{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:DCNA6OEOQQUYIP3RXWTIRWY5QT","short_pith_number":"pith:DCNA6OEO","schema_version":"1.0","canonical_sha256":"189a0f388e8429843f71bda688db1d84da12e15bc3d0eaf4f4729e98ae33e6e6","source":{"kind":"arxiv","id":"1312.0345","version":1},"attestation_state":"computed","paper":{"title":"Optimal Transportation for Generalized Lagrangian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.DS","authors_text":"Jianlu Zhang, Ji Li","submitted_at":"2013-12-02T06:59:35Z","abstract_excerpt":"In this paper, we study the optimal transportation for generalized Lagrangian $L=L(x, u,t)$, and consider the cost function as following: $$c(x, y)=\\inf_{\\substack{x(0)=x\\\\x(1)=y\\\\u\\in\\mathcal{U}}}\\int_0^1L(x(s), u(x(s),s), s)ds.$$ Where $\\mathcal{U}$ is a control set, and $x$ satisfies the following ordinary equation: $$\\dot{x}(s)=f(x(s),u(x(s),s)).$$ We prove that under the condition that the initial measure $\\mu_0$ is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the correspond"},"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":"1312.0345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-02T06:59:35Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"471c8438ba308aed823555cfac8c612f1c349edac335d9199b44a4485fd6f2f6","abstract_canon_sha256":"9e54d6449d33f969cf01951b8001cd8797db744b8fcf59048475bef799383446"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:45.968618Z","signature_b64":"cNdeAbLP14G9UeG5ty8OvjMzFgEMmFCdxjGoIdrmNqLn7SP5VC+jPXtDCcapbBPVzU/qbyE7anUKd71m32beDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"189a0f388e8429843f71bda688db1d84da12e15bc3d0eaf4f4729e98ae33e6e6","last_reissued_at":"2026-05-18T03:05:45.967998Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:45.967998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Transportation for Generalized Lagrangian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.DS","authors_text":"Jianlu Zhang, Ji Li","submitted_at":"2013-12-02T06:59:35Z","abstract_excerpt":"In this paper, we study the optimal transportation for generalized Lagrangian $L=L(x, u,t)$, and consider the cost function as following: $$c(x, y)=\\inf_{\\substack{x(0)=x\\\\x(1)=y\\\\u\\in\\mathcal{U}}}\\int_0^1L(x(s), u(x(s),s), s)ds.$$ Where $\\mathcal{U}$ is a control set, and $x$ satisfies the following ordinary equation: $$\\dot{x}(s)=f(x(s),u(x(s),s)).$$ We prove that under the condition that the initial measure $\\mu_0$ is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the correspond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0345","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":""},"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":"1312.0345","created_at":"2026-05-18T03:05:45.968088+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.0345v1","created_at":"2026-05-18T03:05:45.968088+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0345","created_at":"2026-05-18T03:05:45.968088+00:00"},{"alias_kind":"pith_short_12","alias_value":"DCNA6OEOQQUY","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"DCNA6OEOQQUYIP3R","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"DCNA6OEO","created_at":"2026-05-18T12:27:40.988391+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/DCNA6OEOQQUYIP3RXWTIRWY5QT","json":"https://pith.science/pith/DCNA6OEOQQUYIP3RXWTIRWY5QT.json","graph_json":"https://pith.science/api/pith-number/DCNA6OEOQQUYIP3RXWTIRWY5QT/graph.json","events_json":"https://pith.science/api/pith-number/DCNA6OEOQQUYIP3RXWTIRWY5QT/events.json","paper":"https://pith.science/paper/DCNA6OEO"},"agent_actions":{"view_html":"https://pith.science/pith/DCNA6OEOQQUYIP3RXWTIRWY5QT","download_json":"https://pith.science/pith/DCNA6OEOQQUYIP3RXWTIRWY5QT.json","view_paper":"https://pith.science/paper/DCNA6OEO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.0345&json=true","fetch_graph":"https://pith.science/api/pith-number/DCNA6OEOQQUYIP3RXWTIRWY5QT/graph.json","fetch_events":"https://pith.science/api/pith-number/DCNA6OEOQQUYIP3RXWTIRWY5QT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DCNA6OEOQQUYIP3RXWTIRWY5QT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DCNA6OEOQQUYIP3RXWTIRWY5QT/action/storage_attestation","attest_author":"https://pith.science/pith/DCNA6OEOQQUYIP3RXWTIRWY5QT/action/author_attestation","sign_citation":"https://pith.science/pith/DCNA6OEOQQUYIP3RXWTIRWY5QT/action/citation_signature","submit_replication":"https://pith.science/pith/DCNA6OEOQQUYIP3RXWTIRWY5QT/action/replication_record"}},"created_at":"2026-05-18T03:05:45.968088+00:00","updated_at":"2026-05-18T03:05:45.968088+00:00"}