{"as_of":"2026-08-16T22:04:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7438e70e3e75012ec4bf3075ebf2330cb8fe7d67a8fa080dcb175c1e34728595","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":"2026-08-14T15:57:26.596598Z","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":"2026-08-16T06:30:59.297886+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/1908.00531/citation-record","integrity":"/paper/1908.00531/integrity","json":"/paper/1908.00531/citation-record.json","paper":"/paper/1908.00531"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:57:26.767473Z","title":"Aronszajn, Theory of reproducing kernels , Trans","venue":null,"work_id":"c034814e-0911-41a4-9590-4c1be59d4802","year":1950},"citing_paper":{"arxiv_id":"1908.00531","last_updated":"2019-08-01T17:45:54Z","snapshot_observed_at":"2026-08-16T10:27:41.860125Z","submitted_at":"2019-08-01T17:45:54Z","title":"On the optimal error bound for the first step in the method of cyclic alternating projections","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T15:57:26.548786Z"},"links":{"citing_paper":"/paper/1908.00531"},"observation_digest":"sha256:3e636f51b36c1bff16417ac6f94ef683fe5f1467869b19ebf09a87475470df6d","observation_id":"e4990445-789d-4e7f-bbd7-2dd586446d58","resolution":{"observed_at":"2026-08-14T15:57:26.772185Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T15:57:26.755250Z","title":"Badea, S","venue":null,"work_id":"6c1f02d0-3200-452a-a259-196efc3bd48d","year":2010},"citing_paper":{"arxiv_id":"1908.00531","last_updated":"2019-08-01T17:45:54Z","snapshot_observed_at":"2026-08-16T10:27:41.860125Z","submitted_at":"2019-08-01T17:45:54Z","title":"On the optimal error bound for the first step in the method of cyclic alternating projections","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T15:57:26.554197Z"},"links":{"citing_paper":"/paper/1908.00531"},"observation_digest":"sha256:18d0deeff7d3c63a2c1647e0c80d309545a376ba41de5ac5308dda4d66f05481","observation_id":"426725e5-6841-4319-a1e2-8a3572f7bca3","resolution":{"observed_at":"2026-08-14T15:57:26.759690Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T15:57:26.742660Z","title":"Badea, S","venue":null,"work_id":"f3cb234f-895a-4204-a04d-ca517f32bc1f","year":2011},"citing_paper":{"arxiv_id":"1908.00531","last_updated":"2019-08-01T17:45:54Z","snapshot_observed_at":"2026-08-16T10:27:41.860125Z","submitted_at":"2019-08-01T17:45:54Z","title":"On the optimal error bound for the first step in the method of cyclic alternating projections","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T15:57:26.559010Z"},"links":{"citing_paper":"/paper/1908.00531"},"observation_digest":"sha256:997ff6787987f9d1295b5dd819991705eb5978c31d0829f804336d80069b1236","observation_id":"b4659df8-dfa1-49c6-b587-567f47df0905","resolution":{"observed_at":"2026-08-14T15:57:26.746838Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T15:57:26.730826Z","title":"Badea, D","venue":null,"work_id":"6afb557d-c877-4eea-8da5-128846140341","year":2016},"citing_paper":{"arxiv_id":"1908.00531","last_updated":"2019-08-01T17:45:54Z","snapshot_observed_at":"2026-08-16T10:27:41.860125Z","submitted_at":"2019-08-01T17:45:54Z","title":"On the optimal error bound for the first step in the method of cyclic alternating projections","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T15:57:26.563298Z"},"links":{"citing_paper":"/paper/1908.00531"},"observation_digest":"sha256:fb4e6b0f18a75006127c2c607eae9343c3906445f58e7302dba1ca385d2042ad","observation_id":"8f64e605-e40f-4e3d-bb41-dbdb89fc6d63","resolution":{"observed_at":"2026-08-14T15:57:26.734898Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T15:57:26.715927Z","title":"Deutsch, The method of alternating orthogonal projections","venue":null,"work_id":"32dba91d-f12c-478d-8ac8-4c955364136c","year":1992},"citing_paper":{"arxiv_id":"1908.00531","last_updated":"2019-08-01T17:45:54Z","snapshot_observed_at":"2026-08-16T10:27:41.860125Z","submitted_at":"2019-08-01T17:45:54Z","title":"On the optimal error bound for the first step in the method of cyclic alternating projections","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T15:57:26.567575Z"},"links":{"citing_paper":"/paper/1908.00531"},"observation_digest":"sha256:2083c97480a3850c5c8fb1aeec97e4e18be5141923d3506a3ca5e846cdbd8b2f","observation_id":"8968d6dc-8d85-4002-a84d-da495897f719","resolution":{"observed_at":"2026-08-14T15:57:26.721724Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T15:57:26.700400Z","title":"Deutsch, The angle between subspaces of a Hilbert space","venue":null,"work_id":"0a9ae9ab-22e2-47fe-9398-423f03650602","year":1995},"citing_paper":{"arxiv_id":"1908.00531","last_updated":"2019-08-01T17:45:54Z","snapshot_observed_at":"2026-08-16T10:27:41.860125Z","submitted_at":"2019-08-01T17:45:54Z","title":"On the optimal error bound for the first step in the method of cyclic alternating projections","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T15:57:26.571827Z"},"links":{"citing_paper":"/paper/1908.00531"},"observation_digest":"sha256:059732583ec937f5fdf6879072613dade7f2940d6df3f0faa5beff92b1d3f9a9","observation_id":"4e4b5304-73fa-42cb-ab08-d6fdb885dbab","resolution":{"observed_at":"2026-08-14T15:57:26.705350Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T15:57:26.681420Z","title":"Halperin, The product of projection operators , Acta Sci","venue":null,"work_id":"f8dc6f21-ec6f-4000-a1af-5164449f8c1d","year":1962},"citing_paper":{"arxiv_id":"1908.00531","last_updated":"2019-08-01T17:45:54Z","snapshot_observed_at":"2026-08-16T10:27:41.860125Z","submitted_at":"2019-08-01T17:45:54Z","title":"On the optimal error bound for the first step in the method of cyclic alternating projections","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T15:57:26.578729Z"},"links":{"citing_paper":"/paper/1908.00531"},"observation_digest":"sha256:71a9f3c7b68597ec98fd49e0bdf126f45b3d81ba18d610a0838838242129becc","observation_id":"51afaaa7-7509-46d6-8bff-ecb0d3e30e0a","resolution":{"observed_at":"2026-08-14T15:57:26.687884Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T15:57:26.660323Z","title":"Kayalar, H","venue":null,"work_id":"ac81627f-9ffd-4859-a435-bfaa2d411be3","year":1988},"citing_paper":{"arxiv_id":"1908.00531","last_updated":"2019-08-01T17:45:54Z","snapshot_observed_at":"2026-08-16T10:27:41.860125Z","submitted_at":"2019-08-01T17:45:54Z","title":"On the optimal error bound for the first step in the method of cyclic alternating projections","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T15:57:26.587106Z"},"links":{"citing_paper":"/paper/1908.00531"},"observation_digest":"sha256:8ade73b50a623aa96db0132b843008ce9ed80e49726d5bb0888123760fac4a66","observation_id":"794272b0-7f37-4b65-a36e-19a437cd5424","resolution":{"observed_at":"2026-08-14T15:57:26.665544Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T15:57:26.645322Z","title":"Netyanun, D.C","venue":null,"work_id":"f1bff8d8-b232-4626-855c-210180ad98cf","year":2006},"citing_paper":{"arxiv_id":"1908.00531","last_updated":"2019-08-01T17:45:54Z","snapshot_observed_at":"2026-08-16T10:27:41.860125Z","submitted_at":"2019-08-01T17:45:54Z","title":"On the optimal error bound for the first step in the method of cyclic alternating projections","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T15:57:26.591714Z"},"links":{"citing_paper":"/paper/1908.00531"},"observation_digest":"sha256:48f1d1f5f1aebb9f259487966ac4c869a6064b15d1eca73f28866d9a69556296","observation_id":"cc99ea5e-583f-4cb1-b7a1-7d486e4c4786","resolution":{"observed_at":"2026-08-14T15:57:26.649820Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T15:57:26.629520Z","title":"von Neumann, Functional Operators—Vol","venue":null,"work_id":"af07eee7-1c75-428d-b301-bbd75bc12b90","year":1950},"citing_paper":{"arxiv_id":"1908.00531","last_updated":"2019-08-01T17:45:54Z","snapshot_observed_at":"2026-08-16T10:27:41.860125Z","submitted_at":"2019-08-01T17:45:54Z","title":"On the optimal error bound for the first step in the method of cyclic alternating projections","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T15:57:26.596598Z"},"links":{"citing_paper":"/paper/1908.00531"},"observation_digest":"sha256:506c24ab344591a484262fd995c18646f73286f319ff0335630ec12cf0d3ca5e","observation_id":"df6839f6-0352-4404-bfa4-f3953dfc0fe3","resolution":{"observed_at":"2026-08-14T15:57:26.635765Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.00531","last_updated":"2019-08-01T17:45:54Z","latest_version":1,"primary_category":"math.FA","snapshot_observed_at":"2026-08-16T10:27:41.860125Z","submitted_at":"2019-08-01T17:45:54Z","title":"On the optimal error bound for the first step in the method of cyclic alternating projections"},"reference_resolution":{"displayed":10,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":10},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:1908.00531."}