{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:LAIWZTZ6IJ5ZRHJQO4U4PIAYAR","short_pith_number":"pith:LAIWZTZ6","canonical_record":{"source":{"id":"2403.20238","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-03-29T15:31:13Z","cross_cats_sorted":["cs.NA","math.AP","math.NA","math.PR"],"title_canon_sha256":"5bba77d66ce91a8af13f76a6bd84f482958613821dacb9aec824e87f29bd5dd1","abstract_canon_sha256":"c8c550487add1a12ecc1e822d24a86c95a0c2ca27153c920b268b8b1d5d5f61e"},"schema_version":"1.0"},"canonical_sha256":"58116ccf3e427b989d307729c7a01804517de86ac5be700033e7891256d8fe1e","source":{"kind":"arxiv","id":"2403.20238","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.20238","created_at":"2026-07-05T08:02:16Z"},{"alias_kind":"arxiv_version","alias_value":"2403.20238v1","created_at":"2026-07-05T08:02:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.20238","created_at":"2026-07-05T08:02:16Z"},{"alias_kind":"pith_short_12","alias_value":"LAIWZTZ6IJ5Z","created_at":"2026-07-05T08:02:16Z"},{"alias_kind":"pith_short_16","alias_value":"LAIWZTZ6IJ5ZRHJQ","created_at":"2026-07-05T08:02:16Z"},{"alias_kind":"pith_short_8","alias_value":"LAIWZTZ6","created_at":"2026-07-05T08:02:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:LAIWZTZ6IJ5ZRHJQO4U4PIAYAR","target":"record","payload":{"canonical_record":{"source":{"id":"2403.20238","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-03-29T15:31:13Z","cross_cats_sorted":["cs.NA","math.AP","math.NA","math.PR"],"title_canon_sha256":"5bba77d66ce91a8af13f76a6bd84f482958613821dacb9aec824e87f29bd5dd1","abstract_canon_sha256":"c8c550487add1a12ecc1e822d24a86c95a0c2ca27153c920b268b8b1d5d5f61e"},"schema_version":"1.0"},"canonical_sha256":"58116ccf3e427b989d307729c7a01804517de86ac5be700033e7891256d8fe1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:02:16.223521Z","signature_b64":"5Iq6QXEHvsDCyLBcQegHzj93WZGabXmB4OvQCUuLTSAhjQsQUfgJ/Mr6f69eaIhxhINTMEsIf3Ja3DZa3sUDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58116ccf3e427b989d307729c7a01804517de86ac5be700033e7891256d8fe1e","last_reissued_at":"2026-07-05T08:02:16.223126Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:02:16.223126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.20238","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":"2026-07-05T08:02:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HXgOyN5gAwBj0iKsC38sMC2j/uI5n4iQU/NXL7OzQMbh5vW3grp9JzaIdSrdmGOO66t3uJCocm3n/HBxmGhnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T15:48:53.851915Z"},"content_sha256":"e54798b5cd8f5206bc194e0eb72128cef4f30a412de273bf3161b3f3e76e09eb","schema_version":"1.0","event_id":"sha256:e54798b5cd8f5206bc194e0eb72128cef4f30a412de273bf3161b3f3e76e09eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:LAIWZTZ6IJ5ZRHJQO4U4PIAYAR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An ordinary differential equation for entropic optimal transport and its linearly constrained variants","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.AP","math.NA","math.PR"],"primary_cat":"math.OC","authors_text":"Brendan Pass, Joshua Zoen-Git Hiew, Luca Nenna","submitted_at":"2024-03-29T15:31:13Z","abstract_excerpt":"We characterize the solution to the entropically regularized optimal transport problem by a well-posed ordinary differential equation (ODE). Our approach works for discrete marginals and general cost functions, and in addition to two marginal problems, applies to multi-marginal problems and those with additional linear constraints. Solving the ODE gives a new numerical method to solve the optimal transport problem, which has the advantage of yielding the solution for all intermediate values of the ODE parameter (which is equivalent to the usual regularization parameter). We illustrate this met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.20238","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/2403.20238/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":"2026-07-05T08:02:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hq2WsBEcAZ/xruuTwX/+GrCWwDhKfiiRvwinNeXeBCrUudaQuDeUTp+7cREPvmLK0x1k6/h8i+FmlJEjZQ2bDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T15:48:53.853482Z"},"content_sha256":"34ec36952631136d85f7fac349816a75c2db6f312f62e55faeaf65d5d30ab38b","schema_version":"1.0","event_id":"sha256:34ec36952631136d85f7fac349816a75c2db6f312f62e55faeaf65d5d30ab38b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LAIWZTZ6IJ5ZRHJQO4U4PIAYAR/bundle.json","state_url":"https://pith.science/pith/LAIWZTZ6IJ5ZRHJQO4U4PIAYAR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LAIWZTZ6IJ5ZRHJQO4U4PIAYAR/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":"2026-08-18T15:48:53Z","links":{"resolver":"https://pith.science/pith/LAIWZTZ6IJ5ZRHJQO4U4PIAYAR","bundle":"https://pith.science/pith/LAIWZTZ6IJ5ZRHJQO4U4PIAYAR/bundle.json","state":"https://pith.science/pith/LAIWZTZ6IJ5ZRHJQO4U4PIAYAR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LAIWZTZ6IJ5ZRHJQO4U4PIAYAR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LAIWZTZ6IJ5ZRHJQO4U4PIAYAR","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":"c8c550487add1a12ecc1e822d24a86c95a0c2ca27153c920b268b8b1d5d5f61e","cross_cats_sorted":["cs.NA","math.AP","math.NA","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-03-29T15:31:13Z","title_canon_sha256":"5bba77d66ce91a8af13f76a6bd84f482958613821dacb9aec824e87f29bd5dd1"},"schema_version":"1.0","source":{"id":"2403.20238","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.20238","created_at":"2026-07-05T08:02:16Z"},{"alias_kind":"arxiv_version","alias_value":"2403.20238v1","created_at":"2026-07-05T08:02:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.20238","created_at":"2026-07-05T08:02:16Z"},{"alias_kind":"pith_short_12","alias_value":"LAIWZTZ6IJ5Z","created_at":"2026-07-05T08:02:16Z"},{"alias_kind":"pith_short_16","alias_value":"LAIWZTZ6IJ5ZRHJQ","created_at":"2026-07-05T08:02:16Z"},{"alias_kind":"pith_short_8","alias_value":"LAIWZTZ6","created_at":"2026-07-05T08:02:16Z"}],"graph_snapshots":[{"event_id":"sha256:34ec36952631136d85f7fac349816a75c2db6f312f62e55faeaf65d5d30ab38b","target":"graph","created_at":"2026-07-05T08:02:16Z","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/2403.20238/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We characterize the solution to the entropically regularized optimal transport problem by a well-posed ordinary differential equation (ODE). Our approach works for discrete marginals and general cost functions, and in addition to two marginal problems, applies to multi-marginal problems and those with additional linear constraints. Solving the ODE gives a new numerical method to solve the optimal transport problem, which has the advantage of yielding the solution for all intermediate values of the ODE parameter (which is equivalent to the usual regularization parameter). We illustrate this met","authors_text":"Brendan Pass, Joshua Zoen-Git Hiew, Luca Nenna","cross_cats":["cs.NA","math.AP","math.NA","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-03-29T15:31:13Z","title":"An ordinary differential equation for entropic optimal transport and its linearly constrained variants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.20238","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:e54798b5cd8f5206bc194e0eb72128cef4f30a412de273bf3161b3f3e76e09eb","target":"record","created_at":"2026-07-05T08:02:16Z","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":"c8c550487add1a12ecc1e822d24a86c95a0c2ca27153c920b268b8b1d5d5f61e","cross_cats_sorted":["cs.NA","math.AP","math.NA","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-03-29T15:31:13Z","title_canon_sha256":"5bba77d66ce91a8af13f76a6bd84f482958613821dacb9aec824e87f29bd5dd1"},"schema_version":"1.0","source":{"id":"2403.20238","kind":"arxiv","version":1}},"canonical_sha256":"58116ccf3e427b989d307729c7a01804517de86ac5be700033e7891256d8fe1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58116ccf3e427b989d307729c7a01804517de86ac5be700033e7891256d8fe1e","first_computed_at":"2026-07-05T08:02:16.223126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:02:16.223126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Iq6QXEHvsDCyLBcQegHzj93WZGabXmB4OvQCUuLTSAhjQsQUfgJ/Mr6f69eaIhxhINTMEsIf3Ja3DZa3sUDBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:02:16.223521Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.20238","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e54798b5cd8f5206bc194e0eb72128cef4f30a412de273bf3161b3f3e76e09eb","sha256:34ec36952631136d85f7fac349816a75c2db6f312f62e55faeaf65d5d30ab38b"],"state_sha256":"9f4ce5df1f1ff32b3cf0ebda2bf60dddb0047831e8b03ee15c6455d158721ffa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"38+6GqiTlk4qjLlyMAVUZPk2Ia7qESxW4KyjZ2ErYgDBNtxUrL0RE5g3pFZURuXW1G926+uDqmGB2UJLE0ptCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T15:48:53.861308Z","bundle_sha256":"68daeaf9f902c2524a80d65761d6849c1730586f7e5e2f7b0f2f93486ec48fe9"}}