{"as_of":"2026-08-18T07:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:095f6d13da9805024cdf16eaaa27b133beaac95895486d67f19e4dc0e33a2926","coverage":[{"denominator":10,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":10,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-13T02:46:27.154020Z","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":"2026-08-18T06:34:40.430872+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/2607.09472/citation-record","integrity":"/paper/2607.09472/integrity","json":"/paper/2607.09472/citation-record.json","paper":"/paper/2607.09472"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3842/sigma.2024.035.zbl","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:49:20.633653Z","title":"Symmetry, Integrability and Geometry: Methods and Applications20(2024), paper 035, 26, DOI 10.3842/SIGMA.2024.035.Zbl 1570.53032","venue":null,"work_id":"99a1d919-b3e6-47fa-b101-fac32c590697","year":2024},"citing_paper":{"arxiv_id":"2607.09472","last_updated":"2026-07-10T14:44:25Z","snapshot_observed_at":"2026-08-14T07:49:58.816646Z","submitted_at":"2026-07-10T14:44:25Z","title":"Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifolds","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-13T02:46:27.154020Z"},"links":{"citing_paper":"/paper/2607.09472"},"observation_digest":"sha256:2a202cbe13fa7d710f7895b25435d7c785e30fa927445f4e00aa3f4221cde47b","observation_id":"67c8da69-f875-42ae-bd2b-c0407ce89aed","resolution":{"observed_at":"2026-07-13T02:49:20.637303Z","resolver_source":"doi","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":"2026-07-20T18:51:56.43864+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T18:51:56.43864+00:00","source":"openalex_status_cache"},{"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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:46:27.154020Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.09472","last_updated":"2026-07-10T14:44:25Z","snapshot_observed_at":"2026-08-14T07:49:58.816646Z","submitted_at":"2026-07-10T14:44:25Z","title":"Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifolds","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-13T02:46:27.154020Z"},"links":{"citing_paper":"/paper/2607.09472"},"observation_digest":"sha256:2f940aa22f237c189923890a81371d16128a5804a68f257ea203e6516b6c94b6","observation_id":"b0bf78bf-2921-49d0-a3e4-9c8babb8c490","resolution":{"observed_at":"2026-07-13T02:46:27.154020Z","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":"10.4171/jems/1514.zbl","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:49:20.608325Z","title":"6, 2549–2579, DOI 10.4171/jems/1514.Zbl 08176144","venue":null,"work_id":"daff02a3-f98e-4258-b011-0123911fbab9","year":2026},"citing_paper":{"arxiv_id":"2607.09472","last_updated":"2026-07-10T14:44:25Z","snapshot_observed_at":"2026-08-14T07:49:58.816646Z","submitted_at":"2026-07-10T14:44:25Z","title":"Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifolds","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-13T02:46:27.154020Z"},"links":{"citing_paper":"/paper/2607.09472"},"observation_digest":"sha256:91f850d576e65db15fa809ba065e6306332c287f80a3eb5305b947b67b680559","observation_id":"bc905fd5-22ef-4391-8e2f-5975b23ed25f","resolution":{"observed_at":"2026-07-13T02:49:20.610201Z","resolver_source":"doi","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":"2026-07-20T18:51:56.69536+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T18:51:56.69536+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.14054","last_updated":"2025-06-18T16:43:50Z","snapshot_observed_at":"2026-08-10T08:53:18.514076Z","submitted_at":"2025-05-20T07:56:30Z","title":"Abstract cone operators and Lipschitz rigidity for scalar curvature on singular manifolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.14054","snapshot_observed_at":"2026-07-13T02:46:27.154020Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.09472","last_updated":"2026-07-10T14:44:25Z","snapshot_observed_at":"2026-08-14T07:49:58.816646Z","submitted_at":"2026-07-10T14:44:25Z","title":"Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifolds","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-13T02:46:27.154020Z"},"links":{"cited_paper":"/paper/2505.14054","citing_paper":"/paper/2607.09472"},"observation_digest":"sha256:8de580fec78a63f77680d25221d3be718caaed56aceb5d4a9cc81232c283536b","observation_id":"a304389d-03e4-4158-a976-1b1b0e179bd1","resolution":{"observed_at":"2026-07-13T02:46:27.154020Z","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":"2026-07-13T02:46:27.154020Z","title":"Goette and U","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.09472","last_updated":"2026-07-10T14:44:25Z","snapshot_observed_at":"2026-08-14T07:49:58.816646Z","submitted_at":"2026-07-10T14:44:25Z","title":"Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifolds","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-13T02:46:27.154020Z"},"links":{"citing_paper":"/paper/2607.09472"},"observation_digest":"sha256:bca31b6977596642c0008ed0af8681c5e44161eeba0d2a5b76c56df64f46d8a3","observation_id":"bc3a4034-6bae-4dc2-9621-757df3df342a","resolution":{"observed_at":"2026-07-13T02:46:27.154020Z","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":"2026-07-13T02:46:27.154020Z","title":"Blaine jun","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2607.09472","last_updated":"2026-07-10T14:44:25Z","snapshot_observed_at":"2026-08-14T07:49:58.816646Z","submitted_at":"2026-07-10T14:44:25Z","title":"Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifolds","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-13T02:46:27.154020Z"},"links":{"citing_paper":"/paper/2607.09472"},"observation_digest":"sha256:259b5f83ebd17cb34cb0ecbcaf409ccd21a71c4b530d29bc80a4475efcdbc039","observation_id":"4402777a-ddad-4b02-b858-01b30bc5ebda","resolution":{"observed_at":"2026-07-13T02:46:27.154020Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2207.11017","last_updated":"2022-07-22T11:42:50Z","snapshot_observed_at":"2026-08-16T16:44:04.768030Z","submitted_at":"2022-07-22T11:42:50Z","title":"Rigidity of Lipschitz map using harmonic map heat flow","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2207.11017","snapshot_observed_at":"2026-07-13T02:46:27.154020Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.09472","last_updated":"2026-07-10T14:44:25Z","snapshot_observed_at":"2026-08-14T07:49:58.816646Z","submitted_at":"2026-07-10T14:44:25Z","title":"Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifolds","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-13T02:46:27.154020Z"},"links":{"cited_paper":"/paper/2207.11017","citing_paper":"/paper/2607.09472"},"observation_digest":"sha256:98ea0016ee777b54efcccfe1ecca2a20ae7ee3e83a4a870125ab5e5b4140b381","observation_id":"cb71508e-4e81-4e4c-ad6c-801bb6adf167","resolution":{"observed_at":"2026-07-13T02:46:27.154020Z","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":"10.1007/s11425-023-2138-5.zbl","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:49:20.626610Z","title":"Mathematics67(2024), no","venue":null,"work_id":"328b5bc8-a6a2-473b-a313-8a82dc9009f2","year":2024},"citing_paper":{"arxiv_id":"2607.09472","last_updated":"2026-07-10T14:44:25Z","snapshot_observed_at":"2026-08-14T07:49:58.816646Z","submitted_at":"2026-07-10T14:44:25Z","title":"Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifolds","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-13T02:46:27.154020Z"},"links":{"citing_paper":"/paper/2607.09472"},"observation_digest":"sha256:a6aa9fca6f4aa8b1dea6af8751f4fe2eda1f38b4574eaae14e4f4cb1de91dbdc","observation_id":"621bd20c-7437-41e2-8d99-b8fcbd8a6c57","resolution":{"observed_at":"2026-07-13T02:49:20.629304Z","resolver_source":"doi","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":"2026-07-20T18:51:56.920026+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T18:51:56.920026+00:00","source":"openalex_status_cache"},{"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":"10.1007/s002080050136.zbl","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:49:20.619244Z","title":"1, 55–71, DOI 10.1007/s002080050136.Zbl 0895.53037","venue":null,"work_id":"eb09ae5d-13f5-45ba-825f-c887ee281834","year":1998},"citing_paper":{"arxiv_id":"2607.09472","last_updated":"2026-07-10T14:44:25Z","snapshot_observed_at":"2026-08-14T07:49:58.816646Z","submitted_at":"2026-07-10T14:44:25Z","title":"Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifolds","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-13T02:46:27.154020Z"},"links":{"citing_paper":"/paper/2607.09472"},"observation_digest":"sha256:866468229190f6e47e8b5b4b1157edcf9bf2b71bf498797e095fc496f8e88fbb","observation_id":"297d0caa-77d2-4c63-b4a0-a5e09d52213c","resolution":{"observed_at":"2026-07-13T02:49:20.621638Z","resolver_source":"doi","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":"2026-07-20T18:51:57.14184+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T18:51:57.14184+00:00","source":"openalex_status_cache"},{"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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:46:27.154020Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.09472","last_updated":"2026-07-10T14:44:25Z","snapshot_observed_at":"2026-08-14T07:49:58.816646Z","submitted_at":"2026-07-10T14:44:25Z","title":"Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifolds","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-13T02:46:27.154020Z"},"links":{"citing_paper":"/paper/2607.09472"},"observation_digest":"sha256:7c29197d7571dad4721741e8d4e4ab386cffac628bae3746bca469bb19432f4f","observation_id":"a6fa0977-f28d-46f9-98e4-e1440bcc2c66","resolution":{"observed_at":"2026-07-13T02:46:27.154020Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.09472","last_updated":"2026-07-10T14:44:25Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-08-14T07:49:58.816646Z","submitted_at":"2026-07-10T14:44:25Z","title":"Scalar Curvature Rigidity for Products of convex Hypersurfaces and even dimensional Manifolds"},"reference_resolution":{"displayed":10,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":4,"verified_fuzzy":0},"total_outbound_references":10},"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 18 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:2607.09472."}