{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HNWP5G5ZFZGLD3SXBVEAW374JZ","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":"1a80c56f4af40b0e21b7c45d08df9dc9cabdce391bba768c44e9418e02aa2329","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-08T14:08:33Z","title_canon_sha256":"acb12b268d2096b52d11f3e957b92f56e7537fcb0aee254a1e25995481b2e4da"},"schema_version":"1.0","source":{"id":"1609.02438","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02438","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02438v2","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02438","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"HNWP5G5ZFZGL","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HNWP5G5ZFZGLD3SX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HNWP5G5Z","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:3827b49cbc4a8c0e76eacfaf51676f0a8b227b610ea88f565b57ba8f0260a0a4","target":"graph","created_at":"2026-05-18T00:41:53Z","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 an infinite dimensional integration by parts formula on the law of the modulus of the Brownian bridge $BB=(BB_t)_{0 \\leq t \\leq 1}$ from $0$ to $0$ in use of methods from white noise analysis and Dirichlet form theory. Additionally to the usual drift term, this formula contains a distribution which is constructed in the space of Hida distributions by means of a Wick product with Donsker's delta (which correlates with the local time of $|BB|$ at zero). This additional distribution corresponds to the reflection at zero caused by the modulus.","authors_text":"Martin Grothaus, Robert Vo{\\ss}hall","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-08T14:08:33Z","title":"Integration by parts on the law of the modulus of the Brownian bridge"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02438","kind":"arxiv","version":2},"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:cba2862e4c86206ddc9ee9d4d9a738bd8a4364cbb455b9b865836317fbc460ac","target":"record","created_at":"2026-05-18T00:41:53Z","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":"1a80c56f4af40b0e21b7c45d08df9dc9cabdce391bba768c44e9418e02aa2329","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-08T14:08:33Z","title_canon_sha256":"acb12b268d2096b52d11f3e957b92f56e7537fcb0aee254a1e25995481b2e4da"},"schema_version":"1.0","source":{"id":"1609.02438","kind":"arxiv","version":2}},"canonical_sha256":"3b6cfe9bb92e4cb1ee570d480b6ffc4e458023fbc250a670e2a8da554f83d057","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b6cfe9bb92e4cb1ee570d480b6ffc4e458023fbc250a670e2a8da554f83d057","first_computed_at":"2026-05-18T00:41:53.502488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:53.502488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I2L8Nmn0EJYpxn2e2B8PzYqV87UvsnOvhoIR7VWWV2imBSr52A2jsUozhDxuU09oOP0/U3U9NXZNFE71wfTACA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:53.503198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02438","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cba2862e4c86206ddc9ee9d4d9a738bd8a4364cbb455b9b865836317fbc460ac","sha256:3827b49cbc4a8c0e76eacfaf51676f0a8b227b610ea88f565b57ba8f0260a0a4"],"state_sha256":"2e73f04de43f11c1e7fc048bac21a414d2e84a38ce2bbf0c491a73d9e4c0a28a"}