{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:NF7EK7RPYSMGARHMQL7TTV33FB","short_pith_number":"pith:NF7EK7RP","schema_version":"1.0","canonical_sha256":"697e457e2fc4986044ec82ff39d77b287d75def941f8a837de24d59f17bebcd9","source":{"kind":"arxiv","id":"2412.20263","version":2},"attestation_state":"computed","paper":{"title":"Ramanujan Property and Edge Universality of Random Regular Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.SP"],"primary_cat":"math.PR","authors_text":"Horng-Tzer Yau, Jiaoyang Huang, Theo McKenzie","submitted_at":"2024-12-28T20:34:12Z","abstract_excerpt":"We consider the normalized adjacency matrix of a random $d$-regular graph on $N$ vertices with any fixed degree $d\\geq 3$ and denote its eigenvalues as $\\lambda_1=d/\\sqrt{d-1}\\geq \\lambda_2\\geq\\lambda_3\\cdots\\geq \\lambda_N$. We establish the following two results as $N\\rightarrow \\infty$. (i) With high probability, all eigenvalues are optimally rigid, up to an additional $N^{{\\rm o}(1)}$ factor. Specifically, the fluctuations of bulk eigenvalues are bounded by $N^{-1+{\\rm o}(1)}$, and the fluctuations of edge eigenvalues are bounded by $N^{-2/3+{\\rm o}(1)}$. (ii) Edge universality holds for ra"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2412.20263","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-28T20:34:12Z","cross_cats_sorted":["math-ph","math.CO","math.MP","math.SP"],"title_canon_sha256":"29cbbc051915b87240cb78b5f76c3e3c3d0f2fb94f6038d6e107f7280d782f5e","abstract_canon_sha256":"f036df27aabb748ac241e01613284fd55b60f510ed33ffe08bbc3043b26677f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:08:26.898340Z","signature_b64":"SPl6EJzJR/rVi3InwcwHAr0jpiu2WpqeyqsXCRfM7Qf5cjjDp/GHytRpJ5CrKOEEsznsvOpmXLD5yeW75hCaAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"697e457e2fc4986044ec82ff39d77b287d75def941f8a837de24d59f17bebcd9","last_reissued_at":"2026-07-05T10:08:26.897831Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:08:26.897831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ramanujan Property and Edge Universality of Random Regular Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.SP"],"primary_cat":"math.PR","authors_text":"Horng-Tzer Yau, Jiaoyang Huang, Theo McKenzie","submitted_at":"2024-12-28T20:34:12Z","abstract_excerpt":"We consider the normalized adjacency matrix of a random $d$-regular graph on $N$ vertices with any fixed degree $d\\geq 3$ and denote its eigenvalues as $\\lambda_1=d/\\sqrt{d-1}\\geq \\lambda_2\\geq\\lambda_3\\cdots\\geq \\lambda_N$. We establish the following two results as $N\\rightarrow \\infty$. (i) With high probability, all eigenvalues are optimally rigid, up to an additional $N^{{\\rm o}(1)}$ factor. Specifically, the fluctuations of bulk eigenvalues are bounded by $N^{-1+{\\rm o}(1)}$, and the fluctuations of edge eigenvalues are bounded by $N^{-2/3+{\\rm o}(1)}$. (ii) Edge universality holds for ra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20263","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.20263/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2412.20263","created_at":"2026-07-05T10:08:26.897890+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.20263v2","created_at":"2026-07-05T10:08:26.897890+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.20263","created_at":"2026-07-05T10:08:26.897890+00:00"},{"alias_kind":"pith_short_12","alias_value":"NF7EK7RPYSMG","created_at":"2026-07-05T10:08:26.897890+00:00"},{"alias_kind":"pith_short_16","alias_value":"NF7EK7RPYSMGARHM","created_at":"2026-07-05T10:08:26.897890+00:00"},{"alias_kind":"pith_short_8","alias_value":"NF7EK7RP","created_at":"2026-07-05T10:08:26.897890+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":8,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2607.07617","citing_title":"Loop Equations Characterize Random Matrix Statistics","ref_index":52,"is_internal_anchor":true},{"citing_arxiv_id":"2607.06331","citing_title":"Bass notes of random hyperbolic surfaces of large genus","ref_index":27,"is_internal_anchor":true},{"citing_arxiv_id":"2605.16203","citing_title":"Discrete Mixed Quantization","ref_index":38,"is_internal_anchor":false},{"citing_arxiv_id":"2308.13913","citing_title":"Spectral Theory of Isogeny Graphs","ref_index":39,"is_internal_anchor":false},{"citing_arxiv_id":"2605.16162","citing_title":"Deconfinement For $\\mathrm{SO}(3)$ Lattice Yang-Mills at Strong Coupling","ref_index":201,"is_internal_anchor":false},{"citing_arxiv_id":"2605.16203","citing_title":"Discrete Mixed Quantization","ref_index":38,"is_internal_anchor":false},{"citing_arxiv_id":"2604.17907","citing_title":"On Spielman's Laplacian Eigenratio Conjecture and Related Problems","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2604.20215","citing_title":"Edge Universality for Inhomogeneous Random Matrices II: Markov Chain Comparison and Critical Statistics","ref_index":30,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NF7EK7RPYSMGARHMQL7TTV33FB","json":"https://pith.science/pith/NF7EK7RPYSMGARHMQL7TTV33FB.json","graph_json":"https://pith.science/api/pith-number/NF7EK7RPYSMGARHMQL7TTV33FB/graph.json","events_json":"https://pith.science/api/pith-number/NF7EK7RPYSMGARHMQL7TTV33FB/events.json","paper":"https://pith.science/paper/NF7EK7RP"},"agent_actions":{"view_html":"https://pith.science/pith/NF7EK7RPYSMGARHMQL7TTV33FB","download_json":"https://pith.science/pith/NF7EK7RPYSMGARHMQL7TTV33FB.json","view_paper":"https://pith.science/paper/NF7EK7RP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.20263&json=true","fetch_graph":"https://pith.science/api/pith-number/NF7EK7RPYSMGARHMQL7TTV33FB/graph.json","fetch_events":"https://pith.science/api/pith-number/NF7EK7RPYSMGARHMQL7TTV33FB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NF7EK7RPYSMGARHMQL7TTV33FB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NF7EK7RPYSMGARHMQL7TTV33FB/action/storage_attestation","attest_author":"https://pith.science/pith/NF7EK7RPYSMGARHMQL7TTV33FB/action/author_attestation","sign_citation":"https://pith.science/pith/NF7EK7RPYSMGARHMQL7TTV33FB/action/citation_signature","submit_replication":"https://pith.science/pith/NF7EK7RPYSMGARHMQL7TTV33FB/action/replication_record"}},"created_at":"2026-07-05T10:08:26.897890+00:00","updated_at":"2026-07-05T10:08:26.897890+00:00"}