{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:WXLOVWFC7WBBMY7WNAR7YSDBAJ","short_pith_number":"pith:WXLOVWFC","schema_version":"1.0","canonical_sha256":"b5d6ead8a2fd821663f66823fc4861025f7813e96d851ad8f421cacab97093ba","source":{"kind":"arxiv","id":"2502.10607","version":1},"attestation_state":"computed","paper":{"title":"Time Parameterized Optimal Transport","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kaiwen Shi","submitted_at":"2025-02-14T23:48:13Z","abstract_excerpt":"Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution dissimilarities. While extensive research has focused on optimal transport and its regularized variants (such as entropy, sparsity, and capacity constraints) the role of time has been largely overlooked. However, time is a critical factor in real world transport problems.\n  In this work, we introduce a time parameterized formulation of the optimal transport pr"},"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":"2502.10607","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-02-14T23:48:13Z","cross_cats_sorted":[],"title_canon_sha256":"231ff5ea39599611adbb07007ebcec70ccf483203372af7c1573f9ccb8b32ea8","abstract_canon_sha256":"d94cad41292064feffd42ed12e794b200fee87f09384dbf4d04c29ce866f6634"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:14:55.155541Z","signature_b64":"iGJkvwPYFZ8RhYXD6jJ6K73Qsl6pYVbnsAsQIfajyQbKF3kquwrTuH120aye32tynQV0FpQFUHA5rbYUgjUZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5d6ead8a2fd821663f66823fc4861025f7813e96d851ad8f421cacab97093ba","last_reissued_at":"2026-07-05T10:14:55.155000Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:14:55.155000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Time Parameterized Optimal Transport","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kaiwen Shi","submitted_at":"2025-02-14T23:48:13Z","abstract_excerpt":"Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution dissimilarities. While extensive research has focused on optimal transport and its regularized variants (such as entropy, sparsity, and capacity constraints) the role of time has been largely overlooked. However, time is a critical factor in real world transport problems.\n  In this work, we introduce a time parameterized formulation of the optimal transport pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.10607","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/2502.10607/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2502.10607","created_at":"2026-07-05T10:14:55.155055+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.10607v1","created_at":"2026-07-05T10:14:55.155055+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.10607","created_at":"2026-07-05T10:14:55.155055+00:00"},{"alias_kind":"pith_short_12","alias_value":"WXLOVWFC7WBB","created_at":"2026-07-05T10:14:55.155055+00:00"},{"alias_kind":"pith_short_16","alias_value":"WXLOVWFC7WBBMY7W","created_at":"2026-07-05T10:14:55.155055+00:00"},{"alias_kind":"pith_short_8","alias_value":"WXLOVWFC","created_at":"2026-07-05T10:14:55.155055+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.10917","citing_title":"Optimal and Scalable MAPF via Multi-Marginal Optimal Transport and Schr\\\"odinger Bridges","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WXLOVWFC7WBBMY7WNAR7YSDBAJ","json":"https://pith.science/pith/WXLOVWFC7WBBMY7WNAR7YSDBAJ.json","graph_json":"https://pith.science/api/pith-number/WXLOVWFC7WBBMY7WNAR7YSDBAJ/graph.json","events_json":"https://pith.science/api/pith-number/WXLOVWFC7WBBMY7WNAR7YSDBAJ/events.json","paper":"https://pith.science/paper/WXLOVWFC"},"agent_actions":{"view_html":"https://pith.science/pith/WXLOVWFC7WBBMY7WNAR7YSDBAJ","download_json":"https://pith.science/pith/WXLOVWFC7WBBMY7WNAR7YSDBAJ.json","view_paper":"https://pith.science/paper/WXLOVWFC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.10607&json=true","fetch_graph":"https://pith.science/api/pith-number/WXLOVWFC7WBBMY7WNAR7YSDBAJ/graph.json","fetch_events":"https://pith.science/api/pith-number/WXLOVWFC7WBBMY7WNAR7YSDBAJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WXLOVWFC7WBBMY7WNAR7YSDBAJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WXLOVWFC7WBBMY7WNAR7YSDBAJ/action/storage_attestation","attest_author":"https://pith.science/pith/WXLOVWFC7WBBMY7WNAR7YSDBAJ/action/author_attestation","sign_citation":"https://pith.science/pith/WXLOVWFC7WBBMY7WNAR7YSDBAJ/action/citation_signature","submit_replication":"https://pith.science/pith/WXLOVWFC7WBBMY7WNAR7YSDBAJ/action/replication_record"}},"created_at":"2026-07-05T10:14:55.155055+00:00","updated_at":"2026-07-05T10:14:55.155055+00:00"}