{"as_of":"2026-08-21T13:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:98099328f0262d731551ec58db89a3b865eaa93d95abe6d976072dd3c7ec668c","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T11:47:03.568486Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-13T03:51:58.803017Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.22566","snapshot_observed_at":"2026-07-13T03:51:58.803017Z","title":"Palomo and Alfonso Romero","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.09325","last_updated":"2026-07-10T12:06:25Z","snapshot_observed_at":"2026-08-14T10:46:43.522886Z","submitted_at":"2026-07-10T12:06:25Z","title":"A note on the stability of surfaces along null cones under area-preserving variations","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-13T03:51:58.803017Z"},"links":{"cited_paper":"/paper/2507.22566","citing_paper":"/paper/2607.09325"},"observation_digest":"sha256:37f51fc00a601e037566653b6709782a55c4a016cdfb1939d2f15b34d6324969","observation_id":"3f1ee128-3b43-4391-b5fc-fd331fc4a381","resolution":{"observed_at":"2026-07-13T03:51:58.803017Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2507.22566/citation-record","integrity":"/paper/2507.22566/integrity","json":"/paper/2507.22566/citation-record.json","paper":"/paper/2507.22566"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.904737Z","title":"Al ´ ıas, V.L","venue":null,"work_id":"a4fdd575-87f7-413a-884e-82a67a19e57c","year":2019},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:02.444961Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:f20c607309023a10c53836a29a9eeb301b31d7e4e4a39c830285d7ff0f270bcc","observation_id":"514836de-7cdc-4316-82af-b8da98e99fc4","resolution":{"observed_at":"2026-08-06T11:47:03.908212Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.892768Z","title":"Al ´ ıas, F.J.M","venue":null,"work_id":"84def344-580b-41cb-b679-35f7142dfc36","year":1997},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:02.563211Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:6681bf03816f7809f373c16f7906b4e5423a774f10906e895055c798eb4bc8be","observation_id":"3871e36a-9ad9-4d62-a460-dcbbb8531239","resolution":{"observed_at":"2026-08-06T11:47:03.896967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.880451Z","title":"Asperti and M","venue":null,"work_id":"ac938d6f-b23d-421e-a40b-2940ceecdfe5","year":1989},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:02.786156Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:ac7f089e82e19654a19ae74defc27b1d69bae86ccafea82cc7c96a5158f17600","observation_id":"69b11104-6ce5-4fa7-a1b0-9daf26af3997","resolution":{"observed_at":"2026-08-06T11:47:03.884063Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.867810Z","title":"Avez, Applications de la formule de Gauss-Bonnet-Chern aux vari´ et´ es ` a quatre dimensions,C","venue":null,"work_id":"3efb6770-6c99-4646-aa79-5a1672c554a3","year":1963},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:02.898783Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:e5e7e0d1ad51dbc040b7fbc9519ef273fea0e3fe64800b27580a16a8cbda060a","observation_id":"bda4e215-beb0-4cda-b988-c2e19a7f2294","resolution":{"observed_at":"2026-08-06T11:47:03.872116Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.854363Z","title":"Besse, Einstein manifolds , Springer-Verlag, Berlin, Heidelberg, 1987","venue":null,"work_id":"8b80d43d-3cdf-47af-ae5a-de9ac727a018","year":1987},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:02.976463Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:f7eef85143d554d43e1a48a1002996b1361e6a6e9d2de7fce866bf4179367e77","observation_id":"ecbc42c9-a880-4ff3-ba23-c2214dd48473","resolution":{"observed_at":"2026-08-06T11:47:03.859290Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.842395Z","title":"Brinkmann, On Riemannian spaces conformal to Euclidean space, Proc","venue":null,"work_id":"7785612a-e99c-4f36-a1b9-cc925fe2f76a","year":1923},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.071133Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:dd10dfcb27f8fd8ab06dfcc421e1818080ec1fd8c806e91c4e512496a242feab","observation_id":"c5407d5d-2bbd-4683-8cdc-d91e8c4149cd","resolution":{"observed_at":"2026-08-06T11:47:03.846053Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.829640Z","title":"C´ anovas, D","venue":null,"work_id":"015bb12f-2803-453f-9c5d-eabd4346ffec","year":2021},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.268030Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:9e7068a82f7abc872ab5542911fe8bdcc7111b6bcdf7d28e690d63a2f21b6626","observation_id":"4ef73bbc-838b-4adb-a1f7-5a952a951c04","resolution":{"observed_at":"2026-08-06T11:47:03.834467Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.817891Z","title":"ˇCap and J","venue":null,"work_id":"5ef81f96-ee30-431d-a281-26a9f2b62122","year":2009},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.418588Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:82c5ab58a60fa15d684d48d51e53389bcf9fda8e0c7aa94f9b112e6f42b9f48f","observation_id":"f1c769ce-e1f7-40c1-8d61-99d6449db22d","resolution":{"observed_at":"2026-08-06T11:47:03.821503Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.806024Z","title":"Chen, On the surfaces with parallel mean curvature vector, Indiana Univ","venue":null,"work_id":"e081a31c-44b6-4a4e-8430-ad70762b53c3","year":1972},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.503411Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:c0aff0e57cb5ac93d96b5461ca8251ac08315752f4fa4aff356e7136f973ffb5","observation_id":"9b88a4d3-c07b-4d0d-9ccb-821045e2ad19","resolution":{"observed_at":"2026-08-06T11:47:03.810040Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.794204Z","title":"Chen, Classification of spatial surfaces with parallel mean curvature vector in pseudo-Euclidean spaces of arbitrary dimension, J","venue":null,"work_id":"009e3796-9343-4687-815b-95fa78b634c7","year":2009},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.507366Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:46cc84bc210f2d0472ba007fc7b6b405e3bca13b9ddccaaafd91d732676346f3","observation_id":"2648e3a7-83e5-415f-aa7e-e901114ac2c4","resolution":{"observed_at":"2026-08-06T11:47:03.798143Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.782250Z","title":"Cheng, Complete spacelike submanifolds in a De Sitter space with parallel mean curvature vector, Math","venue":null,"work_id":"c0270596-e364-445c-b924-674e1a036aca","year":1991},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.512238Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:0744d43f59fe80dd2deaed48ac451fcf38e267b5e0f0454e4f9fcfb521763ce8","observation_id":"26553653-b6fe-4501-9b3b-c40c8b0c37da","resolution":{"observed_at":"2026-08-06T11:47:03.786167Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.770304Z","title":"Dajczer, Submanifolds and isometric immersions , Math","venue":null,"work_id":"bc19e683-efb0-4b0f-8f21-20338bb3fb96","year":1990},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.516090Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:bbb8044bff8d42b4e2156f2bc0b1d5f7fce8cdaf910533bd005b815b51bd987e","observation_id":"1c7e3a00-5b7c-4bb4-9ae3-c7523fbdf29f","resolution":{"observed_at":"2026-08-06T11:47:03.774056Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.757362Z","title":"Do Carmo, Differential Geometry of Curves and Surfaces , Revised and updated sec","venue":null,"work_id":"8a63eef6-a883-4e27-a5c5-532eaa770d60","year":2016},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.520028Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:264a0b9807e55c180ee0d65407361d556dcea6e39b9c87945867e85564813ccd","observation_id":"5695df6d-3b5d-4a09-8bde-362cc4ce1697","resolution":{"observed_at":"2026-08-06T11:47:03.761671Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.745613Z","title":"Harris, Closed and complete spacelike hypersurfaces in Minkowski space, Class","venue":null,"work_id":"be5cf3a1-3965-4d21-a893-5fdb8828806f","year":1988},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.523955Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:5a7a9ee35a5bbddc5eaa82148bf70945627d9e7941994c979ca28927d3e84b32","observation_id":"e63c2485-2052-4fe1-a23a-26a6c236d142","resolution":{"observed_at":"2026-08-06T11:47:03.749209Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.733407Z","title":"Hoffman, Surfaces of constant mean curvature in manifolds of constant curvature, J","venue":null,"work_id":"257c5b37-adfd-44d9-9dcc-2351ca9a57c8","year":1973},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.527864Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:ddb7f13f3ed3cfba25d31c82ee65f0770303d65fd9581f648dfb9e0d7dcdeb68","observation_id":"f1a78241-5a08-4a0c-8bf6-9195ccbd21a2","resolution":{"observed_at":"2026-08-06T11:47:03.737483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.720669Z","title":"Izumiya, D","venue":null,"work_id":"4a1a99d4-33eb-44d1-ade1-2584fe152286","year":2004},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.531997Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:b5aa3d2b874f948caf00677039329a7bd0e5716ad54172dca42f669946b07ea7","observation_id":"5bc0cd2e-81b6-4022-b660-ac99d4904f69","resolution":{"observed_at":"2026-08-06T11:47:03.724287Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.708305Z","title":"Lee and T.H","venue":null,"work_id":"c654556f-71ee-4c3c-8757-ff3531dda0da","year":1987},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.535552Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:ceefbd3f00f0f578254c9626878fbf42c0f849a95ba21911f41275b5b383b27b","observation_id":"81ba7d7f-e299-40b7-93fb-c09a98c0bcb4","resolution":{"observed_at":"2026-08-06T11:47:03.712047Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.696197Z","title":"Magid, Isometric immersions of Lorentz space with parallel second fundamental forms, Tsukuba J","venue":null,"work_id":"7686f55b-1d42-483f-a2a2-8400b54d7069","year":1984},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.539060Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:c0c170f96025c5b2685fa46d2c86d6b84621a3e92b1497c57b08b2d306bc7d82","observation_id":"b9a6fc61-3806-41cb-b94d-fc4ed75b88a8","resolution":{"observed_at":"2026-08-06T11:47:03.699991Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.684737Z","title":"Mars and J.M.M","venue":null,"work_id":"b44c61fc-a8ff-4983-8596-07d99e7fa289","year":2003},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.543252Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:285a60eeff431bf5cd238d3d724937c6b36e98112ae83cc8e43bb4c4c0b7ad16","observation_id":"3acb5562-3129-48bb-99a7-96edbce7ee46","resolution":{"observed_at":"2026-08-06T11:47:03.688132Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.672798Z","title":"Obata, The conjectures on conformal transformations of Riemannian manifolds, J","venue":null,"work_id":"fa61ed19-2c7a-4890-92dc-0f80c9e3c825","year":1971},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.546890Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:9dcfa704dc7973fb070cb26752b7e9d6f2ffe5765a33136a25b0311bbfd2590b","observation_id":"e69fb7e8-c505-441a-b531-ebe529a759d9","resolution":{"observed_at":"2026-08-06T11:47:03.676790Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.660025Z","title":"Palmas, F.J","venue":null,"work_id":"b8adcf9d-553c-4415-b03b-e53b5d1a933a","year":2018},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.550519Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:a881d76b153ec672a6b01f7437dd9df6772cfc67043a9e76dfa0a31e65307ea3","observation_id":"fca68a0b-0f1d-4824-a34b-f2795c075271","resolution":{"observed_at":"2026-08-06T11:47:03.664088Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.647243Z","title":"Palmer, Variational problems which are quadratic in the surface curvatures, Curvature and Vari- ational Modeling in Physics and Biophysics , Ed","venue":null,"work_id":"cd81855e-1e3a-4bc5-ad80-5a49f80e377e","year":2008},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.554357Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:271d05d9000726ed350ea0ba5b7093a73e2dc20a6a6c6cfe6f7dbc1413a54ad6","observation_id":"ff727994-e370-4276-8dd7-e708497b2d11","resolution":{"observed_at":"2026-08-06T11:47:03.650927Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.635254Z","title":"Palomo and A","venue":null,"work_id":"e2d17c75-55ee-4571-9bbc-398a59ad5238","year":2013},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.557984Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:3cdc321bc5a301b9a5f93f285e6d1c50f49d76a243fe8614dee1a1ce00eab09a","observation_id":"feb875d2-b1cc-4fba-9dbe-ab1abaf535f8","resolution":{"observed_at":"2026-08-06T11:47:03.638958Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.622041Z","title":"Santos, Submanifolds with parallel mean curvature vector in spheres, Tˆ ohoku Math","venue":null,"work_id":"830e7306-d928-4e96-823b-6da2dc7532ac","year":1994},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.561530Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:b59bc252ba9403a83364c6e45e6490c9423dbf999327eb7bdb2784e584357679","observation_id":"76ed98e6-804d-4621-9bae-2eafda60eb54","resolution":{"observed_at":"2026-08-06T11:47:03.625793Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.609853Z","title":"Wente, Counterexample to a conjecture of H","venue":null,"work_id":"078a5266-c1b8-4992-a55c-6a21196475e6","year":1986},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.565010Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:08c1559e8c40f7f002c8504c75834a8a704001a6112f7889097f555249f8d148","observation_id":"438f19a8-0996-4b18-b890-fa32f85c01d6","resolution":{"observed_at":"2026-08-06T11:47:03.613578Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:47:03.595241Z","title":"Yau, Submanifolds with constant mean curvature","venue":null,"work_id":"551f9ba7-c722-4453-a09d-61395db3aa06","year":1974},"citing_paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T11:47:03.568486Z"},"links":{"citing_paper":"/paper/2507.22566"},"observation_digest":"sha256:60e2a54c7b49b49f1d47348da512afac865d1439f137dff1f90116a485aabfa3","observation_id":"d865b6ae-3d81-4373-8ef3-0dc3f29ad6d9","resolution":{"observed_at":"2026-08-06T11:47:03.600794Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.22566","last_updated":"2025-07-30T10:47:45Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-08-13T18:26:20.114547Z","submitted_at":"2025-07-30T10:47:45Z","title":"Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":26},"total_outbound_references":26},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 1 inbound Pith citation observation for arXiv:2507.22566."}