{"as_of":"2026-08-19T04:24:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:57775e3bfc0431d3d8afafed09c852c970f471c1f382f3689ac15ea67f660342","coverage":[{"denominator":5,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-09T15:42:49.947215Z","state":"measured"},{"denominator":8,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":8,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T18:44:21.554047Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-04T12:19:50.161265Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2502.01353","last_updated":"2025-02-03T13:42:56Z","snapshot_observed_at":"2026-08-18T12:33:38.327347Z","submitted_at":"2025-02-03T13:42:56Z","title":"A coupling approach to Lipschitz transport maps","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.01353","snapshot_observed_at":"2026-08-15T18:44:21.554047Z","title":"A coupling approach to lipschitz transport maps","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.19559","last_updated":"2025-06-24T12:16:06Z","snapshot_observed_at":"2026-08-17T13:40:30.522209Z","submitted_at":"2025-06-24T12:16:06Z","title":"Regularity of the score function in generative models","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-15T18:44:21.554047Z"},"links":{"cited_paper":"/paper/2502.01353","citing_paper":"/paper/2506.19559"},"observation_digest":"sha256:585969341de207c590809558c03e1975f68b3c02dd1a15d43a3e2ded99f96b9b","observation_id":"4d907b2b-4afa-47ef-add6-4a9d7314f7f2","resolution":{"observed_at":"2026-08-15T18:44:21.554047Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.01353","last_updated":"2025-02-03T13:42:56Z","snapshot_observed_at":"2026-08-18T12:33:38.327347Z","submitted_at":"2025-02-03T13:42:56Z","title":"A coupling approach to Lipschitz transport maps","version":1},"cited_work":{"arxiv_id":"2502.01353","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.01353","snapshot_observed_at":"2026-07-04T12:19:50.161265Z","title":"A coupling approach to Lipschitz transport maps.arXiv preprint arXiv:2502.01353","venue":null,"work_id":"4a6e5e70-edc9-4856-bef5-a42071421c09","year":null},"citing_paper":{"arxiv_id":"2604.06065","last_updated":"2026-04-07T16:46:40Z","snapshot_observed_at":"2026-08-18T08:48:50.766786Z","submitted_at":"2026-04-07T16:46:40Z","title":"Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalities","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-10T18:15:58.587798Z"},"links":{"cited_paper":"/paper/2502.01353","citing_paper":"/paper/2604.06065"},"observation_digest":"sha256:bc37ae2ba6b333744940d643936db240103f7bdef9dd5ec24a804037e179c06a","observation_id":"c9f1792b-98a4-4be8-bc0a-e8757575ea29","resolution":{"observed_at":"2026-05-11T05:10:55.338137Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.01353","last_updated":"2025-02-03T13:42:56Z","snapshot_observed_at":"2026-08-18T12:33:38.327347Z","submitted_at":"2025-02-03T13:42:56Z","title":"A coupling approach to Lipschitz transport maps","version":1},"cited_work":{"arxiv_id":"2502.01353","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.01353","snapshot_observed_at":"2026-07-04T12:19:50.161265Z","title":"A coupling approach to Lipschitz transport maps.arXiv preprint arXiv:2502.01353","venue":null,"work_id":"4a6e5e70-edc9-4856-bef5-a42071421c09","year":null},"citing_paper":{"arxiv_id":"2606.23383","last_updated":"2026-06-22T14:12:03Z","snapshot_observed_at":"2026-08-15T07:22:52.763796Z","submitted_at":"2026-06-22T14:12:03Z","title":"Near-Lipschitz stability of the Kim--Milman flow map","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-26T06:59:49.987931Z"},"links":{"cited_paper":"/paper/2502.01353","citing_paper":"/paper/2606.23383"},"observation_digest":"sha256:1424f7a7da73a0562caa4fcbf7cab2e242f92d9e27f330665a5056c72c583c33","observation_id":"700c9758-eb40-4aa9-a366-aa0162d26ad4","resolution":{"observed_at":"2026-07-04T12:19:50.162691Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2502.01353/citation-record","integrity":"/paper/2502.01353/integrity","json":"/paper/2502.01353/citation-record.json","paper":"/paper/2502.01353"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T15:42:50.011570Z","title":"Existence of Strong Soluti ons for Itˆ o’s Stochastic Equa- tions via Approximations","venue":null,"work_id":"d36d53b8-57f8-4478-9621-d97d8a89be00","year":2023},"citing_paper":{"arxiv_id":"2502.01353","last_updated":"2025-02-03T13:42:56Z","snapshot_observed_at":"2026-08-18T12:33:38.327347Z","submitted_at":"2025-02-03T13:42:56Z","title":"A coupling approach to Lipschitz transport maps","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-09T15:42:49.937563Z"},"links":{"citing_paper":"/paper/2502.01353"},"observation_digest":"sha256:ad21236cb3515652b7ab632877804af52cd34f00a7ec786ecd052bff3132aab4","observation_id":"5b6b4980-2e64-4c52-9076-95e7f19242a9","resolution":{"observed_at":"2026-08-09T15:42:50.016596Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T15:42:49.995614Z","title":"Mass Transportation and Contrac tions","venue":null,"work_id":"967fbb2b-8f33-45cb-9020-0097e0b7dd0d","year":2011},"citing_paper":{"arxiv_id":"2502.01353","last_updated":"2025-02-03T13:42:56Z","snapshot_observed_at":"2026-08-18T12:33:38.327347Z","submitted_at":"2025-02-03T13:42:56Z","title":"A coupling approach to Lipschitz transport maps","version":1},"reference_index":967,"source":"pdf_text","source_observed_at":"2026-08-09T15:42:49.942355Z"},"links":{"citing_paper":"/paper/2502.01353"},"observation_digest":"sha256:f049bbaed9a7a53129ca7c8552499503f9a573597321255480e806da0f815cd6","observation_id":"3c424320-affc-48ed-9ac1-4c8bd29e91cf","resolution":{"observed_at":"2026-08-09T15:42:50.000847Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T15:42:50.027109Z","title":"Coupling by Reflection for Controlled Diffusion Processes: Turnpike Prop- erty and Large Time Behavior of Hamilton–Jacobi–Bellman Eq uations","venue":null,"work_id":"00ed5c8c-f0e1-4f31-b0e4-efec8beb90dc","year":2023},"citing_paper":{"arxiv_id":"2502.01353","last_updated":"2025-02-03T13:42:56Z","snapshot_observed_at":"2026-08-18T12:33:38.327347Z","submitted_at":"2025-02-03T13:42:56Z","title":"A coupling approach to Lipschitz transport maps","version":1},"reference_index":2015,"source":"pdf_text","source_observed_at":"2026-08-09T15:42:49.932649Z"},"links":{"citing_paper":"/paper/2502.01353"},"observation_digest":"sha256:b4302f23a4e7acdd2e47b32bebc4e9771092c4609fe01959d3d2b02c660c3765","observation_id":"575cc1e0-5d57-4c4a-b510-fd3b53dd66d1","resolution":{"observed_at":"2026-08-09T15:42:50.032321Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T15:42:49.977840Z","title":"Behavior of the Poincar´ e Constant alon g the Polchinski Renormalization Flow","venue":null,"work_id":"1910522d-9634-4f2c-bade-be79352adce3","year":2024},"citing_paper":{"arxiv_id":"2502.01353","last_updated":"2025-02-03T13:42:56Z","snapshot_observed_at":"2026-08-18T12:33:38.327347Z","submitted_at":"2025-02-03T13:42:56Z","title":"A coupling approach to Lipschitz transport maps","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-09T15:42:49.947215Z"},"links":{"citing_paper":"/paper/2502.01353"},"observation_digest":"sha256:aeef6a6878d5cf23f278cf061f89bb9fc3400dbf7a9d53309e398dfbdf36af07","observation_id":"f842cbe6-0a08-4b07-9bc6-570b4b66a779","resolution":{"observed_at":"2026-08-09T15:42:49.984625Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T15:42:50.042154Z","title":"Monotonicity Properties of Optim al Transportation and the FKG and Related Inequalities","venue":null,"work_id":"640d3cc4-8f84-4499-bd42-02a67669dc09","year":2000},"citing_paper":{"arxiv_id":"2502.01353","last_updated":"2025-02-03T13:42:56Z","snapshot_observed_at":"2026-08-18T12:33:38.327347Z","submitted_at":"2025-02-03T13:42:56Z","title":"A coupling approach to Lipschitz transport maps","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-09T15:42:49.927260Z"},"links":{"citing_paper":"/paper/2502.01353"},"observation_digest":"sha256:7b3c067e3d589512615b50d2892a96cbd2b6e7eab5829f905dcc177873f891f8","observation_id":"3545c4e6-cdbd-464b-87f2-26268a5e84f5","resolution":{"observed_at":"2026-08-09T15:42:50.046891Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2502.01353","last_updated":"2025-02-03T13:42:56Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-18T12:33:38.327347Z","submitted_at":"2025-02-03T13:42:56Z","title":"A coupling approach to Lipschitz transport maps"},"reference_resolution":{"displayed":5,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":5},"total_outbound_references":5},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 5 of 5 outbound references and 3 inbound Pith citation observations for arXiv:2502.01353."}