{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:54USS6MIQRB7MURH4Y2XCFZFLA","short_pith_number":"pith:54USS6MI","schema_version":"1.0","canonical_sha256":"ef292979888443f65227e63571172558202f1667107c535feddbee037a45d101","source":{"kind":"arxiv","id":"2309.11181","version":1},"attestation_state":"computed","paper":{"title":"The Bass functional of martingale transport","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bertram Tschiderer, Julio Backhoff-Veraguas, Walter Schachermayer","submitted_at":"2023-09-20T10:06:33Z","abstract_excerpt":"An interesting question in the field of martingale optimal transport, is to determine the martingale with prescribed initial and terminal marginals which is most correlated to Brownian motion. Under a necessary and sufficient irreducibility condition, the answer to this question is given by a $\\textit{Bass martingale}$. At an intuitive level, the latter can be imagined as an order-preserving and martingale-preserving space transformation of an underlying Brownian motion starting with an initial law $\\alpha$ which is tuned to ensure the marginal constraints.\n  In this article we study how to de"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2309.11181","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-09-20T10:06:33Z","cross_cats_sorted":[],"title_canon_sha256":"09edebfe1928130584b71ea9abb367b6e5c492a8c0ee3f3a844a2bbefd55fd04","abstract_canon_sha256":"c635ace6548ae0da92a257f3663d422e3cab6d2e3a684d90bc037c3e3d5679cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:52:32.378493Z","signature_b64":"SuL5q/VRoXC93CnQGPZfLlsFSbqiE2L59fOTD/RlJpiX1ZyGmBE69kGt9Bti+Cdn3koGfTdqoCLGs+cPglyyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef292979888443f65227e63571172558202f1667107c535feddbee037a45d101","last_reissued_at":"2026-07-05T06:52:32.378025Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:52:32.378025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Bass functional of martingale transport","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bertram Tschiderer, Julio Backhoff-Veraguas, Walter Schachermayer","submitted_at":"2023-09-20T10:06:33Z","abstract_excerpt":"An interesting question in the field of martingale optimal transport, is to determine the martingale with prescribed initial and terminal marginals which is most correlated to Brownian motion. Under a necessary and sufficient irreducibility condition, the answer to this question is given by a $\\textit{Bass martingale}$. At an intuitive level, the latter can be imagined as an order-preserving and martingale-preserving space transformation of an underlying Brownian motion starting with an initial law $\\alpha$ which is tuned to ensure the marginal constraints.\n  In this article we study how to de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.11181","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.11181/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2309.11181","created_at":"2026-07-05T06:52:32.378085+00:00"},{"alias_kind":"arxiv_version","alias_value":"2309.11181v1","created_at":"2026-07-05T06:52:32.378085+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.11181","created_at":"2026-07-05T06:52:32.378085+00:00"},{"alias_kind":"pith_short_12","alias_value":"54USS6MIQRB7","created_at":"2026-07-05T06:52:32.378085+00:00"},{"alias_kind":"pith_short_16","alias_value":"54USS6MIQRB7MURH","created_at":"2026-07-05T06:52:32.378085+00:00"},{"alias_kind":"pith_short_8","alias_value":"54USS6MI","created_at":"2026-07-05T06:52:32.378085+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.01299","citing_title":"Bridging classical and martingale Schr\\\"odinger bridges","ref_index":12,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/54USS6MIQRB7MURH4Y2XCFZFLA","json":"https://pith.science/pith/54USS6MIQRB7MURH4Y2XCFZFLA.json","graph_json":"https://pith.science/api/pith-number/54USS6MIQRB7MURH4Y2XCFZFLA/graph.json","events_json":"https://pith.science/api/pith-number/54USS6MIQRB7MURH4Y2XCFZFLA/events.json","paper":"https://pith.science/paper/54USS6MI"},"agent_actions":{"view_html":"https://pith.science/pith/54USS6MIQRB7MURH4Y2XCFZFLA","download_json":"https://pith.science/pith/54USS6MIQRB7MURH4Y2XCFZFLA.json","view_paper":"https://pith.science/paper/54USS6MI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2309.11181&json=true","fetch_graph":"https://pith.science/api/pith-number/54USS6MIQRB7MURH4Y2XCFZFLA/graph.json","fetch_events":"https://pith.science/api/pith-number/54USS6MIQRB7MURH4Y2XCFZFLA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/54USS6MIQRB7MURH4Y2XCFZFLA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/54USS6MIQRB7MURH4Y2XCFZFLA/action/storage_attestation","attest_author":"https://pith.science/pith/54USS6MIQRB7MURH4Y2XCFZFLA/action/author_attestation","sign_citation":"https://pith.science/pith/54USS6MIQRB7MURH4Y2XCFZFLA/action/citation_signature","submit_replication":"https://pith.science/pith/54USS6MIQRB7MURH4Y2XCFZFLA/action/replication_record"}},"created_at":"2026-07-05T06:52:32.378085+00:00","updated_at":"2026-07-05T06:52:32.378085+00:00"}