{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:SCHY7AQK2SJ5QX6CSXFNUKDZU3","short_pith_number":"pith:SCHY7AQK","schema_version":"1.0","canonical_sha256":"908f8f820ad493d85fc295cada2879a6ce050c4065708bb82261e2b355420f02","source":{"kind":"arxiv","id":"2608.02487","version":1},"attestation_state":"computed","paper":{"title":"Computational and Statistical Guarantees of the \\textit{c}-Rectified flow","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.LG","math.OC","math.PR","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Harrison H. Zhou, Leda Wang, Qiang Liu, Zhehao Xu","submitted_at":"2026-08-03T16:53:29Z","abstract_excerpt":"Recently, rectified flow has emerged as a fundamental framework for large-scale image generation, powering state-of-the-art systems such as FLUX.1 and Stable Diffusion 3. Despite its remarkable empirical success, the computational and statistical guarantees of iterative rectified flow have remained largely unexplored. We address this problem by studying \\textit{c}-rectified flow, a cost-aware class of rectified flow that projects velocity fields onto a gradient class while preserving endpoint marginals. The ordinary rectified flow can fail to recover the optimal transport coupling: in a Gaussi"},"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":"2608.02487","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ML","submitted_at":"2026-08-03T16:53:29Z","cross_cats_sorted":["cs.LG","math.OC","math.PR","math.ST","stat.TH"],"title_canon_sha256":"0d68b9da88735ed1cceb1cb4951e3cd3bd8cc3dea4c9b7860a4f4e5aea0aca41","abstract_canon_sha256":"026ed144bf209ff06ae7d4c5c71aec5d417443fcb22d0a71ead1d711bda5d8b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T02:43:46.838413Z","signature_b64":"VIOfeKWdQWmHcXP7Pp1kG5uWcRU+jKdaUVSl71UhSKrxB5PuOq/P0vAOHjZrl36mJkUfBh4YcXHyc0YAlgO3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"908f8f820ad493d85fc295cada2879a6ce050c4065708bb82261e2b355420f02","last_reissued_at":"2026-08-04T02:43:46.835995Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T02:43:46.835995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computational and Statistical Guarantees of the \\textit{c}-Rectified flow","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.LG","math.OC","math.PR","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Harrison H. Zhou, Leda Wang, Qiang Liu, Zhehao Xu","submitted_at":"2026-08-03T16:53:29Z","abstract_excerpt":"Recently, rectified flow has emerged as a fundamental framework for large-scale image generation, powering state-of-the-art systems such as FLUX.1 and Stable Diffusion 3. Despite its remarkable empirical success, the computational and statistical guarantees of iterative rectified flow have remained largely unexplored. We address this problem by studying \\textit{c}-rectified flow, a cost-aware class of rectified flow that projects velocity fields onto a gradient class while preserving endpoint marginals. The ordinary rectified flow can fail to recover the optimal transport coupling: in a Gaussi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02487","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/2608.02487/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":"2608.02487","created_at":"2026-08-04T02:43:46.838332+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.02487v1","created_at":"2026-08-04T02:43:46.838332+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.02487","created_at":"2026-08-04T02:43:46.838332+00:00"},{"alias_kind":"pith_short_12","alias_value":"SCHY7AQK2SJ5","created_at":"2026-08-04T02:43:46.838332+00:00"},{"alias_kind":"pith_short_16","alias_value":"SCHY7AQK2SJ5QX6C","created_at":"2026-08-04T02:43:46.838332+00:00"},{"alias_kind":"pith_short_8","alias_value":"SCHY7AQK","created_at":"2026-08-04T02:43:46.838332+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/SCHY7AQK2SJ5QX6CSXFNUKDZU3","json":"https://pith.science/pith/SCHY7AQK2SJ5QX6CSXFNUKDZU3.json","graph_json":"https://pith.science/api/pith-number/SCHY7AQK2SJ5QX6CSXFNUKDZU3/graph.json","events_json":"https://pith.science/api/pith-number/SCHY7AQK2SJ5QX6CSXFNUKDZU3/events.json","paper":"https://pith.science/paper/SCHY7AQK"},"agent_actions":{"view_html":"https://pith.science/pith/SCHY7AQK2SJ5QX6CSXFNUKDZU3","download_json":"https://pith.science/pith/SCHY7AQK2SJ5QX6CSXFNUKDZU3.json","view_paper":"https://pith.science/paper/SCHY7AQK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.02487&json=true","fetch_graph":"https://pith.science/api/pith-number/SCHY7AQK2SJ5QX6CSXFNUKDZU3/graph.json","fetch_events":"https://pith.science/api/pith-number/SCHY7AQK2SJ5QX6CSXFNUKDZU3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SCHY7AQK2SJ5QX6CSXFNUKDZU3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SCHY7AQK2SJ5QX6CSXFNUKDZU3/action/storage_attestation","attest_author":"https://pith.science/pith/SCHY7AQK2SJ5QX6CSXFNUKDZU3/action/author_attestation","sign_citation":"https://pith.science/pith/SCHY7AQK2SJ5QX6CSXFNUKDZU3/action/citation_signature","submit_replication":"https://pith.science/pith/SCHY7AQK2SJ5QX6CSXFNUKDZU3/action/replication_record"}},"created_at":"2026-08-04T02:43:46.838332+00:00","updated_at":"2026-08-04T02:43:46.838332+00:00"}