{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:3RVZTBSMXEFCS4Z767SVP37V2N","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":"2c57ce6a6da453f55a1f97e180bc91d459aededff9835b13c99ca09f4e158e85","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-04T01:29:29Z","title_canon_sha256":"3c9e55648344c73c07c030c557ff9f6acf24fc6cce761a9981950ef5dfc94854"},"schema_version":"1.0","source":{"id":"2412.02948","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.02948","created_at":"2026-07-05T09:44:55Z"},{"alias_kind":"arxiv_version","alias_value":"2412.02948v2","created_at":"2026-07-05T09:44:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.02948","created_at":"2026-07-05T09:44:55Z"},{"alias_kind":"pith_short_12","alias_value":"3RVZTBSMXEFC","created_at":"2026-07-05T09:44:55Z"},{"alias_kind":"pith_short_16","alias_value":"3RVZTBSMXEFCS4Z7","created_at":"2026-07-05T09:44:55Z"},{"alias_kind":"pith_short_8","alias_value":"3RVZTBSM","created_at":"2026-07-05T09:44:55Z"}],"graph_snapshots":[{"event_id":"sha256:402ff429110d77ff2300fdc526b3e1f006c11730e4ffe00c9450cdc2365d8a91","target":"graph","created_at":"2026-07-05T09:44:55Z","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/2412.02948/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study properties of causal couplings for probability measures on the space of continuous functions. We first provide a characterization of bicausal couplings between weak solutions of stochastic differential equations. We then provide a complete description of all such bicausal Monge couplings. In particular, we show that bicausal Monge couplings of $d$-dimensional Wiener measures are induced by stochastic integrals of rotation-valued integrands. As an application, we give necessary and sufficient conditions for bicausal couplings to be induced by Monge maps and show that such bicausal Mong","authors_text":"Fang Rui Lim, Rama Cont","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-04T01:29:29Z","title":"Causal transport on path space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.02948","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:f9b8a1445c6391b85ebc50d2835f1b1b91489e4fa3dce64009b2588b9e8029bb","target":"record","created_at":"2026-07-05T09:44:55Z","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":"2c57ce6a6da453f55a1f97e180bc91d459aededff9835b13c99ca09f4e158e85","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-04T01:29:29Z","title_canon_sha256":"3c9e55648344c73c07c030c557ff9f6acf24fc6cce761a9981950ef5dfc94854"},"schema_version":"1.0","source":{"id":"2412.02948","kind":"arxiv","version":2}},"canonical_sha256":"dc6b99864cb90a29733ff7e557eff5d35bcedb692dbadc9405d987d5a1ea2767","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc6b99864cb90a29733ff7e557eff5d35bcedb692dbadc9405d987d5a1ea2767","first_computed_at":"2026-07-05T09:44:55.527973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:44:55.527973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cs80AMd934vpwyxv22iCqdAnPGcGoi2bWXdQ/h3n7xOdUGWKDgqpbsbnozab6KHMAkiIfcADojASNDp48hHbCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:44:55.528459Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.02948","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9b8a1445c6391b85ebc50d2835f1b1b91489e4fa3dce64009b2588b9e8029bb","sha256:402ff429110d77ff2300fdc526b3e1f006c11730e4ffe00c9450cdc2365d8a91"],"state_sha256":"93013c2e69f404946c3c51e3a51420592f6dd928fb0a913c2a9863deee36f347"}