{"as_of":"2026-08-11T03:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c8ef8a8eccf3e3e39f9cef5e75d61600248cb0dd15292d4df48fffda41d3dc0b","coverage":[{"denominator":13,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":13,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T07:41:24.138175Z","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":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.21423/citation-record","integrity":"/paper/2607.21423/integrity","json":"/paper/2607.21423/citation-record.json","paper":"/paper/2607.21423"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4310/cag.2008.v16.n2.a1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Alexander and Richard L","venue":"Communications in Analysis and Geometry","work_id":"8836291f-0832-46c7-bd3e-14304adb3443","year":2008},"citing_paper":{"arxiv_id":"2607.21423","last_updated":"2026-07-23T15:26:26Z","snapshot_observed_at":"2026-08-09T22:39:56.822789Z","submitted_at":"2026-07-23T15:26:26Z","title":"Doubling for chronological diamonds in Lorentzian geometry","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T07:41:24.109253Z"},"links":{"citing_paper":"/paper/2607.21423"},"observation_digest":"sha256:164f49f44233ce29691a053f707b8e435526bfa9facbc3959e97690b6e34155e","observation_id":"7e918cbf-c6d8-4eda-b1c1-bae25b67394a","resolution":{"observed_at":"2026-08-01T07:44:06.763807Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-01T09:38:25.850521+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-01T09:38:25.850521+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2605.11271","last_updated":"2026-06-08T09:36:30Z","snapshot_observed_at":"2026-07-06T23:23:06.755816Z","submitted_at":"2026-05-11T21:50:56Z","title":"Convergence of Lorentzian spaces and curvature bounds for generalized cones","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2605.11271","snapshot_observed_at":"2026-08-01T07:41:24.124487Z","title":"[KP67] E","venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2607.21423","last_updated":"2026-07-23T15:26:26Z","snapshot_observed_at":"2026-08-09T22:39:56.822789Z","submitted_at":"2026-07-23T15:26:26Z","title":"Doubling for chronological diamonds in Lorentzian geometry","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T07:41:24.124487Z"},"links":{"cited_paper":"/paper/2605.11271","citing_paper":"/paper/2607.21423"},"observation_digest":"sha256:d9658bb85b45e40805b22288953e3164ab7c389bf6c66ba395ccd4774fee6296","observation_id":"dc741f85-0607-4e14-999c-1d836ba17349","resolution":{"observed_at":"2026-08-01T07:41:24.124487Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2504.10380","last_updated":"2026-06-18T08:19:39Z","snapshot_observed_at":"2026-08-10T19:06:35.550332Z","submitted_at":"2025-04-14T16:25:36Z","title":"Lorentzian Gromov-Hausdorff convergence and pre-compactness","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.10380","snapshot_observed_at":"2026-08-01T07:41:24.129165Z","title":"[MS22] Robert J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.21423","last_updated":"2026-07-23T15:26:26Z","snapshot_observed_at":"2026-08-09T22:39:56.822789Z","submitted_at":"2026-07-23T15:26:26Z","title":"Doubling for chronological diamonds in Lorentzian geometry","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T07:41:24.129165Z"},"links":{"cited_paper":"/paper/2504.10380","citing_paper":"/paper/2607.21423"},"observation_digest":"sha256:d91fcef15c9bc8b43e261a276a3884880d0256b2c7421e4f42491e673203f21e","observation_id":"58925b2d-9fcf-4802-8981-8cc088e92930","resolution":{"observed_at":"2026-08-01T07:41:24.129165Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T07:41:24.131648Z","title":"[Stu06a] Karl-Theodor Sturm","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.21423","last_updated":"2026-07-23T15:26:26Z","snapshot_observed_at":"2026-08-09T22:39:56.822789Z","submitted_at":"2026-07-23T15:26:26Z","title":"Doubling for chronological diamonds in Lorentzian geometry","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T07:41:24.131648Z"},"links":{"citing_paper":"/paper/2607.21423"},"observation_digest":"sha256:ce2407c274851775fa912505bc5f9770aff8cf9f91b2866b5fffd67b89894fd0","observation_id":"7ea3214b-86f8-4e04-929f-03d9c34a8f58","resolution":{"observed_at":"2026-08-01T07:41:24.131648Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T07:41:24.135989Z","title":"[SV16] Christina Sormani and Carlos Vega","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.21423","last_updated":"2026-07-23T15:26:26Z","snapshot_observed_at":"2026-08-09T22:39:56.822789Z","submitted_at":"2026-07-23T15:26:26Z","title":"Doubling for chronological diamonds in Lorentzian geometry","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T07:41:24.135989Z"},"links":{"citing_paper":"/paper/2607.21423"},"observation_digest":"sha256:3f1ac68de24d0ba2c8b61df2a4d7c9afddea75e997bd1a6b07cdc332f459024a","observation_id":"27ff7496-c271-4699-9d90-521b2218be5f","resolution":{"observed_at":"2026-08-01T07:41:24.135989Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T07:41:24.138175Z","title":"doi: 10.1007/978-3-540-71050-9","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.21423","last_updated":"2026-07-23T15:26:26Z","snapshot_observed_at":"2026-08-09T22:39:56.822789Z","submitted_at":"2026-07-23T15:26:26Z","title":"Doubling for chronological diamonds in Lorentzian geometry","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T07:41:24.138175Z"},"links":{"citing_paper":"/paper/2607.21423"},"observation_digest":"sha256:ea34d6ca142675eb949d671d4865cb5f79e2688c7cea131e747d5358212a7321","observation_id":"e68604cd-9d9a-4312-8b12-ff788baddefc","resolution":{"observed_at":"2026-08-01T07:41:24.138175Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1512/iumj.1982.31.31026","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Lafontaine and P","venue":"Indiana University Mathematics Journal","work_id":"3b92feea-5506-4316-8e7c-498237b66058","year":1982},"citing_paper":{"arxiv_id":"2607.21423","last_updated":"2026-07-23T15:26:26Z","snapshot_observed_at":"2026-08-09T22:39:56.822789Z","submitted_at":"2026-07-23T15:26:26Z","title":"Doubling for chronological diamonds in Lorentzian geometry","version":1},"reference_index":1981,"source":"pdf_text","source_observed_at":"2026-08-01T07:41:24.122001Z"},"links":{"citing_paper":"/paper/2607.21423"},"observation_digest":"sha256:6214dedc48492d81d512524ee9e1050579335efa51337c250ddf9c9e5c104ce1","observation_id":"f795cb56-dfd5-411a-b7c1-1a3309457fb8","resolution":{"observed_at":"2026-08-01T07:44:06.633718Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-01T09:38:26.586592+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-01T09:38:26.586592+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.15968","last_updated":"2025-03-20T08:26:55Z","snapshot_observed_at":"2026-08-10T17:46:12.648747Z","submitted_at":"2024-08-28T17:42:47Z","title":"A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.15968","snapshot_observed_at":"2026-08-01T07:41:24.112348Z","title":"Ambrosio, N","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.21423","last_updated":"2026-07-23T15:26:26Z","snapshot_observed_at":"2026-08-09T22:39:56.822789Z","submitted_at":"2026-07-23T15:26:26Z","title":"Doubling for chronological diamonds in Lorentzian geometry","version":1},"reference_index":2005,"source":"pdf_text","source_observed_at":"2026-08-01T07:41:24.112348Z"},"links":{"cited_paper":"/paper/2408.15968","citing_paper":"/paper/2607.21423"},"observation_digest":"sha256:b5cf4b59fda34c788e4f25862d03b31eeab899c4f9932b79f7061f1bc6bcf8e7","observation_id":"a1143e4b-e75d-4f5f-bd87-9926ed83401f","resolution":{"observed_at":"2026-08-01T07:41:24.112348Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T07:41:24.133788Z","title":"[Stu06b] Karl-Theodor Sturm","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.21423","last_updated":"2026-07-23T15:26:26Z","snapshot_observed_at":"2026-08-09T22:39:56.822789Z","submitted_at":"2026-07-23T15:26:26Z","title":"Doubling for chronological diamonds in Lorentzian geometry","version":1},"reference_index":2006,"source":"pdf_text","source_observed_at":"2026-08-01T07:41:24.133788Z"},"links":{"citing_paper":"/paper/2607.21423"},"observation_digest":"sha256:b3412f67bcd53aef2f9191984e2cc76938c88fa45ceb8765cd80894c851b16ae","observation_id":"e4961669-1ef4-4bde-a940-a8632a3e96b9","resolution":{"observed_at":"2026-08-01T07:41:24.133788Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T07:41:24.126824Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.21423","last_updated":"2026-07-23T15:26:26Z","snapshot_observed_at":"2026-08-09T22:39:56.822789Z","submitted_at":"2026-07-23T15:26:26Z","title":"Doubling for chronological diamonds in Lorentzian geometry","version":1},"reference_index":2009,"source":"pdf_text","source_observed_at":"2026-08-01T07:41:24.126824Z"},"links":{"citing_paper":"/paper/2607.21423"},"observation_digest":"sha256:a46b8307750df791945f39757cb225aade12cf9918ab7806b71ea6c793c0676d","observation_id":"e34c3f7b-39f3-46bb-b637-2fb3dc8f52e5","resolution":{"observed_at":"2026-08-01T07:41:24.126824Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T07:41:24.117547Z","title":"2024.v12.n2.a3","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.21423","last_updated":"2026-07-23T15:26:26Z","snapshot_observed_at":"2026-08-09T22:39:56.822789Z","submitted_at":"2026-07-23T15:26:26Z","title":"Doubling for chronological diamonds in Lorentzian geometry","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-01T07:41:24.117547Z"},"links":{"citing_paper":"/paper/2607.21423"},"observation_digest":"sha256:6f3c2a03147e2edc286caa5c4680ade7e2068ede2c57993b7be3bc3f016f8869","observation_id":"634b0f56-88ce-4dfb-aef7-d21a5bca128d","resolution":{"observed_at":"2026-08-01T07:41:24.117547Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T07:41:24.115153Z","title":"[CM20] Fabio Cavalletti and Andrea Mondino","venue":null,"work_id":null,"year":2091},"citing_paper":{"arxiv_id":"2607.21423","last_updated":"2026-07-23T15:26:26Z","snapshot_observed_at":"2026-08-09T22:39:56.822789Z","submitted_at":"2026-07-23T15:26:26Z","title":"Doubling for chronological diamonds in Lorentzian geometry","version":1},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-01T07:41:24.115153Z"},"links":{"citing_paper":"/paper/2607.21423"},"observation_digest":"sha256:1e3d781ec5aa9ad31dc4e62409450340536fe23a9eebf9caf8828e7f84d199ad","observation_id":"75cd5a8e-4dca-4141-90dd-bbc6d308330a","resolution":{"observed_at":"2026-08-01T07:41:24.115153Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T07:41:24.119883Z","title":"difgeo.2026.102364","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.21423","last_updated":"2026-07-23T15:26:26Z","snapshot_observed_at":"2026-08-09T22:39:56.822789Z","submitted_at":"2026-07-23T15:26:26Z","title":"Doubling for chronological diamonds in Lorentzian geometry","version":1},"reference_index":2026,"source":"pdf_text","source_observed_at":"2026-08-01T07:41:24.119883Z"},"links":{"citing_paper":"/paper/2607.21423"},"observation_digest":"sha256:38dd4ec87a00cdb6fe91b48246172b9ca19a679cdd6d39a01370d3fbdc9f2732","observation_id":"2e3d4f3f-f87f-427e-ba35-ccc9ccec74c8","resolution":{"observed_at":"2026-08-01T07:41:24.119883Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.21423","last_updated":"2026-07-23T15:26:26Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-08-09T22:39:56.822789Z","submitted_at":"2026-07-23T15:26:26Z","title":"Doubling for chronological diamonds in Lorentzian geometry"},"reference_resolution":{"displayed":13,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":2,"verified_fuzzy":0},"total_outbound_references":13},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2607.21423."}