{"as_of":"2026-08-11T16:42:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:09f938643154e737a6d41881da5d58b4c7bd418fc24c43ed4dd654df0046170c","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":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":13,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":13,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-09T13:43:47.677633Z","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":"2026-07-03T13:18:12.470462Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2311.00221","last_updated":"2023-11-01T01:44:39Z","snapshot_observed_at":"2026-08-01T20:58:26.661584Z","submitted_at":"2023-11-01T01:44:39Z","title":"Sobolev inequalities on K\\\"ahler spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.00221","snapshot_observed_at":"2026-08-09T13:43:47.677633Z","title":"and Sturm, J","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2502.02041","last_updated":"2025-02-04T06:19:44Z","snapshot_observed_at":"2026-08-11T07:48:23.384892Z","submitted_at":"2025-02-04T06:19:44Z","title":"Nash entropy, Calabi energy and geometric regularization of singular K\\\"ahler metrics","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-09T13:43:47.677633Z"},"links":{"cited_paper":"/paper/2311.00221","citing_paper":"/paper/2502.02041"},"observation_digest":"sha256:04a8b2b6039cc4a91fd063c7de0ca7a5219733da5d40f34c7d09ef8d28d4fffb","observation_id":"deb0af44-b884-4ba8-89cb-5803a1fc7a50","resolution":{"observed_at":"2026-08-09T13:43:47.677633Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.00221","last_updated":"2023-11-01T01:44:39Z","snapshot_observed_at":"2026-08-01T20:58:26.661584Z","submitted_at":"2023-11-01T01:44:39Z","title":"Sobolev inequalities on K\\\"ahler spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.00221","snapshot_observed_at":"2026-08-09T12:48:39.122833Z","title":"Guo, D.H","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.02313","last_updated":"2025-02-18T16:37:51Z","snapshot_observed_at":"2026-08-11T03:51:53.161619Z","submitted_at":"2025-02-04T13:32:01Z","title":"Uniform estimates: from Yau to Kolodziej","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-09T12:48:39.122833Z"},"links":{"cited_paper":"/paper/2311.00221","citing_paper":"/paper/2502.02313"},"observation_digest":"sha256:3d9a85da7153c1c65f1ebb9abac39e1967846ff57a6e2459fdb1c51d62ccad04","observation_id":"daaef0b2-7d82-450b-b8d3-a732a17c367a","resolution":{"observed_at":"2026-08-09T12:48:39.122833Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.00221","last_updated":"2023-11-01T01:44:39Z","snapshot_observed_at":"2026-08-01T20:58:26.661584Z","submitted_at":"2023-11-01T01:44:39Z","title":"Sobolev inequalities on K\\\"ahler spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.00221","snapshot_observed_at":"2026-08-07T20:35:39.281376Z","title":"H., Song, J., Sturm, J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.09825","last_updated":"2025-02-13T23:43:58Z","snapshot_observed_at":"2026-08-09T19:41:16.727339Z","submitted_at":"2025-02-13T23:43:58Z","title":"On K\\\"ahler-Einstein Currents","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T20:35:39.281376Z"},"links":{"cited_paper":"/paper/2311.00221","citing_paper":"/paper/2502.09825"},"observation_digest":"sha256:e211378f508021714dbc93a3c50fffac130154c2f912ad24a54d61a960d6bb1a","observation_id":"08ea6df6-7a90-4458-aca5-bef5c0fa600c","resolution":{"observed_at":"2026-08-07T20:35:39.281376Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.00221","last_updated":"2023-11-01T01:44:39Z","snapshot_observed_at":"2026-08-01T20:58:26.661584Z","submitted_at":"2023-11-01T01:44:39Z","title":"Sobolev inequalities on K\\\"ahler spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.00221","snapshot_observed_at":"2026-08-07T15:34:50.795816Z","title":"Phong, Jian Song, and Jacob Sturm","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.14939","last_updated":"2025-05-20T21:58:05Z","snapshot_observed_at":"2026-08-09T19:40:27.951650Z","submitted_at":"2025-05-20T21:58:05Z","title":"Gromov-Hausdorff limits of collapsing Calabi-Yau fibrations","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T15:34:50.795816Z"},"links":{"cited_paper":"/paper/2311.00221","citing_paper":"/paper/2505.14939"},"observation_digest":"sha256:d7eb29be05cd1b590394810a229e23823dfc75dba357643d980db4b739e9e490","observation_id":"9549968c-57c6-4d37-beca-a9860c386e98","resolution":{"observed_at":"2026-08-07T15:34:50.795816Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.00221","last_updated":"2023-11-01T01:44:39Z","snapshot_observed_at":"2026-08-01T20:58:26.661584Z","submitted_at":"2023-11-01T01:44:39Z","title":"Sobolev inequalities on K\\\"ahler spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.00221","snapshot_observed_at":"2026-08-07T11:08:33.960844Z","title":"Heat Kernel Estimates and Lower Bound of Eigenvalues","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2506.03579","last_updated":"2025-06-06T20:59:26Z","snapshot_observed_at":"2026-08-07T10:57:13.661474Z","submitted_at":"2025-06-04T05:02:33Z","title":"Kobayashi-Hitchin Correspondence for Saturated Reflexive Parabolic Sheaves on K\\\"ahler manifolds","version":2},"reference_index":2013,"source":"pdf_text","source_observed_at":"2026-08-07T11:08:33.960844Z"},"links":{"cited_paper":"/paper/2311.00221","citing_paper":"/paper/2506.03579"},"observation_digest":"sha256:b154d5e476f40a6e5f61f1303dc0ffb8e33123b11a89dba5d6b9f1f18a0f88f9","observation_id":"64a61f22-4d93-4c4b-8660-02d9b986000e","resolution":{"observed_at":"2026-08-07T11:08:33.960844Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.00221","last_updated":"2023-11-01T01:44:39Z","snapshot_observed_at":"2026-08-01T20:58:26.661584Z","submitted_at":"2023-11-01T01:44:39Z","title":"Sobolev inequalities on K\\\"ahler spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.00221","snapshot_observed_at":"2026-08-06T18:08:49.967686Z","title":"Guo, D.H","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.09486","last_updated":"2025-07-13T04:10:09Z","snapshot_observed_at":"2026-08-11T04:48:59.556295Z","submitted_at":"2025-07-13T04:10:09Z","title":"Estimates of heat kernels and Sobolev-type inequalities for twisted differential forms on compact K\\\"ahler manifolds","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T18:08:49.967686Z"},"links":{"cited_paper":"/paper/2311.00221","citing_paper":"/paper/2507.09486"},"observation_digest":"sha256:d4ddbd79a8611f3473927c9b690e89cc94c5aa3e0d6f4169c2e33bec12547749","observation_id":"5a1b7235-84ba-42a4-af49-4289f5493de3","resolution":{"observed_at":"2026-08-06T18:08:49.967686Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.00221","last_updated":"2023-11-01T01:44:39Z","snapshot_observed_at":"2026-08-01T20:58:26.661584Z","submitted_at":"2023-11-01T01:44:39Z","title":"Sobolev inequalities on K\\\"ahler spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.00221","snapshot_observed_at":"2026-08-05T14:52:49.546590Z","title":"and Sturm, J","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2508.20933","last_updated":"2025-08-28T15:57:49Z","snapshot_observed_at":"2026-08-05T14:52:48.265712Z","submitted_at":"2025-08-28T15:57:49Z","title":"H\\\"older estimates for degenerate complex Monge-Amp\\`ere equations","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-05T14:52:49.546590Z"},"links":{"cited_paper":"/paper/2311.00221","citing_paper":"/paper/2508.20933"},"observation_digest":"sha256:9253b7a5f62ec7a4007ee71a74a49977b4737df8e0812eda5c4360e3ebb2f840","observation_id":"df92fecf-dc68-4129-86a4-ffbb4b1fe21c","resolution":{"observed_at":"2026-08-05T14:52:49.546590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.00221","last_updated":"2023-11-01T01:44:39Z","snapshot_observed_at":"2026-08-01T20:58:26.661584Z","submitted_at":"2023-11-01T01:44:39Z","title":"Sobolev inequalities on K\\\"ahler spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.00221","snapshot_observed_at":"2026-08-03T10:35:47.393040Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2601.09893","last_updated":"2026-07-02T13:32:31Z","snapshot_observed_at":"2026-08-11T13:52:32.394890Z","submitted_at":"2026-01-14T21:54:33Z","title":"Complex Monge-Amp\\`ere equation in Orlicz space and Diameter Bound","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-03T10:35:47.393040Z"},"links":{"cited_paper":"/paper/2311.00221","citing_paper":"/paper/2601.09893"},"observation_digest":"sha256:518cc83f1de2b03dc67a4fba1ee868c64f407249151a8223b98c31bb2fd76b6f","observation_id":"5858f2cf-9c61-46b1-84c6-15511c53114b","resolution":{"observed_at":"2026-08-03T10:35:47.393040Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.00221","last_updated":"2023-11-01T01:44:39Z","snapshot_observed_at":"2026-08-01T20:58:26.661584Z","submitted_at":"2023-11-01T01:44:39Z","title":"Sobolev inequalities on K\\\"ahler spaces","version":1},"cited_work":{"arxiv_id":"2311.00221","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2311.00221","snapshot_observed_at":"2026-07-03T13:18:12.470462Z","title":"Guo, D.H","venue":null,"work_id":"654ff3de-879f-414e-9d28-7f4cc0409522","year":2024},"citing_paper":{"arxiv_id":"2602.19913","last_updated":"2026-05-19T20:10:57Z","snapshot_observed_at":"2026-07-06T22:46:45.213871Z","submitted_at":"2026-02-23T14:53:07Z","title":"Gromov-Hausdorff limits of immortal K\\\"ahler-Ricci flows","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-21T12:38:19.511651Z"},"links":{"cited_paper":"/paper/2311.00221","citing_paper":"/paper/2602.19913"},"observation_digest":"sha256:c99f0b4f279a43d6c8c9fe6b6153563bd8d9b1aa40f34eeb7a82aab931778653","observation_id":"7126c5e3-f3ae-4a58-b90a-5c5b11e2ac0d","resolution":{"observed_at":"2026-05-21T12:40:08.789223Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.00221","last_updated":"2023-11-01T01:44:39Z","snapshot_observed_at":"2026-08-01T20:58:26.661584Z","submitted_at":"2023-11-01T01:44:39Z","title":"Sobolev inequalities on K\\\"ahler spaces","version":1},"cited_work":{"arxiv_id":"2311.00221","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2311.00221","snapshot_observed_at":"2026-07-03T13:18:12.470462Z","title":"Guo, D.H","venue":null,"work_id":"654ff3de-879f-414e-9d28-7f4cc0409522","year":2024},"citing_paper":{"arxiv_id":"2604.04710","last_updated":"2026-04-21T15:34:45Z","snapshot_observed_at":"2026-08-07T04:30:21.685832Z","submitted_at":"2026-04-06T14:24:09Z","title":"Gromov-Hausdorff limits of the Chern-Ricci flow on smooth Hermitian minimal models of general type","version":2},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-05-10T19:41:14.983115Z"},"links":{"cited_paper":"/paper/2311.00221","citing_paper":"/paper/2604.04710"},"observation_digest":"sha256:ec231ca04f716751c2a13a64b23a937771ee69b21cc9142ecc153bb700ed340f","observation_id":"e2fa9516-0865-42a7-acb5-6fd89cf1026b","resolution":{"observed_at":"2026-05-10T22:35:51.884034Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.00221","last_updated":"2023-11-01T01:44:39Z","snapshot_observed_at":"2026-08-01T20:58:26.661584Z","submitted_at":"2023-11-01T01:44:39Z","title":"Sobolev inequalities on K\\\"ahler spaces","version":1},"cited_work":{"arxiv_id":"2311.00221","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2311.00221","snapshot_observed_at":"2026-07-03T13:18:12.470462Z","title":"Guo, D.H","venue":null,"work_id":"654ff3de-879f-414e-9d28-7f4cc0409522","year":2024},"citing_paper":{"arxiv_id":"2605.08023","last_updated":"2026-05-08T17:10:43Z","snapshot_observed_at":"2026-08-01T03:24:42.298400Z","submitted_at":"2026-05-08T17:10:43Z","title":"Asymptotics of small eigenvalues on degenerations of K\\\"ahler manifolds","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-11T02:28:05.107805Z"},"links":{"cited_paper":"/paper/2311.00221","citing_paper":"/paper/2605.08023"},"observation_digest":"sha256:8ddd1349331f3fa8d32688dbd13486f9209fb565f784f3477fe3271d548b31cf","observation_id":"e7e0d09a-86dc-4e98-a745-06399352eb05","resolution":{"observed_at":"2026-05-11T03:30:56.108479Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.00221","last_updated":"2023-11-01T01:44:39Z","snapshot_observed_at":"2026-08-01T20:58:26.661584Z","submitted_at":"2023-11-01T01:44:39Z","title":"Sobolev inequalities on K\\\"ahler spaces","version":1},"cited_work":{"arxiv_id":"2311.00221","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2311.00221","snapshot_observed_at":"2026-07-03T13:18:12.470462Z","title":"Guo, D.H","venue":null,"work_id":"654ff3de-879f-414e-9d28-7f4cc0409522","year":2024},"citing_paper":{"arxiv_id":"2605.22347","last_updated":"2026-05-21T11:31:35Z","snapshot_observed_at":"2026-08-06T05:21:51.892120Z","submitted_at":"2026-05-21T11:31:35Z","title":"Convergence of the Chern-Ricci flow on complex minimal surfaces of general type","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-05-22T02:42:20.623250Z"},"links":{"cited_paper":"/paper/2311.00221","citing_paper":"/paper/2605.22347"},"observation_digest":"sha256:8aa493d2b7586525058337bcc4ad0b807e7183a36e30bc57d902c9ce0a4142f0","observation_id":"1dcff732-2adb-49ff-a90f-e95ff60b3096","resolution":{"observed_at":"2026-05-22T02:44:32.243479Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.00221","last_updated":"2023-11-01T01:44:39Z","snapshot_observed_at":"2026-08-01T20:58:26.661584Z","submitted_at":"2023-11-01T01:44:39Z","title":"Sobolev inequalities on K\\\"ahler spaces","version":1},"cited_work":{"arxiv_id":"2311.00221","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2311.00221","snapshot_observed_at":"2026-07-03T13:18:12.470462Z","title":"Guo, D.H","venue":null,"work_id":"654ff3de-879f-414e-9d28-7f4cc0409522","year":2024},"citing_paper":{"arxiv_id":"2606.12063","last_updated":"2026-06-10T13:30:51Z","snapshot_observed_at":"2026-07-06T23:51:02.805629Z","submitted_at":"2026-06-10T13:30:51Z","title":"Optimal geometric estimates for compact K\\\"ahler manifolds of a Nash entropy bound","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-27T08:22:34.404523Z"},"links":{"cited_paper":"/paper/2311.00221","citing_paper":"/paper/2606.12063"},"observation_digest":"sha256:d59752b08d53c40061b456b73617cc396eb4adc0c918411768fa682a0ae72df6","observation_id":"03cf2ed7-0095-421c-8dc6-6fa390b6dd78","resolution":{"observed_at":"2026-07-03T13:18:12.472093Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2311.00221/citation-record","integrity":"/paper/2311.00221/integrity","json":"/paper/2311.00221/citation-record.json","paper":"/paper/2311.00221"},"outbound":[],"paper":{"arxiv_id":"2311.00221","last_updated":"2023-11-01T01:44:39Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-08-01T20:58:26.661584Z","submitted_at":"2023-11-01T01:44:39Z","title":"Sobolev inequalities on K\\\"ahler spaces"},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 13 inbound Pith citation observations for arXiv:2311.00221."}