{"as_of":"2026-08-12T11:51:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:18895c40f14d209d20d3e44c1894935baddc19738dc1fd67719e8bbda7f16c21","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":12,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":12,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":12,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T23:27:09.220028Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":1,"source":"pith","source_observed_at":"2026-08-05T02:28:24.338817Z","state":"measured"}],"external_citation_measurements":[{"count":0,"observed_at":"2026-08-05T02:28:24.338817Z","source":"pith"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.20263","last_updated":"2025-02-02T22:46:43Z","snapshot_observed_at":"2026-08-10T23:22:04.877158Z","submitted_at":"2024-12-28T20:34:12Z","title":"Ramanujan Property and Edge Universality of Random Regular Graphs","version":2},"cited_work":{"arxiv_id":"2412.20263","doi":"10.48550/arxiv.2412.20263","metadata_source":"pith","pith_arxiv_id":"2412.20263","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Huang, T","venue":"math.PR","work_id":"fb236f28-c6ad-4e95-a426-c20e663c56e7","year":2024},"citing_paper":{"arxiv_id":"2308.13913","last_updated":"2026-04-07T09:41:03Z","snapshot_observed_at":"2026-08-07T04:41:44.742699Z","submitted_at":"2023-08-26T16:30:32Z","title":"Spectral Theory of Isogeny Graphs","version":5},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-24T07:57:32.973033Z"},"links":{"cited_paper":"/paper/2412.20263","citing_paper":"/paper/2308.13913"},"observation_digest":"sha256:32e6cfc156aabb7a52ffb1d665d71d86faf162f962ab4d1d72ca14825eda71ec","observation_id":"da09681f-cf55-44a1-abd3-617681e8b52d","resolution":{"observed_at":"2026-05-24T07:59:09.362977Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.20263","last_updated":"2025-02-02T22:46:43Z","snapshot_observed_at":"2026-08-10T23:22:04.877158Z","submitted_at":"2024-12-28T20:34:12Z","title":"Ramanujan Property and Edge Universality of Random Regular Graphs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.20263","snapshot_observed_at":"2026-08-07T23:27:09.220028Z","title":"Huang, T","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.08897","last_updated":"2025-02-13T02:22:53Z","snapshot_observed_at":"2026-08-09T08:39:08.280031Z","submitted_at":"2025-02-13T02:22:53Z","title":"Gaussian Waves and Edge Eigenvectors of Random Regular Graphs","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T23:27:09.220028Z"},"links":{"cited_paper":"/paper/2412.20263","citing_paper":"/paper/2502.08897"},"observation_digest":"sha256:95a2a79d6c4c5234d75132a39a136407ed6253a8ec2f65a80e2a2648bcb046e3","observation_id":"42b1451b-1e4d-4133-935a-65c5690bd751","resolution":{"observed_at":"2026-08-07T23:27:09.220028Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.20263","last_updated":"2025-02-02T22:46:43Z","snapshot_observed_at":"2026-08-10T23:22:04.877158Z","submitted_at":"2024-12-28T20:34:12Z","title":"Ramanujan Property and Edge Universality of Random Regular Graphs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.20263","snapshot_observed_at":"2026-08-04T00:16:27.037281Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2511.02517","last_updated":"2026-06-09T14:16:14Z","snapshot_observed_at":"2026-08-09T11:41:46.425680Z","submitted_at":"2025-11-04T12:08:28Z","title":"Nearly optimal spectral gaps for random Belyi surfaces","version":3},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-04T00:16:27.037281Z"},"links":{"cited_paper":"/paper/2412.20263","citing_paper":"/paper/2511.02517"},"observation_digest":"sha256:2cc1a46ab11b6a544eaf8e1eb72f56b9f9deb42e9fb9920811ce37000feae286","observation_id":"6cfa593c-eccc-4afc-bf22-defef82f48e9","resolution":{"observed_at":"2026-08-04T00:16:27.037281Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.20263","last_updated":"2025-02-02T22:46:43Z","snapshot_observed_at":"2026-08-10T23:22:04.877158Z","submitted_at":"2024-12-28T20:34:12Z","title":"Ramanujan Property and Edge Universality of Random Regular Graphs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.20263","snapshot_observed_at":"2026-07-13T14:10:32.422124Z","title":"Huang, T","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2604.01874","last_updated":"2026-07-02T17:00:07Z","snapshot_observed_at":"2026-08-12T08:12:39.337681Z","submitted_at":"2026-04-02T10:30:00Z","title":"Transversal non-Clifford gates on almost-good quantum LDPC and quantum locally testable codes","version":2},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-07-13T14:10:32.422124Z"},"links":{"cited_paper":"/paper/2412.20263","citing_paper":"/paper/2604.01874"},"observation_digest":"sha256:3a179cef80b5e83438a4dd3bcde09f3d22292234cfb4b2d98304d78d5d799b8c","observation_id":"3d21de8a-a2e3-4cb6-9eb8-897a8520abb6","resolution":{"observed_at":"2026-07-13T14:10:32.422124Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.20263","last_updated":"2025-02-02T22:46:43Z","snapshot_observed_at":"2026-08-10T23:22:04.877158Z","submitted_at":"2024-12-28T20:34:12Z","title":"Ramanujan Property and Edge Universality of Random Regular Graphs","version":2},"cited_work":{"arxiv_id":"2412.20263","doi":"10.48550/arxiv.2412.20263","metadata_source":"pith","pith_arxiv_id":"2412.20263","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Huang, T","venue":"math.PR","work_id":"fb236f28-c6ad-4e95-a426-c20e663c56e7","year":2024},"citing_paper":{"arxiv_id":"2604.17907","last_updated":"2026-04-20T07:34:13Z","snapshot_observed_at":"2026-08-02T15:07:54.066954Z","submitted_at":"2026-04-20T07:34:13Z","title":"On Spielman's Laplacian Eigenratio Conjecture and Related Problems","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-10T04:43:23.320977Z"},"links":{"cited_paper":"/paper/2412.20263","citing_paper":"/paper/2604.17907"},"observation_digest":"sha256:cc249265e2468682dbe420cd585d77f040147d8e2dadb8f80141401cf29979e3","observation_id":"fdc201ae-884c-4bfd-b7f4-20e560c10778","resolution":{"observed_at":"2026-05-10T11:50:21.393016Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.20263","last_updated":"2025-02-02T22:46:43Z","snapshot_observed_at":"2026-08-10T23:22:04.877158Z","submitted_at":"2024-12-28T20:34:12Z","title":"Ramanujan Property and Edge Universality of Random Regular Graphs","version":2},"cited_work":{"arxiv_id":"2412.20263","doi":"10.48550/arxiv.2412.20263","metadata_source":"pith","pith_arxiv_id":"2412.20263","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Huang, T","venue":"math.PR","work_id":"fb236f28-c6ad-4e95-a426-c20e663c56e7","year":2024},"citing_paper":{"arxiv_id":"2604.20215","last_updated":"2026-04-22T06:05:08Z","snapshot_observed_at":"2026-07-06T23:06:44.624357Z","submitted_at":"2026-04-22T06:05:08Z","title":"Edge Universality for Inhomogeneous Random Matrices II: Markov Chain Comparison and Critical Statistics","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-05-09T22:50:46.753464Z"},"links":{"cited_paper":"/paper/2412.20263","citing_paper":"/paper/2604.20215"},"observation_digest":"sha256:835e7867ba026b823b88890ee895de99f70bbf70c94a0bf87df90bafd335d32e","observation_id":"3e185d7e-232f-464f-ae34-0fd412a967e9","resolution":{"observed_at":"2026-05-09T22:54:16.369229Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.20263","last_updated":"2025-02-02T22:46:43Z","snapshot_observed_at":"2026-08-10T23:22:04.877158Z","submitted_at":"2024-12-28T20:34:12Z","title":"Ramanujan Property and Edge Universality of Random Regular Graphs","version":2},"cited_work":{"arxiv_id":"2412.20263","doi":"10.48550/arxiv.2412.20263","metadata_source":"pith","pith_arxiv_id":"2412.20263","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Huang, T","venue":"math.PR","work_id":"fb236f28-c6ad-4e95-a426-c20e663c56e7","year":2024},"citing_paper":{"arxiv_id":"2605.16162","last_updated":"2026-05-15T16:40:57Z","snapshot_observed_at":"2026-07-06T23:27:20.429737Z","submitted_at":"2026-05-15T16:40:57Z","title":"Deconfinement For $\\mathrm{SO}(3)$ Lattice Yang-Mills at Strong Coupling","version":1},"reference_index":201,"source":"arxiv_source","source_observed_at":"2026-05-19T18:53:02.558975Z"},"links":{"cited_paper":"/paper/2412.20263","citing_paper":"/paper/2605.16162"},"observation_digest":"sha256:708c4a025fdd334cef016cd5eed9cfa438a3cb40e8f7d5fa4b2bf6124ea4329f","observation_id":"a4b6cfe0-5c42-47a1-9ac9-adb9faf5b737","resolution":{"observed_at":"2026-05-19T18:53:11.445648Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.20263","last_updated":"2025-02-02T22:46:43Z","snapshot_observed_at":"2026-08-10T23:22:04.877158Z","submitted_at":"2024-12-28T20:34:12Z","title":"Ramanujan Property and Edge Universality of Random Regular Graphs","version":2},"cited_work":{"arxiv_id":"2412.20263","doi":"10.48550/arxiv.2412.20263","metadata_source":"pith","pith_arxiv_id":"2412.20263","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Huang, T","venue":"math.PR","work_id":"fb236f28-c6ad-4e95-a426-c20e663c56e7","year":2024},"citing_paper":{"arxiv_id":"2605.16203","last_updated":"2026-05-27T04:54:43Z","snapshot_observed_at":"2026-08-02T23:22:22.429064Z","submitted_at":"2026-05-15T17:21:17Z","title":"Discrete Mixed Quantization","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-19T16:51:37.564623Z"},"links":{"cited_paper":"/paper/2412.20263","citing_paper":"/paper/2605.16203"},"observation_digest":"sha256:0d541c660d92f6b70ef6eaa2754f09628e2b802db8ff8b76082c0d90a3214e1f","observation_id":"c31e9455-5d39-4d02-833f-985625efe046","resolution":{"observed_at":"2026-05-19T16:52:39.739045Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.20263","last_updated":"2025-02-02T22:46:43Z","snapshot_observed_at":"2026-08-10T23:22:04.877158Z","submitted_at":"2024-12-28T20:34:12Z","title":"Ramanujan Property and Edge Universality of Random Regular Graphs","version":2},"cited_work":{"arxiv_id":"2412.20263","doi":"10.48550/arxiv.2412.20263","metadata_source":"pith","pith_arxiv_id":"2412.20263","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Huang, T","venue":"math.PR","work_id":"fb236f28-c6ad-4e95-a426-c20e663c56e7","year":2024},"citing_paper":{"arxiv_id":"2605.16203","last_updated":"2026-05-27T04:54:43Z","snapshot_observed_at":"2026-08-02T23:22:22.429064Z","submitted_at":"2026-05-15T17:21:17Z","title":"Discrete Mixed Quantization","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-06-30T19:45:00.564979Z"},"links":{"cited_paper":"/paper/2412.20263","citing_paper":"/paper/2605.16203"},"observation_digest":"sha256:12a21b5d4a1b85ae4aa9cd23cf5113731f95808d3fed7ca3b378c02671b866b7","observation_id":"7b6e989c-eae2-4e33-bb26-93fa52c9b8f6","resolution":{"observed_at":"2026-07-01T14:55:47.335380Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.20263","last_updated":"2025-02-02T22:46:43Z","snapshot_observed_at":"2026-08-10T23:22:04.877158Z","submitted_at":"2024-12-28T20:34:12Z","title":"Ramanujan Property and Edge Universality of Random Regular Graphs","version":2},"cited_work":{"arxiv_id":"2412.20263","doi":"10.48550/arxiv.2412.20263","metadata_source":"pith","pith_arxiv_id":"2412.20263","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Huang, T","venue":"math.PR","work_id":"fb236f28-c6ad-4e95-a426-c20e663c56e7","year":2024},"citing_paper":{"arxiv_id":"2607.06331","last_updated":"2026-07-07T14:27:15Z","snapshot_observed_at":"2026-08-08T13:21:35.785089Z","submitted_at":"2026-07-07T14:27:15Z","title":"Bass notes of random hyperbolic surfaces of large genus","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-08T09:35:43.652006Z"},"links":{"cited_paper":"/paper/2412.20263","citing_paper":"/paper/2607.06331"},"observation_digest":"sha256:ed927fb168036fa73c26886c0592c4fceab6eeb3d41343fa8a7cad0b5a9c6bf4","observation_id":"753a32b0-5ca8-4b96-9fd6-41e25299390b","resolution":{"observed_at":"2026-07-08T09:44:49.579953Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.20263","last_updated":"2025-02-02T22:46:43Z","snapshot_observed_at":"2026-08-10T23:22:04.877158Z","submitted_at":"2024-12-28T20:34:12Z","title":"Ramanujan Property and Edge Universality of Random Regular Graphs","version":2},"cited_work":{"arxiv_id":"2412.20263","doi":"10.48550/arxiv.2412.20263","metadata_source":"pith","pith_arxiv_id":"2412.20263","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Huang, T","venue":"math.PR","work_id":"fb236f28-c6ad-4e95-a426-c20e663c56e7","year":2024},"citing_paper":{"arxiv_id":"2607.07617","last_updated":"2026-07-08T16:33:33Z","snapshot_observed_at":"2026-08-06T06:55:16.956497Z","submitted_at":"2026-07-08T16:33:33Z","title":"Loop Equations Characterize Random Matrix Statistics","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-07-09T05:16:59.118907Z"},"links":{"cited_paper":"/paper/2412.20263","citing_paper":"/paper/2607.07617"},"observation_digest":"sha256:c445cede307e6aa145c6da7945043d4c926d8c4a6c2e47026851a35a25150d95","observation_id":"8cdcd056-3814-4872-a139-f0361c0da63f","resolution":{"observed_at":"2026-07-09T05:26:02.081206Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.20263","last_updated":"2025-02-02T22:46:43Z","snapshot_observed_at":"2026-08-10T23:22:04.877158Z","submitted_at":"2024-12-28T20:34:12Z","title":"Ramanujan Property and Edge Universality of Random Regular Graphs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.20263","snapshot_observed_at":"2026-08-02T00:05:50.847411Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.15213","last_updated":"2026-07-16T17:17:12Z","snapshot_observed_at":"2026-08-12T11:38:50.593825Z","submitted_at":"2026-07-16T17:17:12Z","title":"Asymptotic Brill-Noether Existence at the Half-Canonical Degree: Energy Pairing, Cheeger Inequality and Covering Radii","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-02T00:05:50.847411Z"},"links":{"cited_paper":"/paper/2412.20263","citing_paper":"/paper/2607.15213"},"observation_digest":"sha256:eb0b20610c1b7b691b0b653ab05dc7d3215e074b5adb7b11d2286c2c766e034f","observation_id":"049258c3-a601-4291-84d1-0ef94f0ae2f7","resolution":{"observed_at":"2026-08-02T00:05:50.847411Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2412.20263/citation-record","integrity":"/paper/2412.20263/integrity","json":"/paper/2412.20263/citation-record.json","paper":"/paper/2412.20263"},"outbound":[],"paper":{"arxiv_id":"2412.20263","last_updated":"2025-02-02T22:46:43Z","latest_version":2,"primary_category":"math.PR","snapshot_observed_at":"2026-08-10T23:22:04.877158Z","submitted_at":"2024-12-28T20:34:12Z","title":"Ramanujan Property and Edge Universality of Random Regular Graphs"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 12 inbound Pith citation observations for arXiv:2412.20263."}