{"as_of":"2026-08-12T03:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c2f090c57f7a1e1c4ac0e1a3cf86310d985f2e396cd1786ccb89235197bb3d55","coverage":[{"denominator":19,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":19,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-12T11:17:11.251985Z","state":"measured"},{"denominator":21,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":21,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T18:27:46.410410Z","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":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.28797","snapshot_observed_at":"2026-08-01T18:27:46.410410Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.17343","last_updated":"2026-07-19T17:07:14Z","snapshot_observed_at":"2026-08-07T18:57:05.187925Z","submitted_at":"2026-07-19T17:07:14Z","title":"Parity families and a kernel-averaged L-function for near-Ramanujan signings","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T18:27:46.410410Z"},"links":{"cited_paper":"/paper/2606.28797","citing_paper":"/paper/2607.17343"},"observation_digest":"sha256:5440cc31d08e1f60faaadc7cbb4e9c6be8b77dcd49d679067f6a1b0aee40203c","observation_id":"76b24eda-50ba-4fd6-90bb-dbcdc4168cb0","resolution":{"observed_at":"2026-08-01T18:27:46.410410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.28797","snapshot_observed_at":"2026-08-01T18:25:42.979330Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.18334","last_updated":"2026-07-19T17:33:48Z","snapshot_observed_at":"2026-08-08T12:17:33.009215Z","submitted_at":"2026-07-19T17:33:48Z","title":"Signed circulants at the Ramanujan bound","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T18:25:42.979330Z"},"links":{"cited_paper":"/paper/2606.28797","citing_paper":"/paper/2607.18334"},"observation_digest":"sha256:434f94d405210d6e4e8986ba13820a7ea163ddfc651a0a689acf84a61c1b4cc3","observation_id":"28e7f388-5828-460e-9e0b-3e7cce084513","resolution":{"observed_at":"2026-08-01T18:25:42.979330Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2606.28797/citation-record","integrity":"/paper/2606.28797/integrity","json":"/paper/2606.28797/citation-record.json","paper":"/paper/2606.28797"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-12T11:17:11.251985Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:208b70dc7a9058397ae35e84924c07c066ed512b323e256bcc5d47696b2e5e27","observation_id":"e92962b1-f087-4da7-a1f1-9726d3569ec0","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":"Bownik,The Kadison–Singer problem, Frames and Harmonic Analysis, 63–92, Contemp","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:29af8532d0a076c32c0a8c0787abcf9ba098da661cedf8ef4385c15d925c96da","observation_id":"6aab3997-0193-42ef-ad34-0b107bc92198","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.18235","last_updated":"2024-05-28T14:45:54Z","snapshot_observed_at":"2026-07-06T18:21:22.569625Z","submitted_at":"2024-05-28T14:45:54Z","title":"Selector form of Weaver's conjecture, Feichtinger's conjecture, and frame sparsification","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.18235","snapshot_observed_at":"2026-07-12T11:17:11.251985Z","title":"Bownik,Selector form of Weaver’s conjecture and frame sparsification, arXiv preprint arXiv:2405.18235, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"cited_paper":"/paper/2405.18235","citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:4c586dabe75762e994c63c7a70ee3891120e9a80d7d17e9dd69ac7775ab1b0fa","observation_id":"be955dc2-6843-4acc-8948-ebefc459ccca","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":"Bownik,On akemann–weaver conjecture, Adv","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:6a994ad9fec3361ffec89e09d1188ad96a7e66ad861ee1fe98700cdc7cc319b6","observation_id":"ecb35dbe-5f5b-4fd9-ad80-369c9d2d37f2","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1809.03255","last_updated":"2018-09-10T12:03:00Z","snapshot_observed_at":"2026-08-11T12:22:25.419106Z","submitted_at":"2018-09-10T12:03:00Z","title":"Hyperbolic polynomials and the Kadison-Singer problem","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1809.03255","snapshot_observed_at":"2026-07-12T11:17:11.251985Z","title":"Brändén,Hyperbolic polynomials and the Kadison–Singer problem, arXiv preprint arXiv:1809.03255, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"cited_paper":"/paper/1809.03255","citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:4c64018951d2b55eb97afc0091532fbf7e6d87688316d903259e6c5f87fca00b","observation_id":"7f752e22-28eb-4b12-82d7-14110551c364","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:d8e99581740c820178a3cae8c07d5967738b40a8f44f19e6c4f4d3065a8899bc","observation_id":"75ec061a-dfd7-4cf7-81cb-ca868338576d","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:66e53fb1d02956fc1795b7c71fadbdfd87879fdc3d22b0bf4b663b097c141a4a","observation_id":"196f3292-291f-45a3-8cd7-acfeb7109f09","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":"Chartrand, P","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:4c65b24aac508e1f011c94d66deef91b5acc97321e60a0a9dd79f46576b54aa3","observation_id":"8efd3db6-a83b-4153-99b8-5ff2c73703e7","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:82733fc177b343f41a109a140cb6cdd1ba04738ea561f060aea8f264bea3aad7","observation_id":"598aa538-008b-49e7-a593-8d2a9582b1e0","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":null,"venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:96e35af64485ddf4921ddf852be066a95430d102e0137faae14668525e5fddd0","observation_id":"2d525e53-3d71-4225-a312-3f8d9cf76dc4","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":null,"venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:9585ae6ea4b3a370f052463ceb194b773694cc0441b44e31ce9389403495b2b6","observation_id":"7095b771-e5da-47da-9791-ed38fd4e5699","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":null,"venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:ae9ff412d2289f7f83c1732d9741cf96935140619d223f26655c7ee616cde80c","observation_id":"8adb34b4-1f1b-4d4b-8826-0cb5a4585168","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":"Lubotzky, R","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:2d625610639efa457b24bdb3dac45ecdbbf3e7cfafce3411474f608cf921523f","observation_id":"ad16f8a3-9f9e-419c-8d4b-4a06345d8912","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":"König,Theorie der endlichen und unendlichen Graphen, Akademische Verlagsgesellschaft, Leipzig, 1936","venue":null,"work_id":null,"year":1936},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:8f31900abb7efd424692327a608d1305550ca5abafe4c5a4726c9ae2e43913b6","observation_id":"b3c76efb-cfb0-45c6-bdec-3fa075507f89","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:85ff08ec1c1647c811180e560dab9b03ca79f568d317d60aa1b93ecf820c50c0","observation_id":"4f7978c1-7921-4c1c-9497-c025c618bf1b","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:e109407b5be5f795482760f824e3055cb2a622900b6885a5d106d89cdbc487bd","observation_id":"8e02b929-0b65-4654-9c81-f9c9f0895499","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:ff669bedf6c5b870eafd34c036a79543ed5d764ab8c57f6b4121e856f10878c5","observation_id":"9e7f155e-e019-488b-890e-80ecae9f74d6","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:2769fc84d902e37a3ca63ee04b283b2f9d442818d4d8328fb907c8830d5f370f","observation_id":"26128ff4-ca1e-47f8-941b-b0e2e1330ce8","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","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":"2026-07-12T11:17:11.251985Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-12T11:17:11.251985Z"},"links":{"citing_paper":"/paper/2606.28797"},"observation_digest":"sha256:1e401700313f62f53c54e78649ea65afa5db4e5ecf21efee97758d689d7ca0e1","observation_id":"b316a045-4942-41b9-8c7c-73a66fd47865","resolution":{"observed_at":"2026-07-12T11:17:11.251985Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.28797","last_updated":"2026-07-09T15:55:53Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-07-12T23:18:44.929809Z","submitted_at":"2026-06-27T08:09:09Z","title":"An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families"},"reference_resolution":{"displayed":19,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":19,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":19},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 2 inbound Pith citation observations for arXiv:2606.28797."}