{"as_of":"2026-08-08T11:42:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:959983bb24b5a7198d41bb6465143e87adab0152d26c2ff1294e46a10cb53094","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":12,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":12,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":12,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T10:47:36.661918Z","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":"2026-07-04T12:39:49.568159Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.04908","last_updated":"2026-07-16T13:51:55Z","snapshot_observed_at":"2026-08-02T12:22:30.993996Z","submitted_at":"2024-11-07T17:48:49Z","title":"Gluing methods for quantitative stability of optimal transport maps","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.04908","snapshot_observed_at":"2026-08-07T10:47:36.661918Z","title":"Gluing methods for quantitative stability of optimal transport maps","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.04480","last_updated":"2026-06-08T03:34:40Z","snapshot_observed_at":"2026-08-07T10:38:47.560001Z","submitted_at":"2025-06-04T22:00:43Z","title":"On the Wasserstein Geodesic Principal Component Analysis of probability measures","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T10:47:36.661918Z"},"links":{"cited_paper":"/paper/2411.04908","citing_paper":"/paper/2506.04480"},"observation_digest":"sha256:cfbfb0bd71611dbfca1095ea01bc012b6fd7978936b7b7f113c4fd5466733fea","observation_id":"8b969083-1a4a-4cf9-9828-97fb17678026","resolution":{"observed_at":"2026-08-07T10:47:36.661918Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.04908","last_updated":"2026-07-16T13:51:55Z","snapshot_observed_at":"2026-08-02T12:22:30.993996Z","submitted_at":"2024-11-07T17:48:49Z","title":"Gluing methods for quantitative stability of optimal transport maps","version":3},"cited_work":{"arxiv_id":"2411.04908","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.04908","snapshot_observed_at":"2026-07-17T01:21:40.205413Z","title":"Gluing methods for quantitative stability of optimal transport maps","venue":null,"work_id":"18b4d8ee-783f-41da-b076-6a9be33a08ff","year":2025},"citing_paper":{"arxiv_id":"2511.01154","last_updated":"2026-04-03T01:50:57Z","snapshot_observed_at":"2026-08-08T02:35:37.283470Z","submitted_at":"2025-11-03T02:04:41Z","title":"Stability of the Kim--Milman flow map","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-18T02:01:46.734223Z"},"links":{"cited_paper":"/paper/2411.04908","citing_paper":"/paper/2511.01154"},"observation_digest":"sha256:516271cb5c2fc93825e609a3429655007a12c0a959f2685ca40c4cf2508e4a42","observation_id":"af1f696b-385c-43f0-9460-714708cbd87f","resolution":{"observed_at":"2026-07-17T01:21:40.205413Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.04908","last_updated":"2026-07-16T13:51:55Z","snapshot_observed_at":"2026-08-02T12:22:30.993996Z","submitted_at":"2024-11-07T17:48:49Z","title":"Gluing methods for quantitative stability of optimal transport maps","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.04908","snapshot_observed_at":"2026-08-03T19:55:14.704566Z","title":"Gluing methods for quantitative stability of optimal transport maps.arXiv preprint arXiv:2411.04908,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2511.22636","last_updated":"2026-07-29T00:25:21Z","snapshot_observed_at":"2026-08-06T08:32:41.995185Z","submitted_at":"2025-11-27T17:14:52Z","title":"Quantitative stability for the Brascamp-Lieb inequality and moment measures","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T19:55:14.704566Z"},"links":{"cited_paper":"/paper/2411.04908","citing_paper":"/paper/2511.22636"},"observation_digest":"sha256:fc0e1c8ffc2b5b09ba5f3794e8141cca4d80dc7df8b328067b54e226e69c5778","observation_id":"033ecbd4-23d8-4579-8661-4be96ef70c87","resolution":{"observed_at":"2026-08-03T19:55:14.704566Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.04908","last_updated":"2026-07-16T13:51:55Z","snapshot_observed_at":"2026-08-02T12:22:30.993996Z","submitted_at":"2024-11-07T17:48:49Z","title":"Gluing methods for quantitative stability of optimal transport maps","version":3},"cited_work":{"arxiv_id":"2411.04908","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.04908","snapshot_observed_at":"2026-07-17T01:21:40.205413Z","title":"Gluing methods for quantitative stability of optimal transport maps","venue":null,"work_id":"18b4d8ee-783f-41da-b076-6a9be33a08ff","year":2025},"citing_paper":{"arxiv_id":"2603.25182","last_updated":"2026-04-10T09:31:37Z","snapshot_observed_at":"2026-08-08T02:30:22.033650Z","submitted_at":"2026-03-26T08:51:51Z","title":"Learning Monge maps with constrained drifting models","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-15T00:47:27.995776Z"},"links":{"cited_paper":"/paper/2411.04908","citing_paper":"/paper/2603.25182"},"observation_digest":"sha256:503d3da2f2677ae7768271449e713f41bef23da5b5c52f6542ea8c8644155a3c","observation_id":"4eec5112-df97-4bcd-ab1e-1be89a1bf88f","resolution":{"observed_at":"2026-07-17T01:21:40.205413Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.04908","last_updated":"2026-07-16T13:51:55Z","snapshot_observed_at":"2026-08-02T12:22:30.993996Z","submitted_at":"2024-11-07T17:48:49Z","title":"Gluing methods for quantitative stability of optimal transport maps","version":3},"cited_work":{"arxiv_id":"2411.04908","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.04908","snapshot_observed_at":"2026-07-17T01:21:40.205413Z","title":"Gluing methods for quantitative stability of optimal transport maps","venue":null,"work_id":"18b4d8ee-783f-41da-b076-6a9be33a08ff","year":2025},"citing_paper":{"arxiv_id":"2604.22366","last_updated":"2026-04-24T08:58:56Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-24T08:58:56Z","title":"Statistical Estimation of Monge Transport Maps via Brenier Potentials","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-05-08T11:03:44.263884Z"},"links":{"cited_paper":"/paper/2411.04908","citing_paper":"/paper/2604.22366"},"observation_digest":"sha256:aba161bc0e8ebded28df8d0840fd1f6b93eff89736bd226edcdd60bf2e718c9e","observation_id":"c2a5f6cd-3dff-468a-805f-76b53b6713a1","resolution":{"observed_at":"2026-07-17T01:21:40.205413Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.04908","last_updated":"2026-07-16T13:51:55Z","snapshot_observed_at":"2026-08-02T12:22:30.993996Z","submitted_at":"2024-11-07T17:48:49Z","title":"Gluing methods for quantitative stability of optimal transport maps","version":3},"cited_work":{"arxiv_id":"2411.04908","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.04908","snapshot_observed_at":"2026-07-17T01:21:40.205413Z","title":"Gluing methods for quantitative stability of optimal transport maps","venue":null,"work_id":"18b4d8ee-783f-41da-b076-6a9be33a08ff","year":2025},"citing_paper":{"arxiv_id":"2605.24232","last_updated":"2026-05-22T21:22:07Z","snapshot_observed_at":"2026-08-06T21:18:10.812389Z","submitted_at":"2026-05-22T21:22:07Z","title":"Stability of optimal transport maps and second variation of the 2-Monge-Kantorovich distance","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-30T14:48:46.558424Z"},"links":{"cited_paper":"/paper/2411.04908","citing_paper":"/paper/2605.24232"},"observation_digest":"sha256:58fb19d90b95fd999eb5bb150f8a5341f092bc8f36e2e62567cd123c8aae1733","observation_id":"85b05029-5f9a-474d-ae20-405a65e5d11c","resolution":{"observed_at":"2026-07-17T01:21:40.205413Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.04908","last_updated":"2026-07-16T13:51:55Z","snapshot_observed_at":"2026-08-02T12:22:30.993996Z","submitted_at":"2024-11-07T17:48:49Z","title":"Gluing methods for quantitative stability of optimal transport maps","version":3},"cited_work":{"arxiv_id":"2411.04908","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.04908","snapshot_observed_at":"2026-07-17T01:21:40.205413Z","title":"Gluing methods for quantitative stability of optimal transport maps","venue":null,"work_id":"18b4d8ee-783f-41da-b076-6a9be33a08ff","year":2025},"citing_paper":{"arxiv_id":"2605.27883","last_updated":"2026-05-27T03:06:54Z","snapshot_observed_at":"2026-08-08T03:23:46.835648Z","submitted_at":"2026-05-27T03:06:54Z","title":"Stability of Quadratically Regularized Optimal Transport","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-29T11:23:25.629557Z"},"links":{"cited_paper":"/paper/2411.04908","citing_paper":"/paper/2605.27883"},"observation_digest":"sha256:8c048ae40464cca49650146690cfea558d88e4b3ecd64917fac54dc018914929","observation_id":"31d2eaaa-635c-4899-ad7b-253f61bd0b36","resolution":{"observed_at":"2026-07-17T01:21:40.205413Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.04908","last_updated":"2026-07-16T13:51:55Z","snapshot_observed_at":"2026-08-02T12:22:30.993996Z","submitted_at":"2024-11-07T17:48:49Z","title":"Gluing methods for quantitative stability of optimal transport maps","version":3},"cited_work":{"arxiv_id":"2411.04908","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.04908","snapshot_observed_at":"2026-07-17T01:21:40.205413Z","title":"Gluing methods for quantitative stability of optimal transport maps","venue":null,"work_id":"18b4d8ee-783f-41da-b076-6a9be33a08ff","year":2025},"citing_paper":{"arxiv_id":"2605.28134","last_updated":"2026-07-13T11:00:54Z","snapshot_observed_at":"2026-08-01T19:13:56.112447Z","submitted_at":"2026-05-27T08:20:24Z","title":"Convergence of empirical subgradients for optimal transport-based objectives","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-06-29T11:18:27.226352Z"},"links":{"cited_paper":"/paper/2411.04908","citing_paper":"/paper/2605.28134"},"observation_digest":"sha256:7a5a22f2027e57907e4f775a44c8e8df1772e44ff2b483925ea00dc7a5eba829","observation_id":"9a8e7151-84fd-40ab-ba9b-ee164a76182f","resolution":{"observed_at":"2026-07-17T01:21:40.205413Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.04908","last_updated":"2026-07-16T13:51:55Z","snapshot_observed_at":"2026-08-02T12:22:30.993996Z","submitted_at":"2024-11-07T17:48:49Z","title":"Gluing methods for quantitative stability of optimal transport maps","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.04908","snapshot_observed_at":"2026-07-14T18:41:00.296741Z","title":"Letrouit and Q","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2605.28134","last_updated":"2026-07-13T11:00:54Z","snapshot_observed_at":"2026-08-01T19:13:56.112447Z","submitted_at":"2026-05-27T08:20:24Z","title":"Convergence of empirical subgradients for optimal transport-based objectives","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-07-14T18:41:00.296741Z"},"links":{"cited_paper":"/paper/2411.04908","citing_paper":"/paper/2605.28134"},"observation_digest":"sha256:d0d913a707e52e5d3f3f15a7226011ebc92a8b1eff0daa85bf6230731b059cb3","observation_id":"0885058a-b180-44bf-bd09-d2d69a034697","resolution":{"observed_at":"2026-07-14T18:41:00.296741Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.04908","last_updated":"2026-07-16T13:51:55Z","snapshot_observed_at":"2026-08-02T12:22:30.993996Z","submitted_at":"2024-11-07T17:48:49Z","title":"Gluing methods for quantitative stability of optimal transport maps","version":3},"cited_work":{"arxiv_id":"2411.04908","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.04908","snapshot_observed_at":"2026-07-17T01:21:40.205413Z","title":"Gluing methods for quantitative stability of optimal transport maps","venue":null,"work_id":"18b4d8ee-783f-41da-b076-6a9be33a08ff","year":2025},"citing_paper":{"arxiv_id":"2606.23037","last_updated":"2026-06-22T08:46:16Z","snapshot_observed_at":"2026-08-08T03:54:03.387547Z","submitted_at":"2026-06-22T08:46:16Z","title":"Two-mode stability for multi-marginal optimal transport maps","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-06-26T06:20:47.333554Z"},"links":{"cited_paper":"/paper/2411.04908","citing_paper":"/paper/2606.23037"},"observation_digest":"sha256:adcc033420840a4c05325ce352e3b1c99bf7ff60f0e50349503392c79f6ad630","observation_id":"0d9fb4b7-5415-47ed-9432-a269f486780e","resolution":{"observed_at":"2026-07-17T01:21:40.205413Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.04908","last_updated":"2026-07-16T13:51:55Z","snapshot_observed_at":"2026-08-02T12:22:30.993996Z","submitted_at":"2024-11-07T17:48:49Z","title":"Gluing methods for quantitative stability of optimal transport maps","version":3},"cited_work":{"arxiv_id":"2411.04908","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.04908","snapshot_observed_at":"2026-07-17T01:21:40.205413Z","title":"Gluing methods for quantitative stability of optimal transport maps","venue":null,"work_id":"18b4d8ee-783f-41da-b076-6a9be33a08ff","year":2025},"citing_paper":{"arxiv_id":"2606.23383","last_updated":"2026-06-22T14:12:03Z","snapshot_observed_at":"2026-08-08T03:53:32.387820Z","submitted_at":"2026-06-22T14:12:03Z","title":"Near-Lipschitz stability of the Kim--Milman flow map","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-26T06:59:49.987931Z"},"links":{"cited_paper":"/paper/2411.04908","citing_paper":"/paper/2606.23383"},"observation_digest":"sha256:4fb569084ca1f018b030d365b5c1a2141dba6e1c1e0247f6d4f0585a6bf62eab","observation_id":"aee2bbf4-b0ab-463e-8e68-1080afac0f27","resolution":{"observed_at":"2026-07-17T01:21:40.205413Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.04908","last_updated":"2026-07-16T13:51:55Z","snapshot_observed_at":"2026-08-02T12:22:30.993996Z","submitted_at":"2024-11-07T17:48:49Z","title":"Gluing methods for quantitative stability of optimal transport maps","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.04908","snapshot_observed_at":"2026-08-04T01:34:20.415099Z","title":"arXiv preprint arXiv:2411.04908 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.00649","last_updated":"2026-08-01T13:09:00Z","snapshot_observed_at":"2026-08-07T05:05:21.965649Z","submitted_at":"2026-08-01T13:09:00Z","title":"Empirical optimal transport potentials: fast rates and a functional central limit theorem","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-04T01:34:20.415099Z"},"links":{"cited_paper":"/paper/2411.04908","citing_paper":"/paper/2608.00649"},"observation_digest":"sha256:1a45bef9dac24e4994c21a566fdeda92b61416db591deb68df6d739d299c6204","observation_id":"f88051de-462c-4288-a3bc-f53a6d611afc","resolution":{"observed_at":"2026-08-04T01:34:20.415099Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2411.04908/citation-record","integrity":"/paper/2411.04908/integrity","json":"/paper/2411.04908/citation-record.json","paper":"/paper/2411.04908"},"outbound":[],"paper":{"arxiv_id":"2411.04908","last_updated":"2026-07-16T13:51:55Z","latest_version":3,"primary_category":"math.AP","snapshot_observed_at":"2026-08-02T12:22:30.993996Z","submitted_at":"2024-11-07T17:48:49Z","title":"Gluing methods for quantitative stability of optimal transport maps"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 12 inbound Pith citation observations for arXiv:2411.04908."}