{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:4TIRLT65RADFDDRNKNB334NBTA","short_pith_number":"pith:4TIRLT65","canonical_record":{"source":{"id":"2508.17641","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-08-25T04:07:40Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"db035fc436956745d5eb17ff5b39cebe88094e4bf3838d031546c3657eb6e0a2","abstract_canon_sha256":"228f155aab6ea078c8651b9e0ef160feeacaf69b8256e7f4dbc752214208cefd"},"schema_version":"1.0"},"canonical_sha256":"e4d115cfdd8806518e2d5343bdf1a198365cf47e82205626fc69c6405cbfa41c","source":{"kind":"arxiv","id":"2508.17641","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.17641","created_at":"2026-07-05T11:58:45Z"},{"alias_kind":"arxiv_version","alias_value":"2508.17641v1","created_at":"2026-07-05T11:58:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.17641","created_at":"2026-07-05T11:58:45Z"},{"alias_kind":"pith_short_12","alias_value":"4TIRLT65RADF","created_at":"2026-07-05T11:58:45Z"},{"alias_kind":"pith_short_16","alias_value":"4TIRLT65RADFDDRN","created_at":"2026-07-05T11:58:45Z"},{"alias_kind":"pith_short_8","alias_value":"4TIRLT65","created_at":"2026-07-05T11:58:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:4TIRLT65RADFDDRNKNB334NBTA","target":"record","payload":{"canonical_record":{"source":{"id":"2508.17641","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-08-25T04:07:40Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"db035fc436956745d5eb17ff5b39cebe88094e4bf3838d031546c3657eb6e0a2","abstract_canon_sha256":"228f155aab6ea078c8651b9e0ef160feeacaf69b8256e7f4dbc752214208cefd"},"schema_version":"1.0"},"canonical_sha256":"e4d115cfdd8806518e2d5343bdf1a198365cf47e82205626fc69c6405cbfa41c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:58:45.074916Z","signature_b64":"kxb3KhRhMo/mi1oqnPYG//obNVdQgrGpvH6OtL9RQSlb2kxApPEi8wxHIrPLJHj/OOzvcizZ0Egsog3vW5RGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4d115cfdd8806518e2d5343bdf1a198365cf47e82205626fc69c6405cbfa41c","last_reissued_at":"2026-07-05T11:58:45.074441Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:58:45.074441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.17641","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:58:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mHJCWoltid334pcq5y/U0Tk0v2w7yTswK1BaOtqYTKl6s3Yx1rUcFlolq0OQbtNbFR+MMfXEt9mSkpNkU05DBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T19:49:39.049996Z"},"content_sha256":"f27366f74c881f6de4682c4b300c3ce1c3c4edd05620839af2c49c26b3328e17","schema_version":"1.0","event_id":"sha256:f27366f74c881f6de4682c4b300c3ce1c3c4edd05620839af2c49c26b3328e17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:4TIRLT65RADFDDRNKNB334NBTA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An efficient algorithm for entropic optimal transport under martingale-type constraints","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Holakou Rahmanian, Lexing Ying, Michael Shavlovsky, Tesi Xiao, Xun Tang","submitted_at":"2025-08-25T04:07:40Z","abstract_excerpt":"This work introduces novel computational methods for entropic optimal transport (OT) problems under martingale-type conditions. The considered problems include the discrete martingale optimal transport (MOT) problem. Moreover, as the (super-)martingale conditions are equivalent to row-wise (in-)equality constraints on the coupling matrix, our work applies to a prevalent class of OT problems with structural constraints. Inspired by the recent empirical success of Sinkhorn-type algorithms, we propose an entropic formulation for the MOT problem and introduce Sinkhorn-type algorithms with sparse N"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.17641","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/2508.17641/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:58:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O7Y83aUBfnu6FJl30tw7SV5hjao6YlO7jiOdNnX+GMdoSJZiPdHJkXPY2mn3dlsOeYKUgBex0/4rV2fBGxk7Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T19:49:39.050494Z"},"content_sha256":"61b7f8666d859ab8e322a760b5310bac493b7a3b56a4d615e5caafb006040346","schema_version":"1.0","event_id":"sha256:61b7f8666d859ab8e322a760b5310bac493b7a3b56a4d615e5caafb006040346"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4TIRLT65RADFDDRNKNB334NBTA/bundle.json","state_url":"https://pith.science/pith/4TIRLT65RADFDDRNKNB334NBTA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4TIRLT65RADFDDRNKNB334NBTA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-20T19:49:39Z","links":{"resolver":"https://pith.science/pith/4TIRLT65RADFDDRNKNB334NBTA","bundle":"https://pith.science/pith/4TIRLT65RADFDDRNKNB334NBTA/bundle.json","state":"https://pith.science/pith/4TIRLT65RADFDDRNKNB334NBTA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4TIRLT65RADFDDRNKNB334NBTA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4TIRLT65RADFDDRNKNB334NBTA","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":"228f155aab6ea078c8651b9e0ef160feeacaf69b8256e7f4dbc752214208cefd","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-08-25T04:07:40Z","title_canon_sha256":"db035fc436956745d5eb17ff5b39cebe88094e4bf3838d031546c3657eb6e0a2"},"schema_version":"1.0","source":{"id":"2508.17641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.17641","created_at":"2026-07-05T11:58:45Z"},{"alias_kind":"arxiv_version","alias_value":"2508.17641v1","created_at":"2026-07-05T11:58:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.17641","created_at":"2026-07-05T11:58:45Z"},{"alias_kind":"pith_short_12","alias_value":"4TIRLT65RADF","created_at":"2026-07-05T11:58:45Z"},{"alias_kind":"pith_short_16","alias_value":"4TIRLT65RADFDDRN","created_at":"2026-07-05T11:58:45Z"},{"alias_kind":"pith_short_8","alias_value":"4TIRLT65","created_at":"2026-07-05T11:58:45Z"}],"graph_snapshots":[{"event_id":"sha256:61b7f8666d859ab8e322a760b5310bac493b7a3b56a4d615e5caafb006040346","target":"graph","created_at":"2026-07-05T11:58:45Z","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/2508.17641/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work introduces novel computational methods for entropic optimal transport (OT) problems under martingale-type conditions. The considered problems include the discrete martingale optimal transport (MOT) problem. Moreover, as the (super-)martingale conditions are equivalent to row-wise (in-)equality constraints on the coupling matrix, our work applies to a prevalent class of OT problems with structural constraints. Inspired by the recent empirical success of Sinkhorn-type algorithms, we propose an entropic formulation for the MOT problem and introduce Sinkhorn-type algorithms with sparse N","authors_text":"Holakou Rahmanian, Lexing Ying, Michael Shavlovsky, Tesi Xiao, Xun Tang","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-08-25T04:07:40Z","title":"An efficient algorithm for entropic optimal transport under martingale-type constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.17641","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:f27366f74c881f6de4682c4b300c3ce1c3c4edd05620839af2c49c26b3328e17","target":"record","created_at":"2026-07-05T11:58:45Z","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":"228f155aab6ea078c8651b9e0ef160feeacaf69b8256e7f4dbc752214208cefd","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-08-25T04:07:40Z","title_canon_sha256":"db035fc436956745d5eb17ff5b39cebe88094e4bf3838d031546c3657eb6e0a2"},"schema_version":"1.0","source":{"id":"2508.17641","kind":"arxiv","version":1}},"canonical_sha256":"e4d115cfdd8806518e2d5343bdf1a198365cf47e82205626fc69c6405cbfa41c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4d115cfdd8806518e2d5343bdf1a198365cf47e82205626fc69c6405cbfa41c","first_computed_at":"2026-07-05T11:58:45.074441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:58:45.074441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kxb3KhRhMo/mi1oqnPYG//obNVdQgrGpvH6OtL9RQSlb2kxApPEi8wxHIrPLJHj/OOzvcizZ0Egsog3vW5RGCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:58:45.074916Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.17641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f27366f74c881f6de4682c4b300c3ce1c3c4edd05620839af2c49c26b3328e17","sha256:61b7f8666d859ab8e322a760b5310bac493b7a3b56a4d615e5caafb006040346"],"state_sha256":"6c298dd360d43314a8b2f34430dd7d2c91195555ee57717edaea19c7badf9029"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HNgNpuqCxLeBfqHvrJNZSbqVQDj6P7mKCBL6ia71YRqb5R5fZrPg3OUo3lRxAX7kIjTRQzllKiQJtzhb6wwECQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T19:49:39.054165Z","bundle_sha256":"7ad4133730bb0faa7d7d8fc20c16d0c4549d8ffb0a2bffb3f847f26896235713"}}