{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:SW3GXLFASXDLKTJTY3F7DPASXV","short_pith_number":"pith:SW3GXLFA","canonical_record":{"source":{"id":"1007.4652","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-27T09:44:30Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"ff9c05fb95e0645489fec2b9fe290be1fca3d2447b0063c62c37800aa5082e77","abstract_canon_sha256":"0b4d61812e2591fccc1a4bbc63ec617d41669a1680d731c313da0f0bc70fab5d"},"schema_version":"1.0"},"canonical_sha256":"95b66baca095c6b54d33c6cbf1bc12bd448b48209a769cb64cd76ce3d08b41c4","source":{"kind":"arxiv","id":"1007.4652","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4652","created_at":"2026-05-18T04:10:12Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4652v7","created_at":"2026-05-18T04:10:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4652","created_at":"2026-05-18T04:10:12Z"},{"alias_kind":"pith_short_12","alias_value":"SW3GXLFASXDL","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SW3GXLFASXDLKTJT","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SW3GXLFA","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:SW3GXLFASXDLKTJTY3F7DPASXV","target":"record","payload":{"canonical_record":{"source":{"id":"1007.4652","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-27T09:44:30Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"ff9c05fb95e0645489fec2b9fe290be1fca3d2447b0063c62c37800aa5082e77","abstract_canon_sha256":"0b4d61812e2591fccc1a4bbc63ec617d41669a1680d731c313da0f0bc70fab5d"},"schema_version":"1.0"},"canonical_sha256":"95b66baca095c6b54d33c6cbf1bc12bd448b48209a769cb64cd76ce3d08b41c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:12.587408Z","signature_b64":"YMIe4vvNPifZcKaNO8JQY+wnGHUovkqhJ6mxI5qAiY2RRPZB5QXPQb4Hpg12fNNCiyOw1whFm/DnSXgXX2cbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95b66baca095c6b54d33c6cbf1bc12bd448b48209a769cb64cd76ce3d08b41c4","last_reissued_at":"2026-05-18T04:10:12.586616Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:12.586616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.4652","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sRaaCgJMHorOD9RduSP0YDb+TlQc/9AeKWvC+SZOi08u8GLTeSvRDI4jf8H1QS1Do4hu6EEBXCDpSjj2toapBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:54:08.557799Z"},"content_sha256":"44362a9e6b59ae6f3567a648afc8134bc7015eedef08ea67117c44dec1a755a4","schema_version":"1.0","event_id":"sha256:44362a9e6b59ae6f3567a648afc8134bc7015eedef08ea67117c44dec1a755a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:SW3GXLFASXDLKTJTY3F7DPASXV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigidity of Eigenvalues of Generalized Wigner Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Horng-Tzer Yau, Jun Yin, Laszlo Erdos","submitted_at":"2010-07-27T09:44:30Z","abstract_excerpt":"Consider $N\\times N$ hermitian or symmetric random matrices $H$ with independent entries, where the distribution of the $(i,j)$ matrix element is given by the probability measure $\\nu_{ij}$ with zero expectation and with variance $\\sigma_{ij}^2$. We assume that the variances satisfy the normalization condition $\\sum_{i} \\sigma^2_{ij} = 1$ for all $j$ and that there is a positive constant $c$ such that $c\\le N \\sigma_{ij}^2 \\le c^{-1}$. We further assume that the probability distributions $\\nu_{ij}$ have a uniform subexponential decay. We prove that the Stieltjes transform of the empirical eige"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4652","kind":"arxiv","version":7},"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":"2026-05-18T04:10:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g1KoPsd+CvKVLSZnh94cCxhlwcOOYkyGdWPptLekrgA1D0BBoTJyJ3ELBybcrwhAeh15sebQIBT8k44IC92kAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:54:08.558513Z"},"content_sha256":"00985773d754d8b830a0c05a1c307e4df8d763fe25eb5a78593fc24f20f225f3","schema_version":"1.0","event_id":"sha256:00985773d754d8b830a0c05a1c307e4df8d763fe25eb5a78593fc24f20f225f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SW3GXLFASXDLKTJTY3F7DPASXV/bundle.json","state_url":"https://pith.science/pith/SW3GXLFASXDLKTJTY3F7DPASXV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SW3GXLFASXDLKTJTY3F7DPASXV/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":"2026-05-26T09:54:08Z","links":{"resolver":"https://pith.science/pith/SW3GXLFASXDLKTJTY3F7DPASXV","bundle":"https://pith.science/pith/SW3GXLFASXDLKTJTY3F7DPASXV/bundle.json","state":"https://pith.science/pith/SW3GXLFASXDLKTJTY3F7DPASXV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SW3GXLFASXDLKTJTY3F7DPASXV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SW3GXLFASXDLKTJTY3F7DPASXV","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":"0b4d61812e2591fccc1a4bbc63ec617d41669a1680d731c313da0f0bc70fab5d","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-27T09:44:30Z","title_canon_sha256":"ff9c05fb95e0645489fec2b9fe290be1fca3d2447b0063c62c37800aa5082e77"},"schema_version":"1.0","source":{"id":"1007.4652","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4652","created_at":"2026-05-18T04:10:12Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4652v7","created_at":"2026-05-18T04:10:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4652","created_at":"2026-05-18T04:10:12Z"},{"alias_kind":"pith_short_12","alias_value":"SW3GXLFASXDL","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SW3GXLFASXDLKTJT","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SW3GXLFA","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:00985773d754d8b830a0c05a1c307e4df8d763fe25eb5a78593fc24f20f225f3","target":"graph","created_at":"2026-05-18T04:10:12Z","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":"Consider $N\\times N$ hermitian or symmetric random matrices $H$ with independent entries, where the distribution of the $(i,j)$ matrix element is given by the probability measure $\\nu_{ij}$ with zero expectation and with variance $\\sigma_{ij}^2$. We assume that the variances satisfy the normalization condition $\\sum_{i} \\sigma^2_{ij} = 1$ for all $j$ and that there is a positive constant $c$ such that $c\\le N \\sigma_{ij}^2 \\le c^{-1}$. We further assume that the probability distributions $\\nu_{ij}$ have a uniform subexponential decay. We prove that the Stieltjes transform of the empirical eige","authors_text":"Horng-Tzer Yau, Jun Yin, Laszlo Erdos","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-27T09:44:30Z","title":"Rigidity of Eigenvalues of Generalized Wigner Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4652","kind":"arxiv","version":7},"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":"sha256:44362a9e6b59ae6f3567a648afc8134bc7015eedef08ea67117c44dec1a755a4","target":"record","created_at":"2026-05-18T04:10:12Z","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":"0b4d61812e2591fccc1a4bbc63ec617d41669a1680d731c313da0f0bc70fab5d","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-27T09:44:30Z","title_canon_sha256":"ff9c05fb95e0645489fec2b9fe290be1fca3d2447b0063c62c37800aa5082e77"},"schema_version":"1.0","source":{"id":"1007.4652","kind":"arxiv","version":7}},"canonical_sha256":"95b66baca095c6b54d33c6cbf1bc12bd448b48209a769cb64cd76ce3d08b41c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95b66baca095c6b54d33c6cbf1bc12bd448b48209a769cb64cd76ce3d08b41c4","first_computed_at":"2026-05-18T04:10:12.586616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:12.586616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YMIe4vvNPifZcKaNO8JQY+wnGHUovkqhJ6mxI5qAiY2RRPZB5QXPQb4Hpg12fNNCiyOw1whFm/DnSXgXX2cbCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:12.587408Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.4652","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44362a9e6b59ae6f3567a648afc8134bc7015eedef08ea67117c44dec1a755a4","sha256:00985773d754d8b830a0c05a1c307e4df8d763fe25eb5a78593fc24f20f225f3"],"state_sha256":"742001558f1a2d558256e8d45a58e4620443ac0c76dce7a39d7baf8e89ad76e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kvJhtBU8RqLpnHBe+HnVyOxCS/Evhh+WXCHbTnYG4r9PjIEMy4umf43x7gZaFJFqCBTgZSvkt2ySEUc39OgaBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T09:54:08.562606Z","bundle_sha256":"97daa5e747043773d0484ac237e35d28b6d30299ba8fd37df839b2077d496ec4"}}