6dfae417de2a543933ee741b7d10c8c5f5b5eddf9a40d8"},"schema_version":"1.0","source":{"id":"1811.06935","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.06935","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"arxiv_version","alias_value":"1811.06935v1","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.06935","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"pith_short_12","alias_value":"C7IGKU5MITPA","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C7IGKU5MITPAQGL6","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C7IGKU5M","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:d9395141fdebf636c532d091b4283a85236b3a239a860c9289bc42e32d1b383f","target":"graph","created_at":"2026-05-18T00:00:33Z","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 that the law of the minimum $m:=\\min_{t\\in[0,1]} \\xi(t)$ of the solution $\\xi$ to a one-dimensional ODE with good nonlinearity has continuous density with respect to the Lebesgue measure. As a byproduct of the procedure, we show that the sets $ \\{ x\\in C([0,1]):\\; \\min x > r\\}$ have finite perimeter with respect to the law $\\nu$ of the solution $\\xi(\\cdot)$ in $L^2(0,1)$.","authors_text":"Alessandra Lunardi, Giuseppe Da Prato, Luciano Tubaro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-16T17:39:07Z","title":"On the law of the minimum of the solutions to a class of unidimensional SDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06935","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":"sha256:5e009b9550744d607d98e5220bf907d52dffedf6abe1f113f7d99b71a168d0d5","target":"record","created_at":"2026-05-18T00:00:33Z","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":"cf6be2e030616fb8f2b1f3a62ad6054eee025e634060b20c1dcc38d6eec2b623","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-16T17:39:07Z","title_canon_sha256":"1f5642683a51d976fc6dfae417de2a543933ee741b7d10c8c5f5b5eddf9a40d8"},"schema_version":"1.0","source":{"id":"1811.06935","kind":"arxiv","version":1}},"canonical_sha256":"17d06553ac44de08197eff49879af131c0aa04d610f132c95af83a3edd397da5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17d06553ac44de08197eff49879af131c0aa04d610f132c95af83a3edd397da5","first_computed_at":"2026-05-18T00:00:33.405215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:33.405215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dbjb8bfMNH8tZFa3Uu/R8ZifcCX7aO5CBDzJ0YJ7WT9LuP+/MoP+DAwPyoKQpPTmDpevQe0b9NeEae8esiKVDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:33.405690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.06935","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e009b9550744d607d98e5220bf907d52dffedf6abe1f113f7d99b71a168d0d5","sha256:d9395141fdebf636c532d091b4283a85236b3a239a860c9289bc42e32d1b383f"],"state_sha256":"4622569bc8dcc194ceb3df766feb73bc226e4bdc2faad8c8baea21d3f26cab75"}