{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:34E55K2U7RDZKTEALLTHWSIQR7","short_pith_number":"pith:34E55K2U","schema_version":"1.0","canonical_sha256":"df09deab54fc47954c805ae67b49108fd02af3742434f2fba162bb2d97855a0e","source":{"kind":"arxiv","id":"2504.12713","version":1},"attestation_state":"computed","paper":{"title":"Efficient Primal-dual Forward-backward Splitting Method for Wasserstein-like Gradient Flows with General Nonlinear Mobilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.OC"],"primary_cat":"math.NA","authors_text":"Chaozhen Wei, Li Wang, Yunhong Deng","submitted_at":"2025-04-17T07:37:08Z","abstract_excerpt":"We construct an efficient primal-dual forward-backward (PDFB) splitting method for computing a class of minimizing movement schemes with nonlinear mobility transport distances, and apply it to computing Wasserstein-like gradient flows. This approach introduces a novel saddle point formulation for the minimizing movement schemes, leveraging a support function form from the Benamou-Brenier dynamical formulation of optimal transport. The resulting framework allows for flexible computation of Wasserstein-like gradient flows by solving the corresponding saddle point problem at the fully discrete le"},"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":"2504.12713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-04-17T07:37:08Z","cross_cats_sorted":["cs.NA","math.OC"],"title_canon_sha256":"e6965d6395c316c688191b9642c1b9800798dcdbe19f783c3d482cc9044507d2","abstract_canon_sha256":"8b906de56a039740837369b38431a5fd91dc6426119ed6f74068fd26c24f9b71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:50:21.118606Z","signature_b64":"N4oPFz8UbWZvoj0HZgu8VhUovCrif0R69m6ykz8koBqg+Q6kRwhBqovFoFx2n5vnqeMe45/k5r0zbhcSOWN4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df09deab54fc47954c805ae67b49108fd02af3742434f2fba162bb2d97855a0e","last_reissued_at":"2026-07-05T10:50:21.118146Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:50:21.118146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient Primal-dual Forward-backward Splitting Method for Wasserstein-like Gradient Flows with General Nonlinear Mobilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.OC"],"primary_cat":"math.NA","authors_text":"Chaozhen Wei, Li Wang, Yunhong Deng","submitted_at":"2025-04-17T07:37:08Z","abstract_excerpt":"We construct an efficient primal-dual forward-backward (PDFB) splitting method for computing a class of minimizing movement schemes with nonlinear mobility transport distances, and apply it to computing Wasserstein-like gradient flows. This approach introduces a novel saddle point formulation for the minimizing movement schemes, leveraging a support function form from the Benamou-Brenier dynamical formulation of optimal transport. The resulting framework allows for flexible computation of Wasserstein-like gradient flows by solving the corresponding saddle point problem at the fully discrete le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.12713","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/2504.12713/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":"2504.12713","created_at":"2026-07-05T10:50:21.118205+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.12713v1","created_at":"2026-07-05T10:50:21.118205+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.12713","created_at":"2026-07-05T10:50:21.118205+00:00"},{"alias_kind":"pith_short_12","alias_value":"34E55K2U7RDZ","created_at":"2026-07-05T10:50:21.118205+00:00"},{"alias_kind":"pith_short_16","alias_value":"34E55K2U7RDZKTEA","created_at":"2026-07-05T10:50:21.118205+00:00"},{"alias_kind":"pith_short_8","alias_value":"34E55K2U","created_at":"2026-07-05T10:50:21.118205+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/34E55K2U7RDZKTEALLTHWSIQR7","json":"https://pith.science/pith/34E55K2U7RDZKTEALLTHWSIQR7.json","graph_json":"https://pith.science/api/pith-number/34E55K2U7RDZKTEALLTHWSIQR7/graph.json","events_json":"https://pith.science/api/pith-number/34E55K2U7RDZKTEALLTHWSIQR7/events.json","paper":"https://pith.science/paper/34E55K2U"},"agent_actions":{"view_html":"https://pith.science/pith/34E55K2U7RDZKTEALLTHWSIQR7","download_json":"https://pith.science/pith/34E55K2U7RDZKTEALLTHWSIQR7.json","view_paper":"https://pith.science/paper/34E55K2U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.12713&json=true","fetch_graph":"https://pith.science/api/pith-number/34E55K2U7RDZKTEALLTHWSIQR7/graph.json","fetch_events":"https://pith.science/api/pith-number/34E55K2U7RDZKTEALLTHWSIQR7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/34E55K2U7RDZKTEALLTHWSIQR7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/34E55K2U7RDZKTEALLTHWSIQR7/action/storage_attestation","attest_author":"https://pith.science/pith/34E55K2U7RDZKTEALLTHWSIQR7/action/author_attestation","sign_citation":"https://pith.science/pith/34E55K2U7RDZKTEALLTHWSIQR7/action/citation_signature","submit_replication":"https://pith.science/pith/34E55K2U7RDZKTEALLTHWSIQR7/action/replication_record"}},"created_at":"2026-07-05T10:50:21.118205+00:00","updated_at":"2026-07-05T10:50:21.118205+00:00"}