{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VFCHF4OY24CBZYJEQOJPSZOUUZ","short_pith_number":"pith:VFCHF4OY","canonical_record":{"source":{"id":"1310.7435","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-28T14:48:47Z","cross_cats_sorted":[],"title_canon_sha256":"27870e523bb01e7fdacd18134bff5b4b92fdd6f2d1f3c6f5b47ce514804abd32","abstract_canon_sha256":"f5a07a519b3c60f53cba87c92464e42f48ba6a3f007ec7b45f54a84629bf3cbb"},"schema_version":"1.0"},"canonical_sha256":"a94472f1d8d7041ce1248392f965d4a6771a0e6b983c7ece7f3a4ff09cb7925e","source":{"kind":"arxiv","id":"1310.7435","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7435","created_at":"2026-05-18T02:50:50Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7435v3","created_at":"2026-05-18T02:50:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7435","created_at":"2026-05-18T02:50:50Z"},{"alias_kind":"pith_short_12","alias_value":"VFCHF4OY24CB","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VFCHF4OY24CBZYJE","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VFCHF4OY","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VFCHF4OY24CBZYJEQOJPSZOUUZ","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7435","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-28T14:48:47Z","cross_cats_sorted":[],"title_canon_sha256":"27870e523bb01e7fdacd18134bff5b4b92fdd6f2d1f3c6f5b47ce514804abd32","abstract_canon_sha256":"f5a07a519b3c60f53cba87c92464e42f48ba6a3f007ec7b45f54a84629bf3cbb"},"schema_version":"1.0"},"canonical_sha256":"a94472f1d8d7041ce1248392f965d4a6771a0e6b983c7ece7f3a4ff09cb7925e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:50.413779Z","signature_b64":"FbnlgJTgEP8WK2TDvEcA01fCZtDC2+MqhwgmEXp6Fk3pWopx5kznTDTVAN2bCzrqCsOtLMaU4Uol2y/USDFQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a94472f1d8d7041ce1248392f965d4a6771a0e6b983c7ece7f3a4ff09cb7925e","last_reissued_at":"2026-05-18T02:50:50.413307Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:50.413307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7435","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":"2026-05-18T02:50:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vBras5j4ss+ubPouzQIsIipNf73z9sH4d96ZHGtMCN3urQYsHyUsP3qOhiv7E7/DaTq8QIW2j012iI0TcYZdBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T19:39:44.672509Z"},"content_sha256":"25fd53492547cf8353e697d69802480327debb43b78c3d6c89e1ac26efd08e82","schema_version":"1.0","event_id":"sha256:25fd53492547cf8353e697d69802480327debb43b78c3d6c89e1ac26efd08e82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VFCHF4OY24CBZYJEQOJPSZOUUZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Central limit theorem for eigenvectors of heavy tailed matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alice Guionnet, Florent Benaych-Georges (MAP5)","submitted_at":"2013-10-28T14:48:47Z","abstract_excerpt":"We consider the eigenvectors of symmetric matrices with independent heavy tailed entries, such as matrices with entries in the domain of attraction of $\\alpha$-stable laws, or adjacencymatrices of Erdos-Renyi graphs. We denote by $U=[u_{ij}]$ the eigenvectors matrix (corresponding to increasing eigenvalues) and prove that the bivariate process $$B^n_{s,t}:=n^{-1/2}\\sum_{1\\le i\\le ns, 1\\le j\\le nt}(|u_{ij}|^2 -n^{-1}),$$ indexed by $s,t\\in [0,1]$, converges in law to a non trivial Gaussian process. An interesting part of this result is the $n^{-1/2}$ rescaling, proving that from this point of v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7435","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":"2026-05-18T02:50:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYMHDfd3XIcys7ehunC12cM38mo+3dnBXWE34kIRNjKpazDOhg10zFS121LsYKCwml1FRBPT2qUhhbMbNfkBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T19:39:44.673065Z"},"content_sha256":"d0fc546ad1f12312a0e806d4128c90d8a38b12a989b8d272da43df57dc7bcb25","schema_version":"1.0","event_id":"sha256:d0fc546ad1f12312a0e806d4128c90d8a38b12a989b8d272da43df57dc7bcb25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VFCHF4OY24CBZYJEQOJPSZOUUZ/bundle.json","state_url":"https://pith.science/pith/VFCHF4OY24CBZYJEQOJPSZOUUZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VFCHF4OY24CBZYJEQOJPSZOUUZ/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":"2026-06-30T19:39:44Z","links":{"resolver":"https://pith.science/pith/VFCHF4OY24CBZYJEQOJPSZOUUZ","bundle":"https://pith.science/pith/VFCHF4OY24CBZYJEQOJPSZOUUZ/bundle.json","state":"https://pith.science/pith/VFCHF4OY24CBZYJEQOJPSZOUUZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VFCHF4OY24CBZYJEQOJPSZOUUZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VFCHF4OY24CBZYJEQOJPSZOUUZ","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":"f5a07a519b3c60f53cba87c92464e42f48ba6a3f007ec7b45f54a84629bf3cbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-28T14:48:47Z","title_canon_sha256":"27870e523bb01e7fdacd18134bff5b4b92fdd6f2d1f3c6f5b47ce514804abd32"},"schema_version":"1.0","source":{"id":"1310.7435","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7435","created_at":"2026-05-18T02:50:50Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7435v3","created_at":"2026-05-18T02:50:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7435","created_at":"2026-05-18T02:50:50Z"},{"alias_kind":"pith_short_12","alias_value":"VFCHF4OY24CB","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VFCHF4OY24CBZYJE","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VFCHF4OY","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:d0fc546ad1f12312a0e806d4128c90d8a38b12a989b8d272da43df57dc7bcb25","target":"graph","created_at":"2026-05-18T02:50:50Z","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 the eigenvectors of symmetric matrices with independent heavy tailed entries, such as matrices with entries in the domain of attraction of $\\alpha$-stable laws, or adjacencymatrices of Erdos-Renyi graphs. We denote by $U=[u_{ij}]$ the eigenvectors matrix (corresponding to increasing eigenvalues) and prove that the bivariate process $$B^n_{s,t}:=n^{-1/2}\\sum_{1\\le i\\le ns, 1\\le j\\le nt}(|u_{ij}|^2 -n^{-1}),$$ indexed by $s,t\\in [0,1]$, converges in law to a non trivial Gaussian process. An interesting part of this result is the $n^{-1/2}$ rescaling, proving that from this point of v","authors_text":"Alice Guionnet, Florent Benaych-Georges (MAP5)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-28T14:48:47Z","title":"Central limit theorem for eigenvectors of heavy tailed matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7435","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":"sha256:25fd53492547cf8353e697d69802480327debb43b78c3d6c89e1ac26efd08e82","target":"record","created_at":"2026-05-18T02:50:50Z","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":"f5a07a519b3c60f53cba87c92464e42f48ba6a3f007ec7b45f54a84629bf3cbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-28T14:48:47Z","title_canon_sha256":"27870e523bb01e7fdacd18134bff5b4b92fdd6f2d1f3c6f5b47ce514804abd32"},"schema_version":"1.0","source":{"id":"1310.7435","kind":"arxiv","version":3}},"canonical_sha256":"a94472f1d8d7041ce1248392f965d4a6771a0e6b983c7ece7f3a4ff09cb7925e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a94472f1d8d7041ce1248392f965d4a6771a0e6b983c7ece7f3a4ff09cb7925e","first_computed_at":"2026-05-18T02:50:50.413307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:50.413307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FbnlgJTgEP8WK2TDvEcA01fCZtDC2+MqhwgmEXp6Fk3pWopx5kznTDTVAN2bCzrqCsOtLMaU4Uol2y/USDFQCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:50.413779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7435","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25fd53492547cf8353e697d69802480327debb43b78c3d6c89e1ac26efd08e82","sha256:d0fc546ad1f12312a0e806d4128c90d8a38b12a989b8d272da43df57dc7bcb25"],"state_sha256":"0ff6d2f91fb828062e2e5fe4d4703b275cc20a27095be69127dc582d9c5e2ca8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oIaXpVT9g8+LcFk812nOqDwYU2ULsAPqdb0Wb2tKfZ6rKz7yUBGHYQs90ZtENbxmxtRS7wWK6RmdDRW0ctICCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T19:39:44.676219Z","bundle_sha256":"795b4fa0b3c00e4541f1358e2ec68fc7c84d844d1d7499d092c932a61987042a"}}