{"as_of":"2026-08-16T21:07:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:30d5a2ecfa81f5d68fa28bd2548b835f33628133abc4c21468805eec38fe1755","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T15:26:37.030025Z","state":"measured"},{"denominator":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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":"2026-08-06T16:27:40.346270Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-06T16:27:40.958316Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1908.01433","last_updated":"2019-08-05T01:05:44Z","snapshot_observed_at":"2026-08-16T10:27:18.838301Z","submitted_at":"2019-08-05T01:05:44Z","title":"Hoffman's bound for hypergraphs","version":1},"cited_work":{"arxiv_id":"1908.01433","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.01433","snapshot_observed_at":"2026-08-06T16:27:40.958316Z","title":"Hoffman's bound for hypergraphs","venue":"math.CO","work_id":"73b3c532-46ba-4f5f-8186-7dfbab2e731c","year":2019},"citing_paper":{"arxiv_id":"2507.13664","last_updated":"2025-07-18T05:19:38Z","snapshot_observed_at":"2026-08-14T05:53:56.822211Z","submitted_at":"2025-07-18T05:19:38Z","title":"Spectral Theory of Hypergraphs: A Survey","version":1},"reference_index":195,"source":"pdf_text","source_observed_at":"2026-08-06T16:27:40.346270Z"},"links":{"cited_paper":"/paper/1908.01433","citing_paper":"/paper/2507.13664"},"observation_digest":"sha256:0492aafbac85f9b52bbc5134df3a637c4abc993e00793c4d7c1dfe2839ceafb6","observation_id":"c9df23fa-fc3d-448f-b2c9-b1fad5ce270a","resolution":{"observed_at":"2026-08-06T16:27:40.962208Z","resolver_source":"local_arxiv","status":"verified_exact"},"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"}}],"links":{"evidence":"/evidence","html":"/paper/1908.01433/citation-record","integrity":"/paper/1908.01433/integrity","json":"/paper/1908.01433/citation-record.json","paper":"/paper/1908.01433"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:26:37.424686Z","title":"Cooper and A","venue":null,"work_id":"ac0d82f1-db46-4e82-a2aa-ae02bd7a7282","year":2012},"citing_paper":{"arxiv_id":"1908.01433","last_updated":"2019-08-05T01:05:44Z","snapshot_observed_at":"2026-08-16T10:27:18.838301Z","submitted_at":"2019-08-05T01:05:44Z","title":"Hoffman's bound for hypergraphs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T15:26:36.924729Z"},"links":{"citing_paper":"/paper/1908.01433"},"observation_digest":"sha256:7a34548bdd679f001d1b662f198b7c4474ae359fb4b79c192f92b1c228695663","observation_id":"6f83ae20-cd4c-4d0d-b0b6-6277c11dbc97","resolution":{"observed_at":"2026-08-14T15:26:37.432314Z","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":"2026-08-14T15:26:37.395479Z","title":"Godsil and G","venue":null,"work_id":"de58b1d1-bb54-49c2-b49b-1f3a8c433d4b","year":2001},"citing_paper":{"arxiv_id":"1908.01433","last_updated":"2019-08-05T01:05:44Z","snapshot_observed_at":"2026-08-16T10:27:18.838301Z","submitted_at":"2019-08-05T01:05:44Z","title":"Hoffman's bound for hypergraphs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T15:26:36.934085Z"},"links":{"citing_paper":"/paper/1908.01433"},"observation_digest":"sha256:7502496b11227b8e8d71bf778382a4fad64525e6e64751dfdebb21fb551fc34d","observation_id":"04534ca8-d3bf-4b81-a2d4-c5bd609efeaa","resolution":{"observed_at":"2026-08-14T15:26:37.401853Z","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":"2026-08-14T15:26:37.364507Z","title":"Hoffman, On eigenvalues and colorings of graphs, in Graph Theory and its Applica- tions, Academic Press, New York (1970), pp","venue":null,"work_id":"4722d27c-e2fc-4597-a489-c4f4dcf7a637","year":1970},"citing_paper":{"arxiv_id":"1908.01433","last_updated":"2019-08-05T01:05:44Z","snapshot_observed_at":"2026-08-16T10:27:18.838301Z","submitted_at":"2019-08-05T01:05:44Z","title":"Hoffman's bound for hypergraphs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T15:26:36.945767Z"},"links":{"citing_paper":"/paper/1908.01433"},"observation_digest":"sha256:8e82a681c3dba67a7ba9498a03ede097346356168f136352cedde6be3fb6050b","observation_id":"b00bbed3-c8c3-4f31-bdf8-45764aeadfbd","resolution":{"observed_at":"2026-08-14T15:26:37.373959Z","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":"2026-08-14T15:26:37.337889Z","title":"Horn and C","venue":null,"work_id":"c3a417b4-9e13-4554-b643-afa8eb8e8684","year":1985},"citing_paper":{"arxiv_id":"1908.01433","last_updated":"2019-08-05T01:05:44Z","snapshot_observed_at":"2026-08-16T10:27:18.838301Z","submitted_at":"2019-08-05T01:05:44Z","title":"Hoffman's bound for hypergraphs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T15:26:36.956480Z"},"links":{"citing_paper":"/paper/1908.01433"},"observation_digest":"sha256:0c351172b4806fcc4d8359831b3cab987b2adb08de8414347d72d0f138ab10ab","observation_id":"17d35bf6-3428-48cb-ad3a-6f8cdcf2ea30","resolution":{"observed_at":"2026-08-14T15:26:37.345775Z","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":"2026-08-14T15:26:37.299396Z","title":"Keevash, J","venue":null,"work_id":"4b9c5ca6-d073-4765-b691-9daa53cd7713","year":2013},"citing_paper":{"arxiv_id":"1908.01433","last_updated":"2019-08-05T01:05:44Z","snapshot_observed_at":"2026-08-16T10:27:18.838301Z","submitted_at":"2019-08-05T01:05:44Z","title":"Hoffman's bound for hypergraphs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T15:26:36.963220Z"},"links":{"citing_paper":"/paper/1908.01433"},"observation_digest":"sha256:111d8c89ba7fe7fa413a9165e92c0fe277eeeb8d5f0613d1fe567aebb98a8efd","observation_id":"39113fd2-1a83-4d8f-938f-a7dd6c5bdbdd","resolution":{"observed_at":"2026-08-14T15:26:37.318686Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T15:26:36.971297Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"1908.01433","last_updated":"2019-08-05T01:05:44Z","snapshot_observed_at":"2026-08-16T10:27:18.838301Z","submitted_at":"2019-08-05T01:05:44Z","title":"Hoffman's bound for hypergraphs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T15:26:36.971297Z"},"links":{"citing_paper":"/paper/1908.01433"},"observation_digest":"sha256:ddfb9d38ccb2cc94f9c790b9ae265c0db88ea400d528b1242678d6aa8a77d6ea","observation_id":"1669950d-7efa-4b61-8221-5db002ea4d25","resolution":{"observed_at":"2026-08-14T15:26:36.971297Z","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":"2026-08-14T15:26:37.257712Z","title":"Kenter, Necessary spectral conditions for coloring h ypergraphs, J","venue":null,"work_id":"a3d454a8-2492-47c1-9e5e-15e4c4846f99","year":2014},"citing_paper":{"arxiv_id":"1908.01433","last_updated":"2019-08-05T01:05:44Z","snapshot_observed_at":"2026-08-16T10:27:18.838301Z","submitted_at":"2019-08-05T01:05:44Z","title":"Hoffman's bound for hypergraphs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T15:26:36.979239Z"},"links":{"citing_paper":"/paper/1908.01433"},"observation_digest":"sha256:8a0dad72d5b16e8993c5db050da51683f30279a1c01aecdddff2eecf70425a6f","observation_id":"f2e3eee6-a6c0-40af-a54c-9bf017dc1474","resolution":{"observed_at":"2026-08-14T15:26:37.265635Z","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":"2026-08-14T15:26:37.221632Z","title":"Lovász, On the Shannon capacity of a graph","venue":null,"work_id":"8a260788-1705-4d12-b2f3-f6912ae88f5b","year":1979},"citing_paper":{"arxiv_id":"1908.01433","last_updated":"2019-08-05T01:05:44Z","snapshot_observed_at":"2026-08-16T10:27:18.838301Z","submitted_at":"2019-08-05T01:05:44Z","title":"Hoffman's bound for hypergraphs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T15:26:36.992377Z"},"links":{"citing_paper":"/paper/1908.01433"},"observation_digest":"sha256:f7548cfa5e0c8a716f4a0d1769405929abfd317b4e4606fa297f77ca3c007e97","observation_id":"f9954def-34e8-4406-afa3-67001764c7ce","resolution":{"observed_at":"2026-08-14T15:26:37.229518Z","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":"2026-08-14T15:26:37.186707Z","title":"Nikiforov , Chromatic number and spectral radius, Linear Algebra Appl","venue":null,"work_id":"48eb1947-8966-4b43-b0f4-248716c59eb5","year":2007},"citing_paper":{"arxiv_id":"1908.01433","last_updated":"2019-08-05T01:05:44Z","snapshot_observed_at":"2026-08-16T10:27:18.838301Z","submitted_at":"2019-08-05T01:05:44Z","title":"Hoffman's bound for hypergraphs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T15:26:37.000212Z"},"links":{"citing_paper":"/paper/1908.01433"},"observation_digest":"sha256:61f30da5353b1ef2d3afdc3884b993b93e512cfe2b6baa288d581163dad542b7","observation_id":"6b3f23fa-6cf8-4332-bf3d-b6e987ae03ab","resolution":{"observed_at":"2026-08-14T15:26:37.193501Z","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":"2026-08-14T15:26:37.161977Z","title":"Nikiforov , Analytic methods for uniform hypergraphs, Linear Algebra Appl","venue":null,"work_id":"78b8669c-861f-48ab-9c7c-94ac5ae9122a","year":2014},"citing_paper":{"arxiv_id":"1908.01433","last_updated":"2019-08-05T01:05:44Z","snapshot_observed_at":"2026-08-16T10:27:18.838301Z","submitted_at":"2019-08-05T01:05:44Z","title":"Hoffman's bound for hypergraphs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T15:26:37.007241Z"},"links":{"citing_paper":"/paper/1908.01433"},"observation_digest":"sha256:839abfb64580ca2efe0715d9e67be4f0b7affbff521c12a8b52c79cb464dee56","observation_id":"b0dd5c47-1385-4d31-83d6-c4d36a3af8eb","resolution":{"observed_at":"2026-08-14T15:26:37.168314Z","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":"2026-08-14T15:26:37.125433Z","title":"Qi, Eigenvalues of a real supersymmetric tensor, J","venue":null,"work_id":"74f18cb5-63c7-4464-8113-9516ac443c92","year":2005},"citing_paper":{"arxiv_id":"1908.01433","last_updated":"2019-08-05T01:05:44Z","snapshot_observed_at":"2026-08-16T10:27:18.838301Z","submitted_at":"2019-08-05T01:05:44Z","title":"Hoffman's bound for hypergraphs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T15:26:37.017974Z"},"links":{"citing_paper":"/paper/1908.01433"},"observation_digest":"sha256:5c95ec90e8e580dd9acbd82ae62df4fadf3888cad23a9e648d6dd73d4547d557","observation_id":"2cfa0553-34b7-4157-b6fe-9824f7906e3d","resolution":{"observed_at":"2026-08-14T15:26:37.140185Z","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":"2026-08-14T15:26:37.079753Z","title":"Qi, Symmetric nonnegative tensors and copositive te nsors, Linear Algebra Appl","venue":null,"work_id":"7ef2a2b2-e65d-44a5-97de-aaa1dba9d2b6","year":2013},"citing_paper":{"arxiv_id":"1908.01433","last_updated":"2019-08-05T01:05:44Z","snapshot_observed_at":"2026-08-16T10:27:18.838301Z","submitted_at":"2019-08-05T01:05:44Z","title":"Hoffman's bound for hypergraphs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T15:26:37.030025Z"},"links":{"citing_paper":"/paper/1908.01433"},"observation_digest":"sha256:9fdabce39cac5751a5ba2cf0db797c355c20030f5fb03f8c653b64cad5d9aea3","observation_id":"5be58c5d-7509-4a3b-8ad2-59988b5a1018","resolution":{"observed_at":"2026-08-14T15:26:37.099059Z","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":"1908.01433","last_updated":"2019-08-05T01:05:44Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-16T10:27:18.838301Z","submitted_at":"2019-08-05T01:05:44Z","title":"Hoffman's bound for hypergraphs"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":0,"verified_fuzzy":11},"total_outbound_references":12},"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 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:1908.01433."}