{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:DGCDFK767KOJPK5LXPQAFOOMDD","short_pith_number":"pith:DGCDFK76","schema_version":"1.0","canonical_sha256":"198432abfefa9c97ababbbe002b9cc18cbb4780b293527bf870b49a34b60aee8","source":{"kind":"arxiv","id":"1802.10071","version":2},"attestation_state":"computed","paper":{"title":"Asymptotic representation theory and the spectrum of a random geometric graph on a compact Lie group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pierre-Lo\\\"ic M\\'eliot","submitted_at":"2018-02-27T18:52:37Z","abstract_excerpt":"Let $G$ be a compact Lie group, $N\\geq 1$ and $L>0$. The random geometric graph on $G$ is the random graph $\\Gamma(N,L)$ whose vertices are $N$ random points $g_1,\\ldots,g_N$ chosen under the Haar measure of $G$, and whose edges are the pairs $\\{g_i,g_j\\}$ with $d(g_i,g_j)\\leq L$, $d$ being the distance associated to the standard Riemannian structure on $G$. In this paper, we describe the asymptotic behavior of the spectrum of the adjacency matrix of $\\Gamma(N,L)$, when $N$ goes to infinity. If $L$ is fixed and $N \\to + \\infty$ (Gaussian regime), then the largest eigenvalues of $\\Gamma(N,L)$ c"},"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":"1802.10071","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-27T18:52:37Z","cross_cats_sorted":[],"title_canon_sha256":"797b7d0f5731d9fc18cbc00cd6897b808905cc21513f92afe512a175ee8d836b","abstract_canon_sha256":"3596400afa49c83f291c87056ce09c59e3330ab5bac9795b5acbee3acda03112"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:01.915926Z","signature_b64":"gAhAREK6/dmxi0YU/GDtpQXKSr0OQcyr+ruzs3JmWepCz1ir9F1icFSGIoo1atpUwQAb4TstGwymHZ7CY4jTAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"198432abfefa9c97ababbbe002b9cc18cbb4780b293527bf870b49a34b60aee8","last_reissued_at":"2026-05-17T23:59:01.915466Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:01.915466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic representation theory and the spectrum of a random geometric graph on a compact Lie group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pierre-Lo\\\"ic M\\'eliot","submitted_at":"2018-02-27T18:52:37Z","abstract_excerpt":"Let $G$ be a compact Lie group, $N\\geq 1$ and $L>0$. The random geometric graph on $G$ is the random graph $\\Gamma(N,L)$ whose vertices are $N$ random points $g_1,\\ldots,g_N$ chosen under the Haar measure of $G$, and whose edges are the pairs $\\{g_i,g_j\\}$ with $d(g_i,g_j)\\leq L$, $d$ being the distance associated to the standard Riemannian structure on $G$. In this paper, we describe the asymptotic behavior of the spectrum of the adjacency matrix of $\\Gamma(N,L)$, when $N$ goes to infinity. If $L$ is fixed and $N \\to + \\infty$ (Gaussian regime), then the largest eigenvalues of $\\Gamma(N,L)$ c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10071","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":""},"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":"1802.10071","created_at":"2026-05-17T23:59:01.915535+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.10071v2","created_at":"2026-05-17T23:59:01.915535+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.10071","created_at":"2026-05-17T23:59:01.915535+00:00"},{"alias_kind":"pith_short_12","alias_value":"DGCDFK767KOJ","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DGCDFK767KOJPK5L","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DGCDFK76","created_at":"2026-05-18T12:32:19.392346+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DGCDFK767KOJPK5LXPQAFOOMDD","json":"https://pith.science/pith/DGCDFK767KOJPK5LXPQAFOOMDD.json","graph_json":"https://pith.science/api/pith-number/DGCDFK767KOJPK5LXPQAFOOMDD/graph.json","events_json":"https://pith.science/api/pith-number/DGCDFK767KOJPK5LXPQAFOOMDD/events.json","paper":"https://pith.science/paper/DGCDFK76"},"agent_actions":{"view_html":"https://pith.science/pith/DGCDFK767KOJPK5LXPQAFOOMDD","download_json":"https://pith.science/pith/DGCDFK767KOJPK5LXPQAFOOMDD.json","view_paper":"https://pith.science/paper/DGCDFK76","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.10071&json=true","fetch_graph":"https://pith.science/api/pith-number/DGCDFK767KOJPK5LXPQAFOOMDD/graph.json","fetch_events":"https://pith.science/api/pith-number/DGCDFK767KOJPK5LXPQAFOOMDD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DGCDFK767KOJPK5LXPQAFOOMDD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DGCDFK767KOJPK5LXPQAFOOMDD/action/storage_attestation","attest_author":"https://pith.science/pith/DGCDFK767KOJPK5LXPQAFOOMDD/action/author_attestation","sign_citation":"https://pith.science/pith/DGCDFK767KOJPK5LXPQAFOOMDD/action/citation_signature","submit_replication":"https://pith.science/pith/DGCDFK767KOJPK5LXPQAFOOMDD/action/replication_record"}},"created_at":"2026-05-17T23:59:01.915535+00:00","updated_at":"2026-05-17T23:59:01.915535+00:00"}