{"as_of":"2026-08-13T05:18:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4603466fd8e18835d60461e83dd6ff6eb94ab245e08b202c6c23c0dda975256d","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T13:07:33.248763Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2411.16589/citation-record","integrity":"/paper/2411.16589/integrity","json":"/paper/2411.16589/citation-record.json","paper":"/paper/2411.16589"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T13:07:33.635159Z","title":null,"venue":null,"work_id":"dfb7e843-b9d6-4bd0-9240-6507bd886917","year":2024},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.135185Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:96d5c822bb78027c1fe220e92f669cda51b5370efaaa4b7c9fcde0455f3ece47","observation_id":"4399e58d-a3b7-4a38-9f3f-bc1184f963a7","resolution":{"observed_at":"2026-08-12T13:07:33.640095Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.619004Z","title":null,"venue":null,"work_id":"b910e0e2-371a-4c28-9b50-ceab91d9c65f","year":1973},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.141342Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:5592a6ca6b6af106998463b2245a701b1dcad2ea8880de2f87bb7865d321aa46","observation_id":"e6ba7ccf-42e5-4c60-8743-96dcddefdd21","resolution":{"observed_at":"2026-08-12T13:07:33.623936Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.603184Z","title":null,"venue":null,"work_id":"67a3d248-16e2-4345-b79c-22e1c9197d70","year":1990},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.146518Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:3127207f443a9ec75c8a62bc60099e7a0733b6cf83baa8edec58a56aed98b11b","observation_id":"4ca5a0d3-878f-4cb1-b8b2-8d6aecbf20d4","resolution":{"observed_at":"2026-08-12T13:07:33.608129Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.587234Z","title":"Riemannian geometry","venue":null,"work_id":"4cfeaa0f-7d4b-42c4-8568-33db9b70a262","year":1992},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.152200Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:1deae247af896354f65539ef93e6db2deb13723963aa48043db05f9ed07ef8d1","observation_id":"1b689424-3021-4a87-afc5-71e6b4a89190","resolution":{"observed_at":"2026-08-12T13:07:33.592160Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.571320Z","title":null,"venue":null,"work_id":"57a9e6e2-b3d0-494d-ab81-420129813d5b","year":2016},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.157533Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:12b737586454b66a8e3c887bbc0df9ff3462fcf7a5c092ff61163f5d013fced6","observation_id":"907c0795-9d3a-46b4-b29b-ef6d39571c34","resolution":{"observed_at":"2026-08-12T13:07:33.576252Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.555041Z","title":"The approximation of one matr ix by another of lower rank","venue":null,"work_id":"789b5a46-908b-469d-90e6-5492d561f6bb","year":1936},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.162787Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:e012fa19bddf0ddbf5559a76c3f8a0f39c6e110b025855850935cbb3f69a9ee9","observation_id":"58d07a4e-a1b0-4b12-8be4-59075b988e8d","resolution":{"observed_at":"2026-08-12T13:07:33.560124Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.538477Z","title":"Feh´ er and´Akos K","venue":null,"work_id":"0cb77621-5e83-4ee7-8de6-f2df834d0a50","year":2016},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.169027Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:9d9187ebfcfc3950e0bd8e4f596fe2f752d0dbe1f662eeaedf42513b1974f4d8","observation_id":"5c54e67b-f68e-4aa9-bec4-0437557340d9","resolution":{"observed_at":"2026-08-12T13:07:33.543426Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.522381Z","title":"Young tableaux, volume 35 of London Mathematical Society Student Texts","venue":null,"work_id":"986959b6-2466-49f3-bcde-fbc8b6b5ab3e","year":1997},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.174442Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:022f4161a7a35854aff8bd6e49e5ff3a28ba22ccd11fe2c855f4be564598dbfa","observation_id":"bedfbe62-6246-4bf2-bf09-5ad7b02cdd03","resolution":{"observed_at":"2026-08-12T13:07:33.527382Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.505006Z","title":"Complexity of co mputations with Pfaffian and Noetherian functions","venue":null,"work_id":"39f78e8a-36d5-4ea1-af42-2488e95bd3cd","year":2004},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.179529Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:45666ef05f17d68e04c71516d8525226b74a36c445e9c1f46ce492f54be2ccd1","observation_id":"117459e7-c270-4f4b-b66b-2d30e9b3d1ca","resolution":{"observed_at":"2026-08-12T13:07:33.510964Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.486973Z","title":null,"venue":null,"work_id":"5b5e17f7-10e0-47cf-b9e2-9c5c7f19cd87","year":2008},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.184612Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:8f5a930a7d5cee9eec4ce4193ac9c91aa83a85281e2f66b1e1fc2cecb46a204f","observation_id":"8015c538-8719-482d-bd62-e5a7f5daed86","resolution":{"observed_at":"2026-08-12T13:07:33.492065Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.08639","last_updated":"2026-05-09T17:42:38Z","snapshot_observed_at":"2026-08-09T04:26:53.118997Z","submitted_at":"2024-02-13T18:06:17Z","title":"Morse theory of Euclidean distance functions from algebraic hypersurfaces","version":4},"cited_work":{"arxiv_id":"2402.08639","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.08639","snapshot_observed_at":"2026-08-12T13:07:33.287909Z","title":"Morse theory of Euclidean distance functions from algebraic hypersurfaces","venue":"math.AG","work_id":"20103808-16cd-4c68-8b66-8d26197fa116","year":2024},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.189832Z"},"links":{"cited_paper":"/paper/2402.08639","citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:141d099c9704a44c219962ab6b01bdee6753f983e32403299714bbdf9eceb3f7","observation_id":"f70a6901-d005-4107-81e6-b7ca42db2d8f","resolution":{"observed_at":"2026-08-12T13:07:33.295626Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.468299Z","title":null,"venue":null,"work_id":"24cda7da-cf9f-4862-b7a4-c846f63f01ee","year":1994},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.195598Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:7359ee15d9981dc37ff90bc1eaea68cecf9bef90de59cb8784153d50411a4c77","observation_id":"14d15e43-ea69-4119-9468-5ea0fc4e1c86","resolution":{"observed_at":"2026-08-12T13:07:33.473604Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.451457Z","title":"Horn and Charles R","venue":null,"work_id":"a2ddab41-1ed9-4c7a-89a9-a8c578261775","year":1991},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.201511Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:887ef9481003af37694097240157bf8c025ec0ee077c955d411aa7e677c7e45b","observation_id":"b5cea300-75e7-4027-a4a9-43c3077134bd","resolution":{"observed_at":"2026-08-12T13:07:33.456645Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.434479Z","title":"Generalized power method for sparse principal component analysis","venue":null,"work_id":"6f36466b-a5bb-4c11-961a-eab64c2fdac0","year":2010},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.206809Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:f04302ab50c047dc71551c7fbe58802703ef054bd7b0647ce1962f0d674b0b00","observation_id":"b8b7bc48-2603-4704-9af3-dde1f042825a","resolution":{"observed_at":"2026-08-12T13:07:33.439880Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.418109Z","title":null,"venue":null,"work_id":"0447f274-1d86-428d-94f5-9c8be435b28e","year":1997},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.212104Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:cfe37933b80e2583c961d1c60ceaef3374190c9f663db0f33fb7babe2c164e38","observation_id":"5bf50180-9cb2-446d-a716-ebf38d0bc1d3","resolution":{"observed_at":"2026-08-12T13:07:33.423078Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.400809Z","title":"Absil Kyle A","venue":null,"work_id":"e194eec3-e95c-47b2-a450-7ef4203057f3","year":null},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.217089Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:0e0f5a0f58b69a0a4b549812f43d4f9a3a78b13de35906e17d3abf050bef0f1b","observation_id":"df362d76-78d3-4b16-bd7a-5c045d6b28d9","resolution":{"observed_at":"2026-08-12T13:07:33.406077Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.222037Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.222037Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:f0d957d9f579ae8ecc1b55ea8858861c59cc9742e2bc3502bfb41518fa700839","observation_id":"2c67f4c7-8b2a-4be8-9187-baebec8db9bc","resolution":{"observed_at":"2026-08-12T13:07:33.222037Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T13:07:33.372888Z","title":null,"venue":null,"work_id":"6fc68c16-25d9-455d-9753-69aea6494750","year":null},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.227114Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:a49d8f426b93083e2b7d8280525f4c84fbc167fc71c82494578e615651b45590","observation_id":"664ba53a-20a0-4239-8762-05636911737c","resolution":{"observed_at":"2026-08-12T13:07:33.378396Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.232569Z","title":"Tame topology and o-minimal structures , volume 248 of London Mathematical Society Lecture Note Series","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.232569Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:422b5bff6b3f1c81280b0b63d2bee18c7184438ec3985f8521cde9c420d24891","observation_id":"53868404-5a70-4c81-a9b8-fe7cea182663","resolution":{"observed_at":"2026-08-12T13:07:33.232569Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T13:07:33.343216Z","title":"Differential geometry of Grassmann man ifolds","venue":null,"work_id":"63e39cdb-98f3-4d38-948e-f28bd66b92c2","year":1967},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.238183Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:7091800c62799115e24a6ffed65838cd8c310fdd4e93bfbaa7a7b8c299cc4a84","observation_id":"84d48a5f-7bd4-447b-89c9-fd1f038b2cc3","resolution":{"observed_at":"2026-08-12T13:07:33.348738Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.325446Z","title":"Schubert varieties and distance s between subspaces of different dimensions","venue":null,"work_id":"45c665d8-66a8-40d0-b474-10dc386b80e5","year":2016},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.243698Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:c38eed31b48a6ff31020321664229016dd18a566ffb39d5c52d978e8852da55f","observation_id":"840ed325-ac4c-4030-ac31-8373b9a58afd","resolution":{"observed_at":"2026-08-12T13:07:33.330846Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T13:07:33.308395Z","title":"Betti numbers of semi-Pfaffian sets","venue":null,"work_id":"9ed5386e-db11-4335-9bd7-8e25341d8844","year":1999},"citing_paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T13:07:33.248763Z"},"links":{"citing_paper":"/paper/2411.16589"},"observation_digest":"sha256:b2131cdbf4f8edfb9f8b5937707e1227cf9c63f07d786e13a491670ed957c481","observation_id":"a1060b16-ab8b-4345-9500-05e8de58147c","resolution":{"observed_at":"2026-08-12T13:07:33.313887Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.16589","last_updated":"2024-11-25T17:24:31Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-08-12T12:55:10.612886Z","submitted_at":"2024-11-25T17:24:31Z","title":"The Grassmann distance complexity"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":1,"verified_fuzzy":11},"total_outbound_references":22},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2411.16589."}