{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:7Z5CUCXXIMVCYIRKCPDRMDFPU2","short_pith_number":"pith:7Z5CUCXX","schema_version":"1.0","canonical_sha256":"fe7a2a0af7432a2c222a13c7160cafa6a23ac7cfff2d4773f9de92bd1371a83b","source":{"kind":"arxiv","id":"2306.11019","version":3},"attestation_state":"computed","paper":{"title":"Existence of Bass martingales and the martingale Benamou$-$Brenier problem in $\\mathbb{R}^{d}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bertram Tschiderer, Julio Backhoff-Veraguas, Mathias Beiglb\\\"ock, Walter Schachermayer","submitted_at":"2023-06-19T15:31:15Z","abstract_excerpt":"In classical optimal transport, the contributions of Benamou$-$Brenier and McCann regarding the time-dependent version of the problem are cornerstones of the field and form the basis for a variety of applications in other mathematical areas.\n  In this article, we characterize solutions to the martingale Benamou$-$Brenier problem as $\\textit{Bass martingales}$, i.e. transformations of Brownian motion through the gradient of a convex function. Our result is based on a new (static) Brenier-type theorem for a particular weak martingale optimal transport problem. As in the classical case, the struc"},"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":"2306.11019","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-06-19T15:31:15Z","cross_cats_sorted":[],"title_canon_sha256":"c5ac994ea929efd1c518b4b975f8ca4988fd7440359d011f420be71b1f28d237","abstract_canon_sha256":"f922bc45ad7bfb70d057c5d875bd8ce9722ac206ab26948e789e5262d2432a76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:41:09.863739Z","signature_b64":"cECImgo2p8tqGle44JTRbBWMSgzqyTg32BdPTf7K3Qk6G6nN1KvCqoYGdAVDKyrCunFLo07D8Q5WRXJJ/dDUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe7a2a0af7432a2c222a13c7160cafa6a23ac7cfff2d4773f9de92bd1371a83b","last_reissued_at":"2026-07-05T10:41:09.863222Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:41:09.863222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of Bass martingales and the martingale Benamou$-$Brenier problem in $\\mathbb{R}^{d}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bertram Tschiderer, Julio Backhoff-Veraguas, Mathias Beiglb\\\"ock, Walter Schachermayer","submitted_at":"2023-06-19T15:31:15Z","abstract_excerpt":"In classical optimal transport, the contributions of Benamou$-$Brenier and McCann regarding the time-dependent version of the problem are cornerstones of the field and form the basis for a variety of applications in other mathematical areas.\n  In this article, we characterize solutions to the martingale Benamou$-$Brenier problem as $\\textit{Bass martingales}$, i.e. transformations of Brownian motion through the gradient of a convex function. Our result is based on a new (static) Brenier-type theorem for a particular weak martingale optimal transport problem. As in the classical case, the struc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.11019","kind":"arxiv","version":3},"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/2306.11019/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":"2306.11019","created_at":"2026-07-05T10:41:09.863282+00:00"},{"alias_kind":"arxiv_version","alias_value":"2306.11019v3","created_at":"2026-07-05T10:41:09.863282+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.11019","created_at":"2026-07-05T10:41:09.863282+00:00"},{"alias_kind":"pith_short_12","alias_value":"7Z5CUCXXIMVC","created_at":"2026-07-05T10:41:09.863282+00:00"},{"alias_kind":"pith_short_16","alias_value":"7Z5CUCXXIMVCYIRK","created_at":"2026-07-05T10:41:09.863282+00:00"},{"alias_kind":"pith_short_8","alias_value":"7Z5CUCXX","created_at":"2026-07-05T10:41:09.863282+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.01299","citing_title":"Bridging classical and martingale Schr\\\"odinger bridges","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7Z5CUCXXIMVCYIRKCPDRMDFPU2","json":"https://pith.science/pith/7Z5CUCXXIMVCYIRKCPDRMDFPU2.json","graph_json":"https://pith.science/api/pith-number/7Z5CUCXXIMVCYIRKCPDRMDFPU2/graph.json","events_json":"https://pith.science/api/pith-number/7Z5CUCXXIMVCYIRKCPDRMDFPU2/events.json","paper":"https://pith.science/paper/7Z5CUCXX"},"agent_actions":{"view_html":"https://pith.science/pith/7Z5CUCXXIMVCYIRKCPDRMDFPU2","download_json":"https://pith.science/pith/7Z5CUCXXIMVCYIRKCPDRMDFPU2.json","view_paper":"https://pith.science/paper/7Z5CUCXX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2306.11019&json=true","fetch_graph":"https://pith.science/api/pith-number/7Z5CUCXXIMVCYIRKCPDRMDFPU2/graph.json","fetch_events":"https://pith.science/api/pith-number/7Z5CUCXXIMVCYIRKCPDRMDFPU2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7Z5CUCXXIMVCYIRKCPDRMDFPU2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7Z5CUCXXIMVCYIRKCPDRMDFPU2/action/storage_attestation","attest_author":"https://pith.science/pith/7Z5CUCXXIMVCYIRKCPDRMDFPU2/action/author_attestation","sign_citation":"https://pith.science/pith/7Z5CUCXXIMVCYIRKCPDRMDFPU2/action/citation_signature","submit_replication":"https://pith.science/pith/7Z5CUCXXIMVCYIRKCPDRMDFPU2/action/replication_record"}},"created_at":"2026-07-05T10:41:09.863282+00:00","updated_at":"2026-07-05T10:41:09.863282+00:00"}