{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GDXHM2THKH4OSZZWU4JGXBE2DY","short_pith_number":"pith:GDXHM2TH","canonical_record":{"source":{"id":"1609.09022","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-28T18:04:02Z","cross_cats_sorted":[],"title_canon_sha256":"ebf2ad28ffcfae731e713d33c0d575f007accbb32c65a983532d660f75dd4404","abstract_canon_sha256":"9ef5ca78cc0bbf4c1b7700d1bab725f31953194b437f8b55e7be83314e67aa02"},"schema_version":"1.0"},"canonical_sha256":"30ee766a6751f8e96736a7126b849a1e04c5936a5866114545ddae1ede2c0daa","source":{"kind":"arxiv","id":"1609.09022","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09022","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09022v3","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09022","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"GDXHM2THKH4O","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GDXHM2THKH4OSZZW","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GDXHM2TH","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GDXHM2THKH4OSZZWU4JGXBE2DY","target":"record","payload":{"canonical_record":{"source":{"id":"1609.09022","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-28T18:04:02Z","cross_cats_sorted":[],"title_canon_sha256":"ebf2ad28ffcfae731e713d33c0d575f007accbb32c65a983532d660f75dd4404","abstract_canon_sha256":"9ef5ca78cc0bbf4c1b7700d1bab725f31953194b437f8b55e7be83314e67aa02"},"schema_version":"1.0"},"canonical_sha256":"30ee766a6751f8e96736a7126b849a1e04c5936a5866114545ddae1ede2c0daa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:18.214678Z","signature_b64":"FrkCRng6u9btamuGbochxTvTKRnF+U7kCx6QT03yHq8KuUnJ2tbhGgbfBM9x6l0NJahYaHaQ7q3Z87EszDi0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30ee766a6751f8e96736a7126b849a1e04c5936a5866114545ddae1ede2c0daa","last_reissued_at":"2026-05-18T00:41:18.214026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:18.214026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.09022","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":"2026-05-18T00:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O2HxMc6skBZeOHODv2u8XZe9+r7XiVnXk56PYe/B4WqC10qy9ldRStQ0z81uuqh7pi4r+s0wY/Y368pzosC9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:20:01.716883Z"},"content_sha256":"1e6561ad0bb7396391a28c95e5625818453de25d18a7df12052c8aba54695664","schema_version":"1.0","event_id":"sha256:1e6561ad0bb7396391a28c95e5625818453de25d18a7df12052c8aba54695664"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GDXHM2THKH4OSZZWU4JGXBE2DY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvector Statistics of Sparse Random Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Horng-Tzer Yau, Jiaoyang Huang, Paul Bourgade","submitted_at":"2016-09-28T18:04:02Z","abstract_excerpt":"We prove that the bulk eigenvectors of sparse random matrices, i.e. the adjacency matrices of Erd\\H{o}s-R\\'enyi graphs or random regular graphs, are asymptotically jointly normal, provided the averaged degree increases with the size of the graphs. Our methodology follows [6] by analyzing the eigenvector flow under Dyson Brownian motion, combining with an isotropic local law for Green's function. As an auxiliary result, we prove that for the eigenvector flow of Dyson Brownian motion with general initial data, the eigenvectors are asymptotically jointly normal in the direction $q$ after time $\\e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09022","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":"2026-05-18T00:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QNovX8OE3rFPNRdAnG26xPVWv8mtmGtcf3bPAuB7U2Yk1DSkdQ9tgFlcHtP9L9HnmjKfDW2V5/QreRjR/sNeCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:20:01.717227Z"},"content_sha256":"3451c38e2962fe264db4445371bc83914bbb25524e4f9b1352822eef31402403","schema_version":"1.0","event_id":"sha256:3451c38e2962fe264db4445371bc83914bbb25524e4f9b1352822eef31402403"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GDXHM2THKH4OSZZWU4JGXBE2DY/bundle.json","state_url":"https://pith.science/pith/GDXHM2THKH4OSZZWU4JGXBE2DY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GDXHM2THKH4OSZZWU4JGXBE2DY/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":"2026-06-02T22:20:01Z","links":{"resolver":"https://pith.science/pith/GDXHM2THKH4OSZZWU4JGXBE2DY","bundle":"https://pith.science/pith/GDXHM2THKH4OSZZWU4JGXBE2DY/bundle.json","state":"https://pith.science/pith/GDXHM2THKH4OSZZWU4JGXBE2DY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GDXHM2THKH4OSZZWU4JGXBE2DY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GDXHM2THKH4OSZZWU4JGXBE2DY","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":"9ef5ca78cc0bbf4c1b7700d1bab725f31953194b437f8b55e7be83314e67aa02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-28T18:04:02Z","title_canon_sha256":"ebf2ad28ffcfae731e713d33c0d575f007accbb32c65a983532d660f75dd4404"},"schema_version":"1.0","source":{"id":"1609.09022","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09022","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09022v3","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09022","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"GDXHM2THKH4O","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GDXHM2THKH4OSZZW","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GDXHM2TH","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:3451c38e2962fe264db4445371bc83914bbb25524e4f9b1352822eef31402403","target":"graph","created_at":"2026-05-18T00:41:18Z","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 prove that the bulk eigenvectors of sparse random matrices, i.e. the adjacency matrices of Erd\\H{o}s-R\\'enyi graphs or random regular graphs, are asymptotically jointly normal, provided the averaged degree increases with the size of the graphs. Our methodology follows [6] by analyzing the eigenvector flow under Dyson Brownian motion, combining with an isotropic local law for Green's function. As an auxiliary result, we prove that for the eigenvector flow of Dyson Brownian motion with general initial data, the eigenvectors are asymptotically jointly normal in the direction $q$ after time $\\e","authors_text":"Horng-Tzer Yau, Jiaoyang Huang, Paul Bourgade","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-28T18:04:02Z","title":"Eigenvector Statistics of Sparse Random Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09022","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":"sha256:1e6561ad0bb7396391a28c95e5625818453de25d18a7df12052c8aba54695664","target":"record","created_at":"2026-05-18T00:41:18Z","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":"9ef5ca78cc0bbf4c1b7700d1bab725f31953194b437f8b55e7be83314e67aa02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-28T18:04:02Z","title_canon_sha256":"ebf2ad28ffcfae731e713d33c0d575f007accbb32c65a983532d660f75dd4404"},"schema_version":"1.0","source":{"id":"1609.09022","kind":"arxiv","version":3}},"canonical_sha256":"30ee766a6751f8e96736a7126b849a1e04c5936a5866114545ddae1ede2c0daa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30ee766a6751f8e96736a7126b849a1e04c5936a5866114545ddae1ede2c0daa","first_computed_at":"2026-05-18T00:41:18.214026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:18.214026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FrkCRng6u9btamuGbochxTvTKRnF+U7kCx6QT03yHq8KuUnJ2tbhGgbfBM9x6l0NJahYaHaQ7q3Z87EszDi0CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:18.214678Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.09022","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e6561ad0bb7396391a28c95e5625818453de25d18a7df12052c8aba54695664","sha256:3451c38e2962fe264db4445371bc83914bbb25524e4f9b1352822eef31402403"],"state_sha256":"7f6df4d2ab582e21668b132616e6e6cbcb647289c52547ef435eaa073fe8fe4f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FppJntrefW5Pn9m/DpItDFxrXINyVUAzt/7TcPeP6hP9hWwNVxyEH8xBUtzi/lPUNtp7K8aoO46ZGDVVjvH1AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:20:01.719187Z","bundle_sha256":"093256f70311c9ba57570b53808f1bb712d7405b2aef58c0e8ac87f2a51597a2"}}