{"as_of":"2026-08-11T08:03:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:45f2d6148b84ce8cfa9271c0d66f21edda4cc60fe715371fa71cffdbce858575","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":10,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":10,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":10,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":10,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-09T21:36:03.034643Z","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":"2026-07-03T13:08:08.101177Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2401.03949","last_updated":"2025-02-03T17:09:29Z","snapshot_observed_at":"2026-08-04T14:46:31.568257Z","submitted_at":"2024-01-08T15:13:34Z","title":"A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.03949","snapshot_observed_at":"2026-08-09T21:36:03.034643Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2501.19071","last_updated":"2025-07-02T13:11:31Z","snapshot_observed_at":"2026-08-10T05:30:22.462949Z","submitted_at":"2025-01-31T11:59:47Z","title":"New perspectives on the d'Alembertian from general relativity. An invitation","version":2},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-09T21:36:03.034643Z"},"links":{"cited_paper":"/paper/2401.03949","citing_paper":"/paper/2501.19071"},"observation_digest":"sha256:ce7e2bbecd8589d0bf1ed9dd69b8444ba7f40b83b9566daa9f92dad2c99c4a1b","observation_id":"730f0326-578d-46cb-b542-c413fa2786b3","resolution":{"observed_at":"2026-08-09T21:36:03.034643Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.03949","last_updated":"2025-02-03T17:09:29Z","snapshot_observed_at":"2026-08-04T14:46:31.568257Z","submitted_at":"2024-01-08T15:13:34Z","title":"A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds","version":2},"cited_work":{"arxiv_id":"2401.03949","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2401.03949","snapshot_observed_at":"2026-07-03T13:08:08.101177Z","title":"Cavalletti and A","venue":null,"work_id":"90d5c074-aa8b-4bc6-86ff-02050540e5b9","year":2024},"citing_paper":{"arxiv_id":"2506.04934","last_updated":"2026-04-29T18:29:45Z","snapshot_observed_at":"2026-07-06T21:37:09.640484Z","submitted_at":"2025-06-05T12:09:09Z","title":"On the geometry of synthetic null hypersurfaces","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-19T11:26:33.006804Z"},"links":{"cited_paper":"/paper/2401.03949","citing_paper":"/paper/2506.04934"},"observation_digest":"sha256:b2b24e1836c98f349a8830feb2b9bec8913e6d0f20d093f9c77d5449c3825d84","observation_id":"557b8234-a5b8-4eff-89a6-48bf7b513040","resolution":{"observed_at":"2026-05-19T11:27:15.880215Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"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":"2401.03949","last_updated":"2025-02-03T17:09:29Z","snapshot_observed_at":"2026-08-04T14:46:31.568257Z","submitted_at":"2024-01-08T15:13:34Z","title":"A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds","version":2},"cited_work":{"arxiv_id":"2401.03949","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2401.03949","snapshot_observed_at":"2026-07-03T13:08:08.101177Z","title":"Cavalletti and A","venue":null,"work_id":"90d5c074-aa8b-4bc6-86ff-02050540e5b9","year":2024},"citing_paper":{"arxiv_id":"2509.05224","last_updated":"2026-05-04T15:32:05Z","snapshot_observed_at":"2026-07-06T22:24:38.247543Z","submitted_at":"2025-09-05T16:37:37Z","title":"Reshetnyak Majorisation and discrete upper curvature bounds for Lorentzian length spaces","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-18T18:26:09.708089Z"},"links":{"cited_paper":"/paper/2401.03949","citing_paper":"/paper/2509.05224"},"observation_digest":"sha256:9168b5af586d9cf95cbbf881c40f0b58db983b6a8eebe1cb025f25e572b9528f","observation_id":"a2f36454-ef03-4cad-b1e9-a29b03b22ca3","resolution":{"observed_at":"2026-05-18T18:26:43.623367Z","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":"2401.03949","last_updated":"2025-02-03T17:09:29Z","snapshot_observed_at":"2026-08-04T14:46:31.568257Z","submitted_at":"2024-01-08T15:13:34Z","title":"A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.03949","snapshot_observed_at":"2026-08-04T07:21:33.954128Z","title":"Cavalletti and A","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.26755","last_updated":"2026-07-17T16:38:44Z","snapshot_observed_at":"2026-08-04T07:18:22.600528Z","submitted_at":"2025-10-30T17:47:53Z","title":"Quantitative Lorentzian isoperimetric inequalities in conical Minkowski spacetimes","version":3},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-04T07:21:33.954128Z"},"links":{"cited_paper":"/paper/2401.03949","citing_paper":"/paper/2510.26755"},"observation_digest":"sha256:832cd61ef8c4e64005c4b4afbcbffe90c3a7f27947536c7e228715cc6d292022","observation_id":"27dc0ee0-3400-4777-8238-fd6187760baa","resolution":{"observed_at":"2026-08-04T07:21:33.954128Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.03949","last_updated":"2025-02-03T17:09:29Z","snapshot_observed_at":"2026-08-04T14:46:31.568257Z","submitted_at":"2024-01-08T15:13:34Z","title":"A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.03949","snapshot_observed_at":"2026-08-03T16:55:08.698743Z","title":"Cavalletti and A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.11626","last_updated":"2026-07-29T15:11:15Z","snapshot_observed_at":"2026-08-06T21:25:27.395649Z","submitted_at":"2025-12-12T15:04:43Z","title":"Differentiability and Other Properties of the Cosmological Volume Function","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T16:55:08.698743Z"},"links":{"cited_paper":"/paper/2401.03949","citing_paper":"/paper/2512.11626"},"observation_digest":"sha256:36994d835ac7f632bb5b1e2d6edcababcdba5eb25233edb523d7d6d0f6c43f2c","observation_id":"6faad38d-4a16-4438-b740-aa83882949f0","resolution":{"observed_at":"2026-08-03T16:55:08.698743Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.03949","last_updated":"2025-02-03T17:09:29Z","snapshot_observed_at":"2026-08-04T14:46:31.568257Z","submitted_at":"2024-01-08T15:13:34Z","title":"A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds","version":2},"cited_work":{"arxiv_id":"2401.03949","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2401.03949","snapshot_observed_at":"2026-07-03T13:08:08.101177Z","title":"Cavalletti and A","venue":null,"work_id":"90d5c074-aa8b-4bc6-86ff-02050540e5b9","year":2024},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"cited_paper":"/paper/2401.03949","citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:b2619891792ca3932a40f47fcb5fd3967d82f3c331d70823165ea5e6b11293da","observation_id":"6a5d7f26-f4ed-49f7-bd1e-53fe0d78e07f","resolution":{"observed_at":"2026-05-13T22:28:21.196682Z","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":"2401.03949","last_updated":"2025-02-03T17:09:29Z","snapshot_observed_at":"2026-08-04T14:46:31.568257Z","submitted_at":"2024-01-08T15:13:34Z","title":"A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds","version":2},"cited_work":{"arxiv_id":"2401.03949","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2401.03949","snapshot_observed_at":"2026-07-03T13:08:08.101177Z","title":"Cavalletti and A","venue":null,"work_id":"90d5c074-aa8b-4bc6-86ff-02050540e5b9","year":2024},"citing_paper":{"arxiv_id":"2604.22420","last_updated":"2026-04-24T10:26:37Z","snapshot_observed_at":"2026-08-11T07:11:01.199784Z","submitted_at":"2026-04-24T10:26:37Z","title":"Infinitesimal Minkowskianity for manifolds with continuous Lorentzian metrics","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-08T09:58:54.917877Z"},"links":{"cited_paper":"/paper/2401.03949","citing_paper":"/paper/2604.22420"},"observation_digest":"sha256:8008d97e7b6a93ab463d064383d20063d13a616ad24a0bb8699ad275343b9d8c","observation_id":"3ef1d712-d97b-4f88-a7b9-511fa3757086","resolution":{"observed_at":"2026-05-11T20:11:12.458027Z","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":"2401.03949","last_updated":"2025-02-03T17:09:29Z","snapshot_observed_at":"2026-08-04T14:46:31.568257Z","submitted_at":"2024-01-08T15:13:34Z","title":"A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds","version":2},"cited_work":{"arxiv_id":"2401.03949","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2401.03949","snapshot_observed_at":"2026-07-03T13:08:08.101177Z","title":"Cavalletti and A","venue":null,"work_id":"90d5c074-aa8b-4bc6-86ff-02050540e5b9","year":2024},"citing_paper":{"arxiv_id":"2605.09101","last_updated":"2026-05-19T09:12:35Z","snapshot_observed_at":"2026-07-06T23:21:16.454273Z","submitted_at":"2026-05-09T18:16:19Z","title":"Lorentzian coarea inequality","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-12T03:11:09.902750Z"},"links":{"cited_paper":"/paper/2401.03949","citing_paper":"/paper/2605.09101"},"observation_digest":"sha256:3bf2f26dab267c8bb7abe5bbebabd8eae4c2e09e1fb5e01cd1e7e1c69aecbc35","observation_id":"4de04e80-203f-4b44-9e6d-23bf9afa9fcc","resolution":{"observed_at":"2026-05-12T03:11:18.645145Z","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":"2401.03949","last_updated":"2025-02-03T17:09:29Z","snapshot_observed_at":"2026-08-04T14:46:31.568257Z","submitted_at":"2024-01-08T15:13:34Z","title":"A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds","version":2},"cited_work":{"arxiv_id":"2401.03949","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2401.03949","snapshot_observed_at":"2026-07-03T13:08:08.101177Z","title":"Cavalletti and A","venue":null,"work_id":"90d5c074-aa8b-4bc6-86ff-02050540e5b9","year":2024},"citing_paper":{"arxiv_id":"2605.09101","last_updated":"2026-05-19T09:12:35Z","snapshot_observed_at":"2026-07-06T23:21:16.454273Z","submitted_at":"2026-05-09T18:16:19Z","title":"Lorentzian coarea inequality","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-20T23:10:33.474875Z"},"links":{"cited_paper":"/paper/2401.03949","citing_paper":"/paper/2605.09101"},"observation_digest":"sha256:33c9354a9a6675732a7d8f575c5c5177e01a828e688aba7417c6288f350b2171","observation_id":"a5e1252f-fd5b-4ea7-aad7-ad7665613379","resolution":{"observed_at":"2026-05-20T23:13:50.597430Z","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":"2401.03949","last_updated":"2025-02-03T17:09:29Z","snapshot_observed_at":"2026-08-04T14:46:31.568257Z","submitted_at":"2024-01-08T15:13:34Z","title":"A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds","version":2},"cited_work":{"arxiv_id":"2401.03949","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2401.03949","snapshot_observed_at":"2026-07-03T13:08:08.101177Z","title":"Cavalletti and A","venue":null,"work_id":"90d5c074-aa8b-4bc6-86ff-02050540e5b9","year":2024},"citing_paper":{"arxiv_id":"2606.11825","last_updated":"2026-06-10T09:03:22Z","snapshot_observed_at":"2026-07-06T23:50:49.040880Z","submitted_at":"2026-06-10T09:03:22Z","title":"A singularity theorem in terms of asymptotic expansion","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-27T08:33:07.176771Z"},"links":{"cited_paper":"/paper/2401.03949","citing_paper":"/paper/2606.11825"},"observation_digest":"sha256:dba8506a3527a46d0160bca84b465ea033b48fcee9ab7769de064652b8540499","observation_id":"bfebd489-b11b-43cb-9f13-e4e1d6eb23e3","resolution":{"observed_at":"2026-07-03T13:08:08.103160Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"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/2401.03949/citation-record","integrity":"/paper/2401.03949/integrity","json":"/paper/2401.03949/citation-record.json","paper":"/paper/2401.03949"},"outbound":[],"paper":{"arxiv_id":"2401.03949","last_updated":"2025-02-03T17:09:29Z","latest_version":2,"primary_category":"math.MG","snapshot_observed_at":"2026-08-04T14:46:31.568257Z","submitted_at":"2024-01-08T15:13:34Z","title":"A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds"},"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 10 inbound Pith citation observations for arXiv:2401.03949."}