{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4HLE7QERFPPPQQ4KUN7OTRBSJ2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"67d319ea2e351e3bce8a21c19943a7928d31b07efba780691036a7b244a6756a","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2024-01-22T13:12:46Z","title_canon_sha256":"4671de66de6115368b5d3d4445908edb975a8b69b97c8980aef1f5c4b6ceda99"},"schema_version":"1.0","source":{"id":"2401.11925","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.11925","created_at":"2026-07-05T07:36:12Z"},{"alias_kind":"arxiv_version","alias_value":"2401.11925v1","created_at":"2026-07-05T07:36:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.11925","created_at":"2026-07-05T07:36:12Z"},{"alias_kind":"pith_short_12","alias_value":"4HLE7QERFPPP","created_at":"2026-07-05T07:36:12Z"},{"alias_kind":"pith_short_16","alias_value":"4HLE7QERFPPPQQ4K","created_at":"2026-07-05T07:36:12Z"},{"alias_kind":"pith_short_8","alias_value":"4HLE7QER","created_at":"2026-07-05T07:36:12Z"}],"graph_snapshots":[{"event_id":"sha256:c148815d3fc3c4c0bc3e0cf26ef9fee9cfcc323237427c87ddfa1d92e0cb16ea","target":"graph","created_at":"2026-07-05T07:36:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2401.11925/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\Xi$ be the adjacency matrix of an Erd\\H{o}s-R\\'enyi graph on $n$ vertices and with parameter $p$ and consider $A$ a $n\\times n$ centered random symmetric matrix with bounded i.i.d. entries above the diagonal. When the mean degree $np$ diverges, the empirical spectral measure of the normalized Hadamard product $(A \\circ \\Xi)/\\sqrt{np}$ converges weakly in probability to the semicircle law. In the regime where $p\\ll 1$ and $ np \\gg \\log n$, we prove a large deviations principle for the empirical spectral measure with speed $n^2p$ and with a good rate function solution of a certain variatio","authors_text":"Fanny Augeri","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2024-01-22T13:12:46Z","title":"Large deviations of the empirical spectral measure of supercritical sparse Wigner matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.11925","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bdd8fa16b4ff334f4ff82a44c3305670368724b4ce53cfbe3c9fefd3e794d343","target":"record","created_at":"2026-07-05T07:36:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"67d319ea2e351e3bce8a21c19943a7928d31b07efba780691036a7b244a6756a","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2024-01-22T13:12:46Z","title_canon_sha256":"4671de66de6115368b5d3d4445908edb975a8b69b97c8980aef1f5c4b6ceda99"},"schema_version":"1.0","source":{"id":"2401.11925","kind":"arxiv","version":1}},"canonical_sha256":"e1d64fc0912bdef8438aa37ee9c4324eb57299fd5316e39bfbd1873d42c3d22d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1d64fc0912bdef8438aa37ee9c4324eb57299fd5316e39bfbd1873d42c3d22d","first_computed_at":"2026-07-05T07:36:12.345833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:36:12.345833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cDdfgH+crkVCYAXf5vh7Am0+edV56/cYsbTksw0CbU6FSUcWlp98RBFJ76pjQ4B+oUxv/1Uq4F9DQEw5rtwYAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:36:12.346329Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.11925","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdd8fa16b4ff334f4ff82a44c3305670368724b4ce53cfbe3c9fefd3e794d343","sha256:c148815d3fc3c4c0bc3e0cf26ef9fee9cfcc323237427c87ddfa1d92e0cb16ea"],"state_sha256":"372d4f2bace0dec5f6e08deefb88f10ff8877de910304ebf389d240eb2fda363"}