{"as_of":"2026-08-10T15:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c85dd31df48ee01490c55bef8e6e030b9a45dbcb7aa799f883ad0924b55acefd","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":"2026-06-26T14:17:57.337260Z","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":"2026-08-10T06:31:04.303077+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":"2026-08-01T10:59:33.649152Z","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":"2606.21233","last_updated":"2026-06-19T08:54:01Z","snapshot_observed_at":"2026-08-10T15:04:02.417844Z","submitted_at":"2026-06-19T08:54:01Z","title":"Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.21233","snapshot_observed_at":"2026-08-01T10:59:33.649152Z","title":"Zhang and Y","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.20051","last_updated":"2026-07-22T11:49:13Z","snapshot_observed_at":"2026-08-09T23:50:26.929677Z","submitted_at":"2026-07-22T11:49:13Z","title":"The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T10:59:33.649152Z"},"links":{"cited_paper":"/paper/2606.21233","citing_paper":"/paper/2607.20051"},"observation_digest":"sha256:f77f368c86d73459906d55d9d12469fcc93df50263718dd16bf5ed0e203f0a9c","observation_id":"8d8e7bd1-e7bb-43b0-b662-3c6c9f06c6c6","resolution":{"observed_at":"2026-08-01T10:59:33.649152Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2606.21233/citation-record","integrity":"/paper/2606.21233/integrity","json":"/paper/2606.21233/citation-record.json","paper":"/paper/2606.21233"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:17:57.337260Z","title":null,"venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2606.21233","last_updated":"2026-06-19T08:54:01Z","snapshot_observed_at":"2026-08-10T15:04:02.417844Z","submitted_at":"2026-06-19T08:54:01Z","title":"Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-26T14:17:57.337260Z"},"links":{"citing_paper":"/paper/2606.21233"},"observation_digest":"sha256:8001728ea65db0459b3c35ce24c9d1224513744f37cc8d87f72d77e2e3b09c97","observation_id":"f600d1c4-4f33-4669-84ab-e5081512ca61","resolution":{"observed_at":"2026-06-26T14:17:57.337260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:17:57.337260Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2606.21233","last_updated":"2026-06-19T08:54:01Z","snapshot_observed_at":"2026-08-10T15:04:02.417844Z","submitted_at":"2026-06-19T08:54:01Z","title":"Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-26T14:17:57.337260Z"},"links":{"citing_paper":"/paper/2606.21233"},"observation_digest":"sha256:2f345db5613154bca2e50e7e8eb9c6b9bb265382bbfe4999a1d45a58ae797605","observation_id":"b46ffd6a-b42d-4398-bdfa-c31531132e2e","resolution":{"observed_at":"2026-06-26T14:17:57.337260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:17:57.337260Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.21233","last_updated":"2026-06-19T08:54:01Z","snapshot_observed_at":"2026-08-10T15:04:02.417844Z","submitted_at":"2026-06-19T08:54:01Z","title":"Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-26T14:17:57.337260Z"},"links":{"citing_paper":"/paper/2606.21233"},"observation_digest":"sha256:48dfa4885804f6df1f82f9faf9b10b044140528543fd5457311f28b9cc8444a8","observation_id":"719f4dc8-a119-4ff7-adc1-827f0f8807b1","resolution":{"observed_at":"2026-06-26T14:17:57.337260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:17:57.337260Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2606.21233","last_updated":"2026-06-19T08:54:01Z","snapshot_observed_at":"2026-08-10T15:04:02.417844Z","submitted_at":"2026-06-19T08:54:01Z","title":"Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-26T14:17:57.337260Z"},"links":{"citing_paper":"/paper/2606.21233"},"observation_digest":"sha256:11694654e0d137aba96522c65f9ff4b080229ec504be2a3c45db0293101710cb","observation_id":"d286ea8b-e233-4c88-b3cf-72fbb336b137","resolution":{"observed_at":"2026-06-26T14:17:57.337260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:17:57.337260Z","title":"Eckmann, Harmonische Funktionen und Randwertaufgaben in einem Komplex, Commentarii Math- ematici Helvetici 17 (1944), 240–255","venue":null,"work_id":null,"year":1944},"citing_paper":{"arxiv_id":"2606.21233","last_updated":"2026-06-19T08:54:01Z","snapshot_observed_at":"2026-08-10T15:04:02.417844Z","submitted_at":"2026-06-19T08:54:01Z","title":"Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-26T14:17:57.337260Z"},"links":{"citing_paper":"/paper/2606.21233"},"observation_digest":"sha256:786304342601e4f4b70ff3ca915d51afac4666cd6baeeef6f42e2b87fae7f903","observation_id":"78702cf2-e62c-4052-a321-0cbde9a8f2bc","resolution":{"observed_at":"2026-06-26T14:17:57.337260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:17:57.337260Z","title":"Fan, H.-F","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.21233","last_updated":"2026-06-19T08:54:01Z","snapshot_observed_at":"2026-08-10T15:04:02.417844Z","submitted_at":"2026-06-19T08:54:01Z","title":"Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-26T14:17:57.337260Z"},"links":{"citing_paper":"/paper/2606.21233"},"observation_digest":"sha256:86590d712dc5dbcc3a6738e71b49c1e24ba17bedee044e2f09d02cb5c639018a","observation_id":"6846bb8a-e202-4d7e-8056-b4b21e42f04c","resolution":{"observed_at":"2026-06-26T14:17:57.337260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:17:57.337260Z","title":"Horak and J","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.21233","last_updated":"2026-06-19T08:54:01Z","snapshot_observed_at":"2026-08-10T15:04:02.417844Z","submitted_at":"2026-06-19T08:54:01Z","title":"Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-26T14:17:57.337260Z"},"links":{"citing_paper":"/paper/2606.21233"},"observation_digest":"sha256:a168116d1f41bd7e825ee583d625a7dd6ba7574cded8e8604c66f85ff6c3846a","observation_id":"66effe34-389f-4190-8787-c732c5f3334a","resolution":{"observed_at":"2026-06-26T14:17:57.337260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:17:57.337260Z","title":"Horak and J","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.21233","last_updated":"2026-06-19T08:54:01Z","snapshot_observed_at":"2026-08-10T15:04:02.417844Z","submitted_at":"2026-06-19T08:54:01Z","title":"Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-26T14:17:57.337260Z"},"links":{"citing_paper":"/paper/2606.21233"},"observation_digest":"sha256:9786a8d7638e17f5c3e12a02de196eeb1e0e32828019b408b249aa8a29e00533","observation_id":"92df800f-4549-49f1-bf35-043af80bd17e","resolution":{"observed_at":"2026-06-26T14:17:57.337260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:17:57.337260Z","title":"Merris, Laplacian matrices of graphs: a survey, Linear Algebra and its Applications , 197–198 (1994), 143–176","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2606.21233","last_updated":"2026-06-19T08:54:01Z","snapshot_observed_at":"2026-08-10T15:04:02.417844Z","submitted_at":"2026-06-19T08:54:01Z","title":"Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-26T14:17:57.337260Z"},"links":{"citing_paper":"/paper/2606.21233"},"observation_digest":"sha256:812f12b661ad6917e8e9db0e00ebc3859bf9f81a61f29b8950e5c59dd56f6d7b","observation_id":"9a938032-2548-4959-889e-8c84a9e14f03","resolution":{"observed_at":"2026-06-26T14:17:57.337260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:17:57.337260Z","title":"Merris, Laplacian graph eigenvectors, Linear Algebra and its Applications , 278 (1998), 221–236","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2606.21233","last_updated":"2026-06-19T08:54:01Z","snapshot_observed_at":"2026-08-10T15:04:02.417844Z","submitted_at":"2026-06-19T08:54:01Z","title":"Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-26T14:17:57.337260Z"},"links":{"citing_paper":"/paper/2606.21233"},"observation_digest":"sha256:e4dbd2f9f74036ea9621004a128da83b3e6e3e28a6746c7c388459caa806087f","observation_id":"29fb911f-051a-4e66-83de-d72843a5afe4","resolution":{"observed_at":"2026-06-26T14:17:57.337260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:17:57.337260Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2606.21233","last_updated":"2026-06-19T08:54:01Z","snapshot_observed_at":"2026-08-10T15:04:02.417844Z","submitted_at":"2026-06-19T08:54:01Z","title":"Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-26T14:17:57.337260Z"},"links":{"citing_paper":"/paper/2606.21233"},"observation_digest":"sha256:45ef37416521a3117aa9523a89df014ee45b04e1e002d2e6abc147c0776af217","observation_id":"54fb5ecc-5a09-40e9-ac2b-0f53c73fe222","resolution":{"observed_at":"2026-06-26T14:17:57.337260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-26T14:17:57.337260Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.21233","last_updated":"2026-06-19T08:54:01Z","snapshot_observed_at":"2026-08-10T15:04:02.417844Z","submitted_at":"2026-06-19T08:54:01Z","title":"Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-26T14:17:57.337260Z"},"links":{"citing_paper":"/paper/2606.21233"},"observation_digest":"sha256:5cf431ddbf772506c8fd95cb937c7e699f078414995fcee4ca8d24e4e2c7e276","observation_id":"bd449843-ade7-4e86-93cb-6a56f8a2340b","resolution":{"observed_at":"2026-06-26T14:17:57.337260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.21233","last_updated":"2026-06-19T08:54:01Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-10T15:04:02.417844Z","submitted_at":"2026-06-19T08:54:01Z","title":"Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":0,"verified_fuzzy":0},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2606.21233."}