{"as_of":"2026-08-15T22:49:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1653eafa7d97744940c15380cd23a1797ebede540d20b65ce09602d26ec40ce3","coverage":[{"denominator":74,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":74,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T23:08:06.999068Z","state":"measured"},{"denominator":78,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":78,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T19:56:06.172251Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-23T01:12:21.496443Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"cited_work":{"arxiv_id":"2501.00234","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2501.00234","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"and Wang, J","venue":null,"work_id":"b0dcd0f4-e566-42da-b61c-8bd20386d878","year":2024},"citing_paper":{"arxiv_id":"2503.08139","last_updated":"2026-04-13T13:50:09Z","snapshot_observed_at":"2026-07-06T20:50:27.661417Z","submitted_at":"2025-03-11T07:59:07Z","title":"The eigenvalue gap of inhomogeneous symmetric discrete random matrix","version":4},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-23T01:08:13.915792Z"},"links":{"cited_paper":"/paper/2501.00234","citing_paper":"/paper/2503.08139"},"observation_digest":"sha256:405afe6331c8d414c9572311b97d53935d2d7535c2b4d2d6c4fe7cbb88572bfa","observation_id":"b93fa305-bb84-4ab7-9b26-bb6b8c54ae63","resolution":{"observed_at":"2026-05-23T01:12:21.498601Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.00234","snapshot_observed_at":"2026-08-06T19:56:06.172251Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.08014","last_updated":"2025-07-06T08:41:30Z","snapshot_observed_at":"2026-08-06T19:48:50.296360Z","submitted_at":"2025-07-06T08:41:30Z","title":"Mass-Scale Analysis of In-the-Wild Conversations Reveals Complexity Bounds on LLM Jailbreaking","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T19:56:06.172251Z"},"links":{"cited_paper":"/paper/2501.00234","citing_paper":"/paper/2507.08014"},"observation_digest":"sha256:345cd5787e13b0ddb3cf08ee400176aa24fd989f093c33da94f16f80f735529d","observation_id":"76914db4-cb3e-4ff1-8607-3cbca2f1b33a","resolution":{"observed_at":"2026-08-06T19:56:06.172251Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.00234","snapshot_observed_at":"2026-08-03T13:03:22.630485Z","title":"and Chandrasekaran, B","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2601.00791","last_updated":"2026-06-10T09:38:19Z","snapshot_observed_at":"2026-08-14T21:11:51.423827Z","submitted_at":"2026-01-02T18:49:37Z","title":"Geometry of Reason: Spectral Signatures of Valid Mathematical Reasoning","version":2},"reference_index":2018,"source":"pdf_text","source_observed_at":"2026-08-03T13:03:22.630485Z"},"links":{"cited_paper":"/paper/2501.00234","citing_paper":"/paper/2601.00791"},"observation_digest":"sha256:6bc2ea2f7edf9f563012b2dc7f21db0383c85cd95982edb95cfaf58dcdfb9f96","observation_id":"17bf06ce-dd9a-4fcf-805b-3a21c9c40910","resolution":{"observed_at":"2026-08-03T13:03:22.630485Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.00234","snapshot_observed_at":"2026-07-30T23:29:40.128476Z","title":"Christoffersen, K","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.26705","last_updated":"2026-07-29T09:51:24Z","snapshot_observed_at":"2026-08-06T04:07:58.234215Z","submitted_at":"2026-07-29T09:51:24Z","title":"Dynamical phase retrieval for Schr{\\\"o}dinger evolution on finite graphs","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-07-30T23:29:40.128476Z"},"links":{"cited_paper":"/paper/2501.00234","citing_paper":"/paper/2607.26705"},"observation_digest":"sha256:4d3ed9abb81149660253832907bba4e7c187e542ab95a1c893e4bac4dda15cf4","observation_id":"5a3084ab-cccb-4b1e-8e62-3aa592112d15","resolution":{"observed_at":"2026-07-30T23:29:40.128476Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2501.00234/citation-record","integrity":"/paper/2501.00234/integrity","json":"/paper/2501.00234/citation-record.json","paper":"/paper/2501.00234"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2010.01179","last_updated":"2021-06-04T14:52:04Z","snapshot_observed_at":"2026-08-13T14:20:35.424484Z","submitted_at":"2020-10-02T19:53:05Z","title":"The Surprising Power of Graph Neural Networks with Random Node Initialization","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.01179","snapshot_observed_at":"2026-08-10T23:08:06.686691Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.686691Z"},"links":{"cited_paper":"/paper/2010.01179","citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:c02725906d2bc9931730fa029a2c77922b3d4e11acb6546a407c898e65dadb45","observation_id":"c4d41318-cb6f-4782-bf23-56e6d2c59713","resolution":{"observed_at":"2026-08-10T23:08:06.686691Z","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":"2026-08-10T23:08:08.171957Z","title":"Quantum walks on graphs","venue":null,"work_id":"b929b0a0-c199-416d-9b23-3c6c0268632c","year":2001},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.691722Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:4718f2a06ccfe97150811561d24d8a81adddb6e051e98e76ea37ce819d72522a","observation_id":"f36b997e-8faa-47b9-8da9-eaa4e613cd5f","resolution":{"observed_at":"2026-08-10T23:08:08.176251Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:08.154126Z","title":"Anderson, Alice Guionnet, and Ofer Zeitouni.An introduction to random matrices, volume 118 ofCambridge Studies in Advanced Mathematics","venue":null,"work_id":"1417a31e-161a-4977-b466-7bb0171dedd2","year":2010},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.696156Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:966a7572a66699b0103ab2b45e618394bc0950050e3098a179366b09792f2044","observation_id":"69d229ee-e34b-4e2e-a02a-0815068b23a8","resolution":{"observed_at":"2026-08-10T23:08:08.160811Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:08.123742Z","title":"Measuring the stability of spectral clustering","venue":null,"work_id":"91482438-b6df-4024-bd5f-31a67e1cc131","year":2021},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.700552Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:fc2598b8f7823cb7ca8bff885289a4838baa9ada384d2623ecfe2f1fb961827b","observation_id":"1279a41c-98ca-4c25-b8b5-476fb9d7421f","resolution":{"observed_at":"2026-08-10T23:08:08.129415Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:08.099221Z","title":"Silverstein.Spectral analysis of large dimensional random matrices","venue":null,"work_id":"20a9deef-d628-4d8c-8d66-4d2a18fb1bfa","year":2010},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.704644Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:4457ed01a1b76d19f3af2903c9224ebfc43cf02df168ee47258500b698f5a08e","observation_id":"269ba661-1cb2-4e6a-a0c5-ab4da386ec04","resolution":{"observed_at":"2026-08-10T23:08:08.103913Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:08.071160Z","title":"Bandeira","venue":null,"work_id":"12ef5f58-b666-4c56-a62b-8c3d61ea27b1","year":2018},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.708896Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:895f94a777b54c8bb9e0714a25292755e7eca578e9b0d6a1770cb0132b19faf8","observation_id":"9842aff6-b05a-474f-bb5a-a27ae147411f","resolution":{"observed_at":"2026-08-10T23:08:08.075947Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:08.052872Z","title":"Cambridge University Press, 2004","venue":null,"work_id":"a570cfc4-3766-4997-82fe-76f3bec2d9b2","year":2004},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.712933Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:0ba232b03d75e70c1c221c941f7925e81c40c49eb6ce9b911f66a88a4400b91f","observation_id":"a62a359d-f84a-45fd-91ec-ab4ae1ec452f","resolution":{"observed_at":"2026-08-10T23:08:08.057371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:08.034692Z","title":"Extreme gaps between eigenvalues of random matrices.Ann","venue":null,"work_id":"71fb346a-e3ae-44a1-a7a8-c4a8bf6830ed","year":2013},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.716801Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:1098c413686c3cfd2fd80dddb4272660a720a0932d8204142cd31c3906052223","observation_id":"a1ce80d8-e998-4d6c-9e78-798e0f2f466a","resolution":{"observed_at":"2026-08-10T23:08:08.040599Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:08.007233Z","title":"Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph.J","venue":null,"work_id":"bcf1ad6e-c77c-41aa-ae4e-5d83657e8b7b","year":2017},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.720447Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:67b109da7f37d5a567486e2f79cf5c80933f4fed7bbab1c22e051eeedc95973c","observation_id":"95ff14af-0e7f-468e-896f-6cc097e2d8db","resolution":{"observed_at":"2026-08-10T23:08:08.016901Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.990499Z","title":null,"venue":null,"work_id":"0ef0fd17-5139-4af5-ba17-03f68c4bc001","year":2004},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.724697Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:50b17b9c3c583f49cfba409215cbe6b66e29e9afbd7588876ef43b348d66cc72","observation_id":"074f109a-58d9-4546-8b17-33147210847a","resolution":{"observed_at":"2026-08-10T23:08:07.994694Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.975979Z","title":"Extreme gaps between eigenvalues of Wigner matrices.J","venue":null,"work_id":"c5199ff9-48fe-4d0b-9633-be556262b1d4","year":2022},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.728206Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:8de9eea9aeb8babac050de215c6370db383b1309d6481b12521c38ed9ebdb103","observation_id":"f7282372-7613-4c42-845a-fbc498ad3155","resolution":{"observed_at":"2026-08-10T23:08:07.981522Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2211.17175","last_updated":"2024-08-19T20:35:17Z","snapshot_observed_at":"2026-08-13T13:30:42.195362Z","submitted_at":"2022-11-30T17:20:24Z","title":"Extreme eigenvalues of Laplacian random matrices with Gaussian entries","version":2},"cited_work":{"arxiv_id":"2211.17175","doi":null,"metadata_source":"pith","pith_arxiv_id":"2211.17175","snapshot_observed_at":"2026-08-10T23:08:07.086252Z","title":"Extreme eigenvalues of Laplacian random matrices with Gaussian entries","venue":"math.PR","work_id":"9bde7207-f08e-4d28-81df-bbf5b1fef08d","year":2022},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.731973Z"},"links":{"cited_paper":"/paper/2211.17175","citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:d5aee7d0f997e2d6356b2ae0761af761a5d52164b95e5ecd74dbb253f98184c9","observation_id":"f15fb832-d6ad-4ff9-a674-a51ce76033d8","resolution":{"observed_at":"2026-08-10T23:08:07.090702Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.960429Z","title":"The least singular value of a random symmetric matrix.Forum Math","venue":null,"work_id":"a0ba0a8f-81d4-4304-9943-b6d7c34c4172","year":2024},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.736184Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:7003ab522be18af3fee51a7fa046fb9b0950a7b1a3e3c9dcbb4376b1203228d4","observation_id":"e8569224-c004-4625-96ca-cb7e1f51d7b1","resolution":{"observed_at":"2026-08-10T23:08:07.965462Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.947078Z","title":"Caputo, I","venue":null,"work_id":"99817267-ce16-4b76-9339-927c3f59a53c","year":2019},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.741267Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:f38a45bf4b113c5c692a531ec508bb6642d44e9c07d58d03921a4bed9c533f82","observation_id":"27f76222-abe4-4658-ac6b-2bf75afecb48","resolution":{"observed_at":"2026-08-10T23:08:07.951882Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2301.08369","last_updated":"2023-01-20T00:24:37Z","snapshot_observed_at":"2026-08-13T13:00:52.060235Z","submitted_at":"2023-01-20T00:24:37Z","title":"Eigenvectors of graph Laplacians: a landscape","version":1},"cited_work":{"arxiv_id":"2301.08369","doi":null,"metadata_source":"pith","pith_arxiv_id":"2301.08369","snapshot_observed_at":"2026-08-10T23:08:07.066538Z","title":"Eigenvectors of graph Laplacians: a landscape","venue":"math.SP","work_id":"56c25a1e-5db8-4a2d-89dc-483daec05b04","year":2023},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.745362Z"},"links":{"cited_paper":"/paper/2301.08369","citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:083d11e2c43c4637b35f63e92f55aa7327f1255651cd49d56badb91298248231","observation_id":"2eaa0326-9aee-4e95-adcd-5227430347ec","resolution":{"observed_at":"2026-08-10T23:08:07.072897Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.932187Z","title":"Oscillations of networks: the role of soft nodes.Journal of Physics A: Mathematical and Theoretical, 46(3):035101, 2012","venue":null,"work_id":"0505197e-22cc-4f90-855f-6bee2636859a","year":2012},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.749412Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:a6059e3952ebb447576fef4a4a2ff7b46b5e5c41f186212e1d69139c4c33edfa","observation_id":"a5a83236-e308-43bb-8ed6-4c02a4be2b00","resolution":{"observed_at":"2026-08-10T23:08:07.938084Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.918286Z","title":"Analog quantum algorithms for the mixing of Markov chains","venue":null,"work_id":"9d6f0e08-2962-41de-8121-25cab04c9a36","year":2020},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.753294Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:d0b47b4d67a8610b039020a52683b84e5b57d6bc21cf6517587983724935bc9f","observation_id":"61d54838-966d-45a6-bff5-695d4cbdf790","resolution":{"observed_at":"2026-08-10T23:08:07.922269Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.906270Z","title":"How fast do quantum walks mix?Phys","venue":null,"work_id":"25b450bd-c10d-4d19-996f-9a2238468fee","year":2020},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.758073Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:e849fa3f3e6b9aac1e4a17b25912f2628cfdf309d3b5cc69349219f08cb294fe","observation_id":"4de2dd80-470c-4272-bb8d-eb3c4de8e35a","resolution":{"observed_at":"2026-08-10T23:08:07.910483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.891682Z","title":"Academic Press, Inc., Orlando, FL, 1984","venue":null,"work_id":"6372099f-e0ad-4b4d-aa75-7c6e02544fce","year":1984},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.761918Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:eb6762a9db7e884a9c9904fcba8705d417646b8cc92d79d0d78b4106ff1cc3a1","observation_id":"6b689953-5c9d-4603-9420-f5f894764686","resolution":{"observed_at":"2026-08-10T23:08:07.896909Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.878127Z","title":"Estimates of the gaps between consecutive eigenvalues of Laplacian","venue":null,"work_id":"6210ea39-30ff-4abe-8806-45d70639ae15","year":2016},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.765722Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:3178585e64ff3575298244b891399b77924707f3bc30a6451821ff10510108b0","observation_id":"3a82ba1e-417c-4bb8-a611-f431a508e188","resolution":{"observed_at":"2026-08-10T23:08:07.883199Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.866589Z","title":"Exponential algorithmic speedup by a quantum walk","venue":null,"work_id":"2957be26-b2fe-4343-9d03-266d89971a62","year":2003},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.769917Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:f16248e652d8d8a4deafb6fe70ce3fb72a155091023b993d19419a2b20f9ec4c","observation_id":"1adbb665-46da-4564-a9c1-1f9d1c3f06fa","resolution":{"observed_at":"2026-08-10T23:08:07.870784Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.852655Z","title":"PhD thesis, Massachusetts Institute of Technology, 2004","venue":null,"work_id":"fe67ee18-d04a-4918-a729-5f45b1e767f3","year":2004},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.773930Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:4b56201b2fe5964a967a67435acb2b5673cb906499c62b481b5690fb5553c15b","observation_id":"95ff27cf-39c2-4644-a528-0597e0ae3e64","resolution":{"observed_at":"2026-08-10T23:08:07.857190Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.838777Z","title":"On the Laplacian eigenvalues ofGn,p","venue":null,"work_id":"907aa8fc-146b-40fb-b30e-709ec912257d","year":2007},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.777047Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:8f0347e737213e852380031c4324581be975f5cf5d25d279031f07a4665a0bb0","observation_id":"5ae66856-5a86-4d38-b248-9729dd255d33","resolution":{"observed_at":"2026-08-10T23:08:07.843680Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.823087Z","title":null,"venue":null,"work_id":"0a510ca0-9f5e-4ed2-964d-7a4e4d55aa75","year":2017},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.781450Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:50038ff7571e1ffbd154acd1cc9d9e14d13c1e1bc3df8bbf46b74542ff7b3245","observation_id":"f626adfc-6259-4b97-9c7e-328bbc84df65","resolution":{"observed_at":"2026-08-10T23:08:07.828626Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.799744Z","title":"Lee, and Nathan Linial","venue":null,"work_id":"17e61972-7a23-496b-9d9a-3295fec5962c","year":2011},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.786954Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:3441efd81bae0a3aed9be133ab0491bda9db3706d1f1b245dc8bf87b29768b9e","observation_id":"21fb4e55-354a-4c28-bbda-4248475b0730","resolution":{"observed_at":"2026-08-10T23:08:07.805731Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.779620Z","title":"Applied numerical linear algebra.SocietyforIndustrialandAppliedMathematics(SIAM),Philadelphia, PA, 1997","venue":null,"work_id":"c5ab8cd5-d369-46c7-a8fe-7dbe15775fdb","year":1997},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.791544Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:d8472ba67faee2a1d51ef385207725a78328015cf4be4c62d5150180df405416","observation_id":"e5bc107d-7aab-4ea9-8e29-3741c3efc10f","resolution":{"observed_at":"2026-08-10T23:08:07.787914Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.762745Z","title":"Spectral distributions of adjacency and Laplacian matrices of random graphs.Ann","venue":null,"work_id":"d5e59929-47c9-4d2a-b1fa-05482b4ad7f8","year":2010},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.796222Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:5e698b0aa984448e97fbb250edb988c7b54a3fca56aa480974a90597ca54b494","observation_id":"0e6cb2b9-eeba-46cc-8859-7d946021e625","resolution":{"observed_at":"2026-08-10T23:08:07.769717Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.744574Z","title":"Spectral statistics of erdős-Rényi Graphs II: Eigenvalue spacing and the extreme eigenvalues.Comm","venue":null,"work_id":"aad407b4-e605-4c60-876b-ad7a2fed7a42","year":2012},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.801992Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:eb342dd6e365aede5ac4cd25545d0e7851e0ce5bec0084ea7f3e006ee02d6330","observation_id":"26558134-24a7-4b9c-9f23-df3dff5ca6f2","resolution":{"observed_at":"2026-08-10T23:08:07.749550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.726108Z","title":"Bulk universality for generalized Wigner matrices.Probab","venue":null,"work_id":"ad600750-9d99-402d-acbf-a01835ca60c4","year":2012},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.806365Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:37336100c48da99f5ab34678fd17acd722ac21b540c42d285fc5c8129d09141a","observation_id":"cfb1c3f9-2ea6-46bd-85ed-f91a84c57953","resolution":{"observed_at":"2026-08-10T23:08:07.733505Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.705051Z","title":"Small gaps of GOE.Geom","venue":null,"work_id":"97260913-b3e5-414d-9bd7-3af1b6c30f36","year":2019},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.810306Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:22b996d0939a81f2478014b20473811cf47cd47e4a802a775d860856f21565ed","observation_id":"b6f8595f-d137-4ecb-afe0-24797c2d1af5","resolution":{"observed_at":"2026-08-10T23:08:07.710607Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.682480Z","title":"Molecular graph eigenvectors for molecular coordinates: System demonstration","venue":null,"work_id":"f18369ee-16a8-40b3-935d-82edb1a44210","year":1994},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.816984Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:e4b64928bb005389acc965e746c5b2a1f6cb9d40b362e217decb1270d14398c1","observation_id":"8625996b-fe42-4cd7-bc16-24230612005c","resolution":{"observed_at":"2026-08-10T23:08:07.687471Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.666267Z","title":"Genericity of simple eigenvalues for a metric graph.Israel J","venue":null,"work_id":"88ec24ef-870a-4e30-8eb5-44900e565028","year":2005},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.824868Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:529d3ba700403f51aadb63a9d43272a57092afa5fc33c06f87ec061541d6461f","observation_id":"47e28918-e2fd-4013-8365-f0501eb70a5c","resolution":{"observed_at":"2026-08-10T23:08:07.672346Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.646201Z","title":"Fyodorov","venue":null,"work_id":"a9730abe-dae0-49e3-af79-fb96f5ee1c6b","year":1999},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.829130Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:07a135cfa707103d86aa4a2413d0571fc32c015df4789e629b7cc6344e79e062","observation_id":"6c462ee8-65a0-4879-881f-e1f030b2f14c","resolution":{"observed_at":"2026-08-10T23:08:07.652824Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.628994Z","title":"Stability properties of graph neural networks.IEEE Trans","venue":null,"work_id":"e05922e5-fead-49cb-afde-7bebcc469a14","year":2020},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.834012Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:e9f7dca297ba7efec0310d6934aba70e7669c587f1b33352a8729fb191ca88c7","observation_id":"a01dc033-0413-45f0-94f8-7b0aab097d8d","resolution":{"observed_at":"2026-08-10T23:08:07.635097Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:06.839836Z","title":"Springer Science & Business Media, 2001","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.839836Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:a727eb305b4272e96c1313888674e3799b2c920deba2735d5c24631600d40745","observation_id":"f3ac7880-6033-4642-8c94-c0084664e586","resolution":{"observed_at":"2026-08-10T23:08:06.839836Z","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":"2026-08-10T23:08:07.598010Z","title":"Golub and Charles F","venue":null,"work_id":"bcb47c97-b04c-40c6-b22f-a8771615a1be","year":2013},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.843235Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:3b9929538124586a33b238ae8e7d91a729a3bc258818fe593eb5babf7d448736","observation_id":"c5023b66-69d4-4c7b-9448-6e621aa6e49d","resolution":{"observed_at":"2026-08-10T23:08:07.603695Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:06.847228Z","title":"New spectral methods for ratio cut partitioning and clustering.IEEE transactions on computer-aided design of integrated circuits and systems, 11(9):1074–1085, 1992","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.847228Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:46990cfa3421c254ed9066c97c8ab91c42a4ad27204aad741d35815fe52fd196","observation_id":"08e5131e-f98e-4b00-b4f2-f118edb5932f","resolution":{"observed_at":"2026-08-10T23:08:06.847228Z","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":"2026-08-10T23:08:07.570140Z","title":"A spectral approach to bandwidth and separator problems in graphs.Linear and Multilinear Algebra, 39(1-2):73–90, 1995","venue":null,"work_id":"22058454-ad07-44d3-b7c7-cfa85d361175","year":1995},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.851552Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:4fa6e75658d1182d2a513f38c75de01c899b29db0a31e3773b581c2d010ecc77","observation_id":"9ee2445d-21b6-43b9-8f8a-42cd836c2ce5","resolution":{"observed_at":"2026-08-10T23:08:07.577106Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.549840Z","title":"Spectral statistics of sparse ő-Rényi graph Laplacians.Ann","venue":null,"work_id":"c40a214f-d0d4-4653-85d9-b7960d6fe577","year":2020},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.855485Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:4fa71881ea35ffb1ee8276f5185f76658b3b8fc03fa913dd05d74b632ac6194c","observation_id":"3522a60b-9174-42cf-b365-c7df7c912244","resolution":{"observed_at":"2026-08-10T23:08:07.559336Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.532434Z","title":"Low eigenvalues of Laplacian matrices of large random graphs.Probab","venue":null,"work_id":"d94a79bb-e89d-4033-9d81-37188495af31","year":2012},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.859311Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:c6a24eb9f2d2af5d1fd8f350b55e532b5e23d6ed753c2b4b10512fc3e0d6d976","observation_id":"d08913ac-175a-4a09-933d-1cd2ac9aeb6f","resolution":{"observed_at":"2026-08-10T23:08:07.537730Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.518439Z","title":"Quantum random walks: an introductory overview.Contemporary Physics, 44(4):307–327, 2003","venue":null,"work_id":"a5b2ac29-1c2a-42e8-9943-c196c2f2f7d4","year":2003},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.863594Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:eb674010597d3d3635c0112b184a58829b4e3ce55586de29f4d37eb87105cfd5","observation_id":"6dda92de-ab37-44ef-9f82-c2b6054e5255","resolution":{"observed_at":"2026-08-10T23:08:07.522909Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:06.867654Z","title":"The expressive power of graph neural networks.Graph Neural Networks: Foundations, Frontiers, and Applications, pages 63–98, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.867654Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:a9506654d5595342fbab72154057819605b8d1be25f6e808b5b72d7b62b0d360","observation_id":"ec0bcf06-da30-4025-84dc-81064861c757","resolution":{"observed_at":"2026-08-10T23:08:06.867654Z","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":"2026-08-10T23:08:06.871990Z","title":"Distance encoding: Design provably more powerful neural networks for graph representation learning.Advances in Neural Information Processing Systems, 33:4465–4478, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.871990Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:92248ae524028daac0587a490dc469b1841895c59958a593033775a73f517c03","observation_id":"055376e1-229b-40b5-8106-3a1d538081e0","resolution":{"observed_at":"2026-08-10T23:08:06.871990Z","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":"2026-08-10T23:08:07.469915Z","title":"Litvak, Anna Lytova, Konstantin Tikhomirov, Nicole Tomczak-Jaegermann, and Pierre Youssef","venue":null,"work_id":"1574f07e-6382-4209-a345-8f96abfcfe87","year":2021},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.875767Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:8af699f3947b6ffe255d33b094f229614e243b437c3b8e9c708ccafa97bf3d57","observation_id":"60055fb2-9331-490b-8125-4021f9b4c900","resolution":{"observed_at":"2026-08-10T23:08:07.474216Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.454399Z","title":"Tail bounds for gaps between eigenvalues of sparse random matrices.Electron","venue":null,"work_id":"09c33a72-1a36-4b60-a54a-2bf0aa15a6a3","year":2021},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.880113Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:96f004687adc95b8b8a7cd4b9143cb7e49bac44dd4863a17d1cd495d0a8afa39","observation_id":"a2360170-d7f7-4567-ae1c-7330dd5d530c","resolution":{"observed_at":"2026-08-10T23:08:07.459312Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.442879Z","title":"Expander graphs in pure and applied mathematics.Bull","venue":null,"work_id":"45a55f61-b404-45cb-9052-90bfba4d651f","year":2012},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.884326Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:b201f2282d72d3da26fb647f337a8669e14b9913537f96d62e9c9d702799aaaf","observation_id":"273c324c-9a87-4b0b-9537-a56aed8e02bd","resolution":{"observed_at":"2026-08-10T23:08:07.446900Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.430843Z","title":"Sparse random matrices have simple spectrum.Ann","venue":null,"work_id":"002e950a-7a8f-48c8-b2e6-a32bfea57c9d","year":2020},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.888170Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:7a586a3334eebc34f1a3114047a4a6301c3d4ace661530d5c87aeae3dc73742b","observation_id":"203ea90f-fdd2-407f-a4fc-c5c1fb6a3e60","resolution":{"observed_at":"2026-08-10T23:08:07.434725Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.419236Z","title":"Laplacian canonization: A minimalist approach to sign and basis invariant spectral embedding.Advances in Neural Information Processing Systems, 36:11296–11337, 2023","venue":null,"work_id":"378e20eb-a253-47bc-b66a-2a685a0e5a89","year":2023},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.891404Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:442a8f294b257f3abed010384b3ef457cee7891a0b5f51f54c86818ce8644d68","observation_id":"b546fd29-972a-40d0-9b26-587b6cc11da1","resolution":{"observed_at":"2026-08-10T23:08:07.422854Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.405431Z","title":null,"venue":null,"work_id":"cfbd5ae5-184f-4e47-9dc6-d6e0312bb809","year":1981},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.894484Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:1428a29d6b672dfaaefa4752a09c810da9e86337fbf7240695d38004f77006cc","observation_id":"11f1324b-5b90-4505-a8fc-b3b6ab5ece4d","resolution":{"observed_at":"2026-08-10T23:08:07.411992Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.386708Z","title":"Eigenvalues in combinatorial optimization","venue":null,"work_id":"88210939-9955-4a85-9b85-fc7ab796fa18","year":1991},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.898087Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:62eaac64a8da7dd087cd3a093d821c2319793240bc413301c0283a4f1f455356","observation_id":"043ff271-2fd8-4a69-b328-fa70e254812e","resolution":{"observed_at":"2026-08-10T23:08:07.391417Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.368656Z","title":"Restricted invertibility revisited","venue":null,"work_id":"8f80d11e-9675-44a1-9166-c2b659e4aa6b","year":2017},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.901889Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:3db563eede3048dcc51af692070955e32cd57b51b148032e0731dc2de691d63c","observation_id":"f68f3ec6-d2a7-403d-ae7a-b3fd7607db32","resolution":{"observed_at":"2026-08-10T23:08:07.373327Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.354968Z","title":"Random matrices: tail bounds for gaps between eigenvalues.Probab","venue":null,"work_id":"19d626a1-f0fc-4b63-81c6-f01d0da9bd41","year":2017},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.907513Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:959dfbd879284ecd96393a27448d53548d434ea8841b8b8c1b02e1b6afc429bf","observation_id":"c113d419-0b4b-485a-9844-7a08bc00b965","resolution":{"observed_at":"2026-08-10T23:08:07.358624Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.342932Z","title":null,"venue":null,"work_id":"86ef34b8-bfb4-4a49-a4c1-f108452bf8dc","year":2018},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.913089Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:0ec5fa5083289249b6a52c84186df6828353b4e270b5831333b6297a62a10ce3","observation_id":"7003fdaf-d134-4ce2-b0c1-30cbfdcc5335","resolution":{"observed_at":"2026-08-10T23:08:07.346954Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.328540Z","title":"Nguyen and Melanie Matchett Wood","venue":null,"work_id":"1be7a708-84be-4421-b12f-330b5ce02262","year":2022},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.916727Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:79a056826515d2d2dc3718374dfd7b7bb5c3a0ac8968051b965348702d08455e","observation_id":"6186e7cf-3e7c-43a5-b221-2cf356aef0c0","resolution":{"observed_at":"2026-08-10T23:08:07.333414Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.316062Z","title":"Local and global universality of random matrix cokernels.Mathematische Annalen, pages 1–94, 2024","venue":null,"work_id":"cdf810fb-3100-4aa3-8a19-90231cabc939","year":2024},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.920354Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:9312c574fdd1812af344b366ba7d6d8123e5b20d701d06d6bb84983ebe815172","observation_id":"db192461-789b-4d5b-ae54-a152ba6f905f","resolution":{"observed_at":"2026-08-10T23:08:07.320754Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.303855Z","title":"PhD thesis, University of Houston, 2014","venue":null,"work_id":"dbdab143-3d0b-4173-bcfb-6971b63c0d81","year":2014},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.925262Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:f5ef4165470bd65e93b72884be5d982d43a3ea324ef05a4fc197e6c960e1b2d4","observation_id":"2e999a8e-ac69-4de5-a10e-b9f150aaa820","resolution":{"observed_at":"2026-08-10T23:08:07.308352Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.292804Z","title":null,"venue":null,"work_id":"52e77a35-1ced-41f8-ba61-c7425d040619","year":2015},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.929324Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:9b27e45923cffdcba122908eea03fb1d7d2c0819861e1cd65c1739fc987e1464","observation_id":"8eb6d8db-f3ec-4fe4-b2e8-acbb5a7f418b","resolution":{"observed_at":"2026-08-10T23:08:07.296624Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.281118Z","title":"The Littlewood-Offord problem and invertibility of random matrices.Adv","venue":null,"work_id":"8edac9d0-c803-4089-ba59-43fc8ac2c5c2","year":2008},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.933589Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:ff19173bd847c13d800f17a5e2d27477402297dc14c00b6e658b9b3da24f0589","observation_id":"4fb5776c-6c3c-47f8-a854-7a7b4611e7c6","resolution":{"observed_at":"2026-08-10T23:08:07.284784Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.269223Z","title":"Smallest singular value of a random rectangular matrix.Comm","venue":null,"work_id":"196b90df-166f-4de3-8206-9b40dbfc21c1","year":2009},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.939040Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:0a7ef5bf64ca5701fc556b36c5d6f303cdd314e49c3a2fc6f0d43f98f679758b","observation_id":"95d4a21f-e7e7-4cd2-9769-7ba780bc5107","resolution":{"observed_at":"2026-08-10T23:08:07.273210Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.256564Z","title":"No-gaps delocalization for general random matrices","venue":null,"work_id":"a32b6e1e-6fa9-4c96-a799-4b589194966b","year":2016},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.942906Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:6991d0a48daa89de5659f3182bc8705d2d0bc3d302e3a24cc94cb90bdaf24b09","observation_id":"1bcf55ef-519a-4544-bf6a-8e335b117a12","resolution":{"observed_at":"2026-08-10T23:08:07.261142Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.245526Z","title":"Partitioning of unstructured problems for parallel processing.Computing systems in engineering, 2(2- 3):135–148, 1991","venue":null,"work_id":"8c11a46d-dd5a-4292-84e1-af6114a5a888","year":1991},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.946924Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:e6a27741431a55e2ff30aa63338fc33182dafce0860d7593a607999b923859ac","observation_id":"e85976d5-169e-45a9-bb74-76b8bafadf59","resolution":{"observed_at":"2026-08-10T23:08:07.249467Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.235196Z","title":"The asymptotic distribution of a single eigenvalue gap of a Wigner matrix.Probab","venue":null,"work_id":"a8ab09ed-0221-4ee8-9c1c-1de2bb207d1e","year":2013},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.950695Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:b61af514217aa36c2717ac2800f93170ec6c847205b963bbddf5d33c59bcf2bb","observation_id":"880138bf-e278-428b-b72f-c862a04ab679","resolution":{"observed_at":"2026-08-10T23:08:07.238640Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.224694Z","title":"Random matrices: universality of local eigenvalue statistics.Acta Math., 206(1):127–204, 2011","venue":null,"work_id":"08a5a116-747a-42be-a4b5-3a855b5df244","year":2011},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.955598Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:ec9218df19753b2bb3811a3013083c310d6dabcdf1b9ca7fb8cce9c24e96ac00","observation_id":"888b20df-6174-472e-bb2b-17f57e0aa483","resolution":{"observed_at":"2026-08-10T23:08:07.228571Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.213193Z","title":"Random matrices have simple spectrum.Combinatorica, 37(3):539–553, 2017","venue":null,"work_id":"116094fc-e636-4f99-add0-2f2886f6a145","year":2017},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.959407Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:f130fe1427085f61cdfedaccb3fb70b861485ce131f1f5a6c72918d134adf7ff","observation_id":"ade163dc-06f8-477f-b601-7fb707cfc4ad","resolution":{"observed_at":"2026-08-10T23:08:07.217467Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.200331Z","title":"Uhlenbeck","venue":null,"work_id":"cfbdff56-33e3-4122-a4aa-fc839152d117","year":1976},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.962947Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:c99ff77c9134c6975aa1260a0cb9ce1d7e324fc5cadd8bb5be635bb492307b2c","observation_id":"d5ab6051-d458-4add-a1b7-b657f9ead61e","resolution":{"observed_at":"2026-08-10T23:08:07.204291Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.188485Z","title":"Invertibility of symmetric random matrices.Random Structures Algorithms, 44(2):135–182, 2014","venue":null,"work_id":"0cf60299-7063-49d4-8d0b-6e14558023c8","year":2014},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.966770Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:73d6b733137a1b1dd7b96f10c646e2fd94b38b82669eb764a982c4dc4bab4733","observation_id":"7f76b152-620b-43e1-9c7f-92534f924022","resolution":{"observed_at":"2026-08-10T23:08:07.192600Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.175798Z","title":"Vinson.Closest spacing of consecutive eigenvalues","venue":null,"work_id":"5d38662f-9011-4fd3-bbc8-0f1ad7295f34","year":2001},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.970511Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:c8b20d4d81e33dcb4e569dc0b894f22beb4d5f26726312c258102e6f6e8057b6","observation_id":"068b1d77-34de-411e-9aa5-2ed7fc8d0155","resolution":{"observed_at":"2026-08-10T23:08:07.180585Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2203.00199","last_updated":"2022-06-22T21:37:18Z","snapshot_observed_at":"2026-08-13T18:57:36.993027Z","submitted_at":"2022-03-01T03:08:47Z","title":"Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2203.00199","snapshot_observed_at":"2026-08-10T23:08:06.974752Z","title":"Equivariant and stable positional encoding for more powerful graph neural networks.arXiv preprint arXiv:2203.00199, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.974752Z"},"links":{"cited_paper":"/paper/2203.00199","citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:c36f1fcc67817d090c670b6bcf68dd1d2deb668d3ca4350a43c8127a2f014768","observation_id":"4d4c01c5-6bbc-46e1-9ce1-04c07ab0f369","resolution":{"observed_at":"2026-08-10T23:08:06.974752Z","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":"2026-08-10T23:08:07.162504Z","title":"Generic properties of Steklov eigenfunctions.Trans","venue":null,"work_id":"1d3eb964-4c32-44bb-91b9-41b16f14c699","year":2022},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.978888Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:c4f5bcd359920bf486a4156061b7c2d17025ed087a110f7789be8191769f50d6","observation_id":"6edbbec1-ab40-4bc6-9fbe-15ecef40f62e","resolution":{"observed_at":"2026-08-10T23:08:07.166944Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.07563","last_updated":"2024-12-11T01:22:57Z","snapshot_observed_at":"2026-08-15T20:11:13.010021Z","submitted_at":"2023-12-09T20:45:17Z","title":"Persistent Topological Laplacians -- a Survey","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.07563","snapshot_observed_at":"2026-08-10T23:08:06.982622Z","title":"Persistent topological laplacians–a survey.arXiv preprint arXiv:2312.07563, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.982622Z"},"links":{"cited_paper":"/paper/2312.07563","citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:d4cdc43c0a9e766e4ebb743f5b7d3a7468fd83e13b9983876ad1940dde5dcfee","observation_id":"25995317-e5ae-4a88-b8f1-d31fadd5da44","resolution":{"observed_at":"2026-08-10T23:08:06.982622Z","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":"2026-08-10T23:08:07.147838Z","title":null,"venue":null,"work_id":"0acce723-a719-455f-b2e7-2fb798c04898","year":1955},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.986529Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:173a220c91d05fd64e268179488df3617719fe04011aebb010d8ab3eeb79bdae","observation_id":"9c20ba1c-52da-4e32-be8a-27f2e7cf5247","resolution":{"observed_at":"2026-08-10T23:08:07.152469Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.135639Z","title":"Graph neural networks: A review of methods and applications.AI open, 1:57–81, 2020","venue":null,"work_id":"cfd5a81f-c04e-4972-a650-621e17ea1158","year":2020},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.990398Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:13f186888fa3bfd9fc5c8baa3ede683c73d6151c8da7d7c28709a6d872fd4f6b","observation_id":"93c9aff7-93a1-4ac0-af25-e0b2566bccd3","resolution":{"observed_at":"2026-08-10T23:08:07.140154Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.124359Z","title":"On the multiplicity one conjecture in min-max theory.Ann","venue":null,"work_id":"65e7df38-4cc2-49ad-b009-98cef169fd61","year":2020},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.994458Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:1f887f915bdf6046dd6d9fad6a5c8071f0e57da78887b5771c28a2221d2e9909","observation_id":"5b0f4f13-afe0-402c-8c41-b7aed3adb0d6","resolution":{"observed_at":"2026-08-10T23:08:07.128300Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T23:08:07.112948Z","title":"Graph convolutional neural networks via scattering.Applied and Computational Har- monic Analysis, 49(3):1046–1074, 2020","venue":null,"work_id":"4c141473-62bd-4194-a831-06aea2ca3565","year":2020},"citing_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-10T23:08:06.999068Z"},"links":{"citing_paper":"/paper/2501.00234"},"observation_digest":"sha256:0cc9254689c3392108577ff0871656e3322b0f648472e871a4a2d26276e5432e","observation_id":"ae78ed36-6996-4389-8064-bb2cd957a1f4","resolution":{"observed_at":"2026-08-10T23:08:07.117024Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","latest_version":2,"primary_category":"math.PR","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs"},"reference_resolution":{"displayed":74,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":13,"verified_exact":2,"verified_fuzzy":59},"total_outbound_references":74},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 74 of 74 outbound references and 4 inbound Pith citation observations for arXiv:2501.00234."}