{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:CYBV2BYZWVMUHIT56BK6TBHPBH","short_pith_number":"pith:CYBV2BYZ","schema_version":"1.0","canonical_sha256":"16035d0719b55943a27df055e984ef09e744894abec7cf86dbc9d3125763f37b","source":{"kind":"arxiv","id":"1703.10588","version":2},"attestation_state":"computed","paper":{"title":"Multiperiod Martingale Transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","q-fin.MF"],"primary_cat":"math.PR","authors_text":"Florian Stebegg, Marcel Nutz, Xiaowei Tan","submitted_at":"2017-03-30T17:38:44Z","abstract_excerpt":"Consider a multiperiod optimal transport problem where distributions $\\mu_{0},\\dots,\\mu_{n}$ are prescribed and a transport corresponds to a scalar martingale $X$ with marginals $X_{t}\\sim\\mu_{t}$. We introduce particular couplings called left-monotone transports; they are characterized equivalently by a no-crossing property of their support, as simultaneous optimizers for a class of bivariate transport cost functions with a Spence--Mirrlees property, and by an order-theoretic minimality property. Left-monotone transports are unique if $\\mu_{0}$ is atomless, but not in general. In the one-peri"},"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":"1703.10588","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-30T17:38:44Z","cross_cats_sorted":["math.OC","q-fin.MF"],"title_canon_sha256":"199e22262e7e2f99c43905b18595fc86d4a98ec0e319e53f9cfe9e8f00913064","abstract_canon_sha256":"a3ccd9ef5d18cd8873a11949b98838cb68e46cf0fb404d8720f94720ed27e455"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:53.577270Z","signature_b64":"dMQ3wgFRY/utaHujkAa68FtvlaxpUt+LmnBbQlnSLhLPBGW8xlUfwR70u0MZfEtMuLxgjHmPkCBW50InnkFHDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16035d0719b55943a27df055e984ef09e744894abec7cf86dbc9d3125763f37b","last_reissued_at":"2026-05-17T23:45:53.576890Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:53.576890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiperiod Martingale Transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","q-fin.MF"],"primary_cat":"math.PR","authors_text":"Florian Stebegg, Marcel Nutz, Xiaowei Tan","submitted_at":"2017-03-30T17:38:44Z","abstract_excerpt":"Consider a multiperiod optimal transport problem where distributions $\\mu_{0},\\dots,\\mu_{n}$ are prescribed and a transport corresponds to a scalar martingale $X$ with marginals $X_{t}\\sim\\mu_{t}$. We introduce particular couplings called left-monotone transports; they are characterized equivalently by a no-crossing property of their support, as simultaneous optimizers for a class of bivariate transport cost functions with a Spence--Mirrlees property, and by an order-theoretic minimality property. Left-monotone transports are unique if $\\mu_{0}$ is atomless, but not in general. In the one-peri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10588","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1703.10588","created_at":"2026-05-17T23:45:53.576950+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.10588v2","created_at":"2026-05-17T23:45:53.576950+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10588","created_at":"2026-05-17T23:45:53.576950+00:00"},{"alias_kind":"pith_short_12","alias_value":"CYBV2BYZWVMU","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"CYBV2BYZWVMUHIT5","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"CYBV2BYZ","created_at":"2026-05-18T12:31:10.602751+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CYBV2BYZWVMUHIT56BK6TBHPBH","json":"https://pith.science/pith/CYBV2BYZWVMUHIT56BK6TBHPBH.json","graph_json":"https://pith.science/api/pith-number/CYBV2BYZWVMUHIT56BK6TBHPBH/graph.json","events_json":"https://pith.science/api/pith-number/CYBV2BYZWVMUHIT56BK6TBHPBH/events.json","paper":"https://pith.science/paper/CYBV2BYZ"},"agent_actions":{"view_html":"https://pith.science/pith/CYBV2BYZWVMUHIT56BK6TBHPBH","download_json":"https://pith.science/pith/CYBV2BYZWVMUHIT56BK6TBHPBH.json","view_paper":"https://pith.science/paper/CYBV2BYZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.10588&json=true","fetch_graph":"https://pith.science/api/pith-number/CYBV2BYZWVMUHIT56BK6TBHPBH/graph.json","fetch_events":"https://pith.science/api/pith-number/CYBV2BYZWVMUHIT56BK6TBHPBH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CYBV2BYZWVMUHIT56BK6TBHPBH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CYBV2BYZWVMUHIT56BK6TBHPBH/action/storage_attestation","attest_author":"https://pith.science/pith/CYBV2BYZWVMUHIT56BK6TBHPBH/action/author_attestation","sign_citation":"https://pith.science/pith/CYBV2BYZWVMUHIT56BK6TBHPBH/action/citation_signature","submit_replication":"https://pith.science/pith/CYBV2BYZWVMUHIT56BK6TBHPBH/action/replication_record"}},"created_at":"2026-05-17T23:45:53.576950+00:00","updated_at":"2026-05-17T23:45:53.576950+00:00"}