{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:PZ5UHMHTAVUUGXG5XVG2GQCRVM","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":"bc2e51f4b86208c3a7e2827c1e853ab9bc8dfa4236c2275d42c89ba14d63e173","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-05-24T03:22:56Z","title_canon_sha256":"4f1a48731969bb23ce4734e7bd0eb220d4d3a89beb5999094baef5640d7d9db5"},"schema_version":"1.0","source":{"id":"0805.3740","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.3740","created_at":"2026-07-04T15:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"0805.3740v1","created_at":"2026-07-04T15:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.3740","created_at":"2026-07-04T15:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"PZ5UHMHTAVUU","created_at":"2026-07-04T15:11:47Z"},{"alias_kind":"pith_short_16","alias_value":"PZ5UHMHTAVUUGXG5","created_at":"2026-07-04T15:11:47Z"},{"alias_kind":"pith_short_8","alias_value":"PZ5UHMHT","created_at":"2026-07-04T15:11:47Z"}],"graph_snapshots":[{"event_id":"sha256:dd2c0b9dd2f3e3c091757f36bd76e23bb9d026f7f08b158b536e6e45011389ed","target":"graph","created_at":"2026-07-04T15:11:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0805.3740/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that a sequence of semi-discrete approximations converges to a multiplicative functional for reflected Brownian motion, which intuitively represents the Lyapunov exponent for the corresponding stochastic flow. The method of proof is based on a study of the deterministic version of the problem and the excursion theory.","authors_text":"John M. Lee, Krzysztof Burdzy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-05-24T03:22:56Z","title":"Multiplicative functional for reflected Brownian motion via deterministic ODE"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.3740","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":"sha256:4f29f67c27c64bcc68cc551efa648387f81b1895851e4e9b359b04ecccf15613","target":"record","created_at":"2026-07-04T15:11:47Z","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":"bc2e51f4b86208c3a7e2827c1e853ab9bc8dfa4236c2275d42c89ba14d63e173","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-05-24T03:22:56Z","title_canon_sha256":"4f1a48731969bb23ce4734e7bd0eb220d4d3a89beb5999094baef5640d7d9db5"},"schema_version":"1.0","source":{"id":"0805.3740","kind":"arxiv","version":1}},"canonical_sha256":"7e7b43b0f30569435cddbd4da34051ab27060dd57ec675ccfdd9630b465da93c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e7b43b0f30569435cddbd4da34051ab27060dd57ec675ccfdd9630b465da93c","first_computed_at":"2026-07-04T15:11:47.345131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:11:47.345131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xQJGEq49sJ5UWwSRD+7HwbKMvuZCTZHkIrSoCCLEKxV/zEe6iR96YcSsoj43PoeUF9T0T/G/LqbsGjUCwJR5CA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:11:47.345535Z","signed_message":"canonical_sha256_bytes"},"source_id":"0805.3740","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f29f67c27c64bcc68cc551efa648387f81b1895851e4e9b359b04ecccf15613","sha256:dd2c0b9dd2f3e3c091757f36bd76e23bb9d026f7f08b158b536e6e45011389ed"],"state_sha256":"42863eb1ae260447e9fb502d514599e00814e2e2567500dad282f815b2e5666f"}