{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:A4L66EQLB5YMGDGDCJQQXMAMGT","short_pith_number":"pith:A4L66EQL","canonical_record":{"source":{"id":"2406.03090","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-06-05T09:29:26Z","cross_cats_sorted":[],"title_canon_sha256":"3d1ab7ef21a72be03d9f455db229fe08810b8e94f6b714f18e1c6a3f7ec14c17","abstract_canon_sha256":"7c8fe3b5a287974bfcf2156955acfd94496db96230c8e5bbdfeaa6c213a4de30"},"schema_version":"1.0"},"canonical_sha256":"0717ef120b0f70c30cc312610bb00c34db3ca265391a2ffa9a395c1cccb4da77","source":{"kind":"arxiv","id":"2406.03090","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.03090","created_at":"2026-07-05T11:29:48Z"},{"alias_kind":"arxiv_version","alias_value":"2406.03090v1","created_at":"2026-07-05T11:29:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.03090","created_at":"2026-07-05T11:29:48Z"},{"alias_kind":"pith_short_12","alias_value":"A4L66EQLB5YM","created_at":"2026-07-05T11:29:48Z"},{"alias_kind":"pith_short_16","alias_value":"A4L66EQLB5YMGDGD","created_at":"2026-07-05T11:29:48Z"},{"alias_kind":"pith_short_8","alias_value":"A4L66EQL","created_at":"2026-07-05T11:29:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:A4L66EQLB5YMGDGDCJQQXMAMGT","target":"record","payload":{"canonical_record":{"source":{"id":"2406.03090","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-06-05T09:29:26Z","cross_cats_sorted":[],"title_canon_sha256":"3d1ab7ef21a72be03d9f455db229fe08810b8e94f6b714f18e1c6a3f7ec14c17","abstract_canon_sha256":"7c8fe3b5a287974bfcf2156955acfd94496db96230c8e5bbdfeaa6c213a4de30"},"schema_version":"1.0"},"canonical_sha256":"0717ef120b0f70c30cc312610bb00c34db3ca265391a2ffa9a395c1cccb4da77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:29:48.350115Z","signature_b64":"HIHfLhhERlsKRCDfUOxWdvBAg2nRsRFDy05Taq25QaOCmFF7jnGRBGTDXvL9edCthlrbV8NDtZEB7KaW2CZTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0717ef120b0f70c30cc312610bb00c34db3ca265391a2ffa9a395c1cccb4da77","last_reissued_at":"2026-07-05T11:29:48.349582Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:29:48.349582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.03090","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":"2026-07-05T11:29:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GLj9+eRnMynp+TTOsJURAJYUEFuV6vPp2QL+mlL1Zg/5XJcgDV7+Id0tVWqxFsvXB1shJOOUqS18C/2pmay4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T23:58:24.758850Z"},"content_sha256":"8342ffc4d706011bd2b3d23863b10fc1678719048b724d33c183517127833f5e","schema_version":"1.0","event_id":"sha256:8342ffc4d706011bd2b3d23863b10fc1678719048b724d33c183517127833f5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:A4L66EQLB5YMGDGDCJQQXMAMGT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Optimal Production Transport: Model and Algorithm","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hao Wu, Jie Fan, Tianhao Wu","submitted_at":"2024-06-05T09:29:26Z","abstract_excerpt":"In this paper, we propose the optimal production transport model, which is an extension of the classical optimal transport model. We observe in economics, the production of the factories can always be adjusted within a certain range, while the classical optimal transport does not take this situation into account. Therefore, differing from the classical optimal transport, one of the marginals is allowed to vary within a certain range in our proposed model. To address this, we introduce a multiple relaxation optimal production transport model and propose the generalized alternating Sinkhorn algo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.03090","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/2406.03090/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":"2026-07-05T11:29:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8y9Pc7h2ce1haJ+VdYaE7HUaEJJlhDWO8ot/wiwRC+7JAd3J2fBV8tdmHnV317V3q/MlTliYGESoYQlOLWl9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T23:58:24.759375Z"},"content_sha256":"1c0e14f25477876c2624d0e5fa1fad76dd78fd0585ddef246fa4d323903f7060","schema_version":"1.0","event_id":"sha256:1c0e14f25477876c2624d0e5fa1fad76dd78fd0585ddef246fa4d323903f7060"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A4L66EQLB5YMGDGDCJQQXMAMGT/bundle.json","state_url":"https://pith.science/pith/A4L66EQLB5YMGDGDCJQQXMAMGT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A4L66EQLB5YMGDGDCJQQXMAMGT/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":"2026-08-05T23:58:24Z","links":{"resolver":"https://pith.science/pith/A4L66EQLB5YMGDGDCJQQXMAMGT","bundle":"https://pith.science/pith/A4L66EQLB5YMGDGDCJQQXMAMGT/bundle.json","state":"https://pith.science/pith/A4L66EQLB5YMGDGDCJQQXMAMGT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A4L66EQLB5YMGDGDCJQQXMAMGT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:A4L66EQLB5YMGDGDCJQQXMAMGT","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":"7c8fe3b5a287974bfcf2156955acfd94496db96230c8e5bbdfeaa6c213a4de30","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-06-05T09:29:26Z","title_canon_sha256":"3d1ab7ef21a72be03d9f455db229fe08810b8e94f6b714f18e1c6a3f7ec14c17"},"schema_version":"1.0","source":{"id":"2406.03090","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.03090","created_at":"2026-07-05T11:29:48Z"},{"alias_kind":"arxiv_version","alias_value":"2406.03090v1","created_at":"2026-07-05T11:29:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.03090","created_at":"2026-07-05T11:29:48Z"},{"alias_kind":"pith_short_12","alias_value":"A4L66EQLB5YM","created_at":"2026-07-05T11:29:48Z"},{"alias_kind":"pith_short_16","alias_value":"A4L66EQLB5YMGDGD","created_at":"2026-07-05T11:29:48Z"},{"alias_kind":"pith_short_8","alias_value":"A4L66EQL","created_at":"2026-07-05T11:29:48Z"}],"graph_snapshots":[{"event_id":"sha256:1c0e14f25477876c2624d0e5fa1fad76dd78fd0585ddef246fa4d323903f7060","target":"graph","created_at":"2026-07-05T11:29:48Z","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/2406.03090/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we propose the optimal production transport model, which is an extension of the classical optimal transport model. We observe in economics, the production of the factories can always be adjusted within a certain range, while the classical optimal transport does not take this situation into account. Therefore, differing from the classical optimal transport, one of the marginals is allowed to vary within a certain range in our proposed model. To address this, we introduce a multiple relaxation optimal production transport model and propose the generalized alternating Sinkhorn algo","authors_text":"Hao Wu, Jie Fan, Tianhao Wu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-06-05T09:29:26Z","title":"The Optimal Production Transport: Model and Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.03090","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":"sha256:8342ffc4d706011bd2b3d23863b10fc1678719048b724d33c183517127833f5e","target":"record","created_at":"2026-07-05T11:29:48Z","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":"7c8fe3b5a287974bfcf2156955acfd94496db96230c8e5bbdfeaa6c213a4de30","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-06-05T09:29:26Z","title_canon_sha256":"3d1ab7ef21a72be03d9f455db229fe08810b8e94f6b714f18e1c6a3f7ec14c17"},"schema_version":"1.0","source":{"id":"2406.03090","kind":"arxiv","version":1}},"canonical_sha256":"0717ef120b0f70c30cc312610bb00c34db3ca265391a2ffa9a395c1cccb4da77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0717ef120b0f70c30cc312610bb00c34db3ca265391a2ffa9a395c1cccb4da77","first_computed_at":"2026-07-05T11:29:48.349582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:29:48.349582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HIHfLhhERlsKRCDfUOxWdvBAg2nRsRFDy05Taq25QaOCmFF7jnGRBGTDXvL9edCthlrbV8NDtZEB7KaW2CZTBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:29:48.350115Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.03090","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8342ffc4d706011bd2b3d23863b10fc1678719048b724d33c183517127833f5e","sha256:1c0e14f25477876c2624d0e5fa1fad76dd78fd0585ddef246fa4d323903f7060"],"state_sha256":"7f2c0231b244ab31faa46eeab7bc84a2f3bbeccd9ba67b5e13122f72ed311f6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SVKRNplNgIUHThYr+LJhxXEw9Nv4gLv/Ck1NRxPpZB/3Tm1HHtjUiDLPf5Mh/Rtr9l7VOqQzEgNCZinFN/SoAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T23:58:24.764831Z","bundle_sha256":"7cbb2f6f79c098a8a163f419181207a03fbde3fdb2b335df3a93763ae9bc6ff9"}}