{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VSONFEJGU6MNOAJIX5XZGDL4HS","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":"f291b4f52bee56f168e60ed46c7d6e0a3d9088a22bf23f7a7c4849b2fa9c86ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-07T14:02:41Z","title_canon_sha256":"722098fcd7b3671e856eacb5678cfc78b1a1407081653fb1a17a24e65816878f"},"schema_version":"1.0","source":{"id":"1301.1199","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1199","created_at":"2026-05-18T03:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1199v1","created_at":"2026-05-18T03:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1199","created_at":"2026-05-18T03:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"VSONFEJGU6MN","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VSONFEJGU6MNOAJI","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VSONFEJG","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:f38ccbd4c9f4de0a16dd986752ae634c1c47e18d44ff3cf1087fbe68dc721701","target":"graph","created_at":"2026-05-18T03:37:06Z","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, on the classical Wiener space, the random variable $\\sup_{0\\le t \\le T} W_t$ admits a measure as second Malliavin derivative, whose total variation measure is finite and singular w.r.t.\\ the Wiener measure.","authors_text":"Dario Trevisan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-07T14:02:41Z","title":"BV-regularity for the Malliavin Derivative of the Maximum of the Wiener Process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1199","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:f65b821268450140fe38ba81ca10b72e77f81e55464a1c73a0bd5e3170777f89","target":"record","created_at":"2026-05-18T03:37:06Z","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":"f291b4f52bee56f168e60ed46c7d6e0a3d9088a22bf23f7a7c4849b2fa9c86ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-07T14:02:41Z","title_canon_sha256":"722098fcd7b3671e856eacb5678cfc78b1a1407081653fb1a17a24e65816878f"},"schema_version":"1.0","source":{"id":"1301.1199","kind":"arxiv","version":1}},"canonical_sha256":"ac9cd29126a798d70128bf6f930d7c3cb30d7154d4e73ca16d59ca18bfe78be0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac9cd29126a798d70128bf6f930d7c3cb30d7154d4e73ca16d59ca18bfe78be0","first_computed_at":"2026-05-18T03:37:06.499697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:06.499697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jofgE+xPu9FhNwOZd4aY5s9Y5pcOn2GnX+2CZrsKoqFpSKT3Qdd3W0ZmyQZL06lQz1wcISKsl3icdcU/JqEPDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:06.500420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1199","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f65b821268450140fe38ba81ca10b72e77f81e55464a1c73a0bd5e3170777f89","sha256:f38ccbd4c9f4de0a16dd986752ae634c1c47e18d44ff3cf1087fbe68dc721701"],"state_sha256":"7148c61680c2132271f38fbdb291f07ea8c9c9870f451fc49ad363d411bec42d"}