{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6GZRF2JPPPTVQJO3S4GDOX5NLJ","short_pith_number":"pith:6GZRF2JP","canonical_record":{"source":{"id":"1511.00862","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-03T11:24:57Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"67d71e21b8cdfffe492461ede9f277f2af3a9ca9f699f3e6375fb711b086abd8","abstract_canon_sha256":"d894586bb5a97f24f80ebdea945fe27b763ccee4f9b734cade99ce63d3d26114"},"schema_version":"1.0"},"canonical_sha256":"f1b312e92f7be75825db970c375fad5a59018e73b5c04d6587b862ab4ece8b88","source":{"kind":"arxiv","id":"1511.00862","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00862","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00862v3","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00862","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"6GZRF2JPPPTV","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6GZRF2JPPPTVQJO3","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6GZRF2JP","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6GZRF2JPPPTVQJO3S4GDOX5NLJ","target":"record","payload":{"canonical_record":{"source":{"id":"1511.00862","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-03T11:24:57Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"67d71e21b8cdfffe492461ede9f277f2af3a9ca9f699f3e6375fb711b086abd8","abstract_canon_sha256":"d894586bb5a97f24f80ebdea945fe27b763ccee4f9b734cade99ce63d3d26114"},"schema_version":"1.0"},"canonical_sha256":"f1b312e92f7be75825db970c375fad5a59018e73b5c04d6587b862ab4ece8b88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:12.405079Z","signature_b64":"ws1xOG9B/HINDxl2fg/pG9uTaRtJjF+ZVnwuTjI6aWwfOSwYoFyG3T2UFAElHPymiS9219OVDKkXPGr4A+/KBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1b312e92f7be75825db970c375fad5a59018e73b5c04d6587b862ab4ece8b88","last_reissued_at":"2026-05-18T00:56:12.404474Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:12.404474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.00862","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b6IIIt15SdyO8k9+EHw6cYgeyNvXNB65D8n2hAG3d21zxXStU8Qpz1I6frxLCyJDUHgN+lIQ1/gWH1HoxmoyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:49:55.167252Z"},"content_sha256":"40f2b1ebe2afb180f83ac0976c6fb6d77cf19623256a95e50a7d25fd9cbbe3e0","schema_version":"1.0","event_id":"sha256:40f2b1ebe2afb180f83ac0976c6fb6d77cf19623256a95e50a7d25fd9cbbe3e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6GZRF2JPPPTVQJO3S4GDOX5NLJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local semicircle law under moment conditions. Part II: Localization and delocalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.PR","authors_text":"Alexander Tikhomirov, Alexey Naumov, Friedrich G\\\"otze","submitted_at":"2015-11-03T11:24:57Z","abstract_excerpt":"We consider a random symmetric matrix ${\\bf X} = [X_{jk}]_{j,k=1}^n$ with upper triangular entries being independent identically distributed random variables with mean zero and unit variance. We additionally suppose that $\\mathbb E |X_{11}|^{4 + \\delta} =: \\mu_{4+\\delta} < C$ for some $\\delta > 0$ and some absolute constant $C$. Under these conditions we show that the typical Kolmogorov distance between the empirical spectral distribution function of eigenvalues of $n^{-1/2} {\\bf X}$ and Wigner's semicircle law is of order $1/n$ up to some logarithmic correction factor. As a direct consequence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00862","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N6r2DSmQKhR4MVxbpadq4TaheVTXB+V4KZlaSkjNPG8DFyYEGrsgQXLWEwZSNR3JuPjlvaY9+xnEJLNyP84yCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:49:55.167906Z"},"content_sha256":"db32bcf9c3960b19c504904dfd951edea01e84a19c6e25cc09157b5877befea7","schema_version":"1.0","event_id":"sha256:db32bcf9c3960b19c504904dfd951edea01e84a19c6e25cc09157b5877befea7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6GZRF2JPPPTVQJO3S4GDOX5NLJ/bundle.json","state_url":"https://pith.science/pith/6GZRF2JPPPTVQJO3S4GDOX5NLJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6GZRF2JPPPTVQJO3S4GDOX5NLJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T21:49:55Z","links":{"resolver":"https://pith.science/pith/6GZRF2JPPPTVQJO3S4GDOX5NLJ","bundle":"https://pith.science/pith/6GZRF2JPPPTVQJO3S4GDOX5NLJ/bundle.json","state":"https://pith.science/pith/6GZRF2JPPPTVQJO3S4GDOX5NLJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6GZRF2JPPPTVQJO3S4GDOX5NLJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6GZRF2JPPPTVQJO3S4GDOX5NLJ","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":"d894586bb5a97f24f80ebdea945fe27b763ccee4f9b734cade99ce63d3d26114","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-03T11:24:57Z","title_canon_sha256":"67d71e21b8cdfffe492461ede9f277f2af3a9ca9f699f3e6375fb711b086abd8"},"schema_version":"1.0","source":{"id":"1511.00862","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00862","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00862v3","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00862","created_at":"2026-05-18T00:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"6GZRF2JPPPTV","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6GZRF2JPPPTVQJO3","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6GZRF2JP","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:db32bcf9c3960b19c504904dfd951edea01e84a19c6e25cc09157b5877befea7","target":"graph","created_at":"2026-05-18T00:56:12Z","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"},"paper":{"abstract_excerpt":"We consider a random symmetric matrix ${\\bf X} = [X_{jk}]_{j,k=1}^n$ with upper triangular entries being independent identically distributed random variables with mean zero and unit variance. We additionally suppose that $\\mathbb E |X_{11}|^{4 + \\delta} =: \\mu_{4+\\delta} < C$ for some $\\delta > 0$ and some absolute constant $C$. Under these conditions we show that the typical Kolmogorov distance between the empirical spectral distribution function of eigenvalues of $n^{-1/2} {\\bf X}$ and Wigner's semicircle law is of order $1/n$ up to some logarithmic correction factor. As a direct consequence","authors_text":"Alexander Tikhomirov, Alexey Naumov, Friedrich G\\\"otze","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-03T11:24:57Z","title":"Local semicircle law under moment conditions. Part II: Localization and delocalization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00862","kind":"arxiv","version":3},"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":"sha256:40f2b1ebe2afb180f83ac0976c6fb6d77cf19623256a95e50a7d25fd9cbbe3e0","target":"record","created_at":"2026-05-18T00:56:12Z","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":"d894586bb5a97f24f80ebdea945fe27b763ccee4f9b734cade99ce63d3d26114","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-03T11:24:57Z","title_canon_sha256":"67d71e21b8cdfffe492461ede9f277f2af3a9ca9f699f3e6375fb711b086abd8"},"schema_version":"1.0","source":{"id":"1511.00862","kind":"arxiv","version":3}},"canonical_sha256":"f1b312e92f7be75825db970c375fad5a59018e73b5c04d6587b862ab4ece8b88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1b312e92f7be75825db970c375fad5a59018e73b5c04d6587b862ab4ece8b88","first_computed_at":"2026-05-18T00:56:12.404474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:12.404474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ws1xOG9B/HINDxl2fg/pG9uTaRtJjF+ZVnwuTjI6aWwfOSwYoFyG3T2UFAElHPymiS9219OVDKkXPGr4A+/KBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:12.405079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.00862","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40f2b1ebe2afb180f83ac0976c6fb6d77cf19623256a95e50a7d25fd9cbbe3e0","sha256:db32bcf9c3960b19c504904dfd951edea01e84a19c6e25cc09157b5877befea7"],"state_sha256":"1e6568a3d514eb6a520b765a9ca1c73e3192990334974b15eff74146c0961868"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mnjGGrKyy6AWLoil4MEAYwJjyqVw0c0su2W9+Wy7Ykvxul1rQ5eqRCadFAYi8e34Il4I95UsB/emrR6T6pZ4Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:49:55.171117Z","bundle_sha256":"3d2e6ed06eb90eeb0311efa40f74dcf7e613e65033581515e308cb2472d1b843"}}