{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:EV6C2FWONQGCYKPBU2EGMT2P24","short_pith_number":"pith:EV6C2FWO","canonical_record":{"source":{"id":"1010.3394","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-10-17T04:04:29Z","cross_cats_sorted":[],"title_canon_sha256":"57a1c4e6b7d71fd72a7f8e665e68073fbcfd51f898cf31edb24f38934ba6a272","abstract_canon_sha256":"7c33a3791e436b15f76ddfe4ed217ed045d3bbf9649d02bdd4a604be5f44bcbd"},"schema_version":"1.0"},"canonical_sha256":"257c2d16ce6c0c2c29e1a688664f4fd713038cba45718fd9eb42a5db884c03a0","source":{"kind":"arxiv","id":"1010.3394","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3394","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3394v2","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3394","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"pith_short_12","alias_value":"EV6C2FWONQGC","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EV6C2FWONQGCYKPB","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EV6C2FWO","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:EV6C2FWONQGCYKPBU2EGMT2P24","target":"record","payload":{"canonical_record":{"source":{"id":"1010.3394","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-10-17T04:04:29Z","cross_cats_sorted":[],"title_canon_sha256":"57a1c4e6b7d71fd72a7f8e665e68073fbcfd51f898cf31edb24f38934ba6a272","abstract_canon_sha256":"7c33a3791e436b15f76ddfe4ed217ed045d3bbf9649d02bdd4a604be5f44bcbd"},"schema_version":"1.0"},"canonical_sha256":"257c2d16ce6c0c2c29e1a688664f4fd713038cba45718fd9eb42a5db884c03a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:50.037399Z","signature_b64":"wzw9QwUwh+kOTN0roXg90bgNVjglh12qAx/dy0Fbfb3Q/MMg7uH834TxUmMrrRCFFWqgN/fYwkRFQNylHso6Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"257c2d16ce6c0c2c29e1a688664f4fd713038cba45718fd9eb42a5db884c03a0","last_reissued_at":"2026-05-18T04:36:50.036880Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:50.036880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.3394","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:36:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4/38gChZ7vAKS3c/mc0bLEbAqFN6cX7DnDTp0+9IsajR1wPKgYrR6nm/orPpL7Z2TIMcjwZARA4Cs0hJbymuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:42:24.343201Z"},"content_sha256":"d3ea68fbb563a13a4541a646988a5c1b218184ecde65c7a966a85af3ecb60a8f","schema_version":"1.0","event_id":"sha256:d3ea68fbb563a13a4541a646988a5c1b218184ecde65c7a966a85af3ecb60a8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:EV6C2FWONQGCYKPBU2EGMT2P24","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fluctuation of Eigenvalues for Random Toeplitz and Related Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dang-Zheng Liu, Xin Sun, Zheng-Dong Wang","submitted_at":"2010-10-17T04:04:29Z","abstract_excerpt":"Consider random symmetric Toeplitz matrices $T_{n}=(a_{i-j})_{i,j=1}^{n}$ with matrix entries $a_{j}, j=0,1,2,...,$ being independent real random variables such that\n  \\be \\mathbb{E}[a_{j}]=0, \\ \\ \\mathbb{E}[|a_{j}|^{2}]=1 \\ \\ \\textrm{for}\\,\\ \\ j=0,1,2,...,\\ee (homogeneity of 4-th moments) \\be{\\kappa=\\mathbb{E}[|a_{j}|^{4}],}\\ee\n  \\noindent and further (uniform boundedness)\\be\\sup\\limits_{j\\geq 0} \\mathbb{E}[|a_{j}|^{k}]=C_{k}<\\iy\\ \\ \\ \\textrm{for} \\ \\ \\ k\\geq 3.\\ee\n  Under the assumption of $a_{0}\\equiv 0$, we prove a central limit theorem for linear statistics of eigenvalues for a fixed poly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3394","kind":"arxiv","version":2},"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":"2026-05-18T04:36:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SKnB1cyQa1T/+rxvnnjHLXNJl6yz/9idWOAi4KICF0V+XSlJsaT5kcHEVTdDubQySSm+BsFqAYKpYXcL2D0YCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:42:24.343793Z"},"content_sha256":"3db5d421b83bad1e442ddc35b5a14d1a045340e3b9f422b6cf7e7f9c53d2b8b2","schema_version":"1.0","event_id":"sha256:3db5d421b83bad1e442ddc35b5a14d1a045340e3b9f422b6cf7e7f9c53d2b8b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EV6C2FWONQGCYKPBU2EGMT2P24/bundle.json","state_url":"https://pith.science/pith/EV6C2FWONQGCYKPBU2EGMT2P24/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EV6C2FWONQGCYKPBU2EGMT2P24/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":"2026-06-11T03:42:24Z","links":{"resolver":"https://pith.science/pith/EV6C2FWONQGCYKPBU2EGMT2P24","bundle":"https://pith.science/pith/EV6C2FWONQGCYKPBU2EGMT2P24/bundle.json","state":"https://pith.science/pith/EV6C2FWONQGCYKPBU2EGMT2P24/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EV6C2FWONQGCYKPBU2EGMT2P24/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EV6C2FWONQGCYKPBU2EGMT2P24","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":"7c33a3791e436b15f76ddfe4ed217ed045d3bbf9649d02bdd4a604be5f44bcbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-10-17T04:04:29Z","title_canon_sha256":"57a1c4e6b7d71fd72a7f8e665e68073fbcfd51f898cf31edb24f38934ba6a272"},"schema_version":"1.0","source":{"id":"1010.3394","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3394","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3394v2","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3394","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"pith_short_12","alias_value":"EV6C2FWONQGC","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EV6C2FWONQGCYKPB","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EV6C2FWO","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:3db5d421b83bad1e442ddc35b5a14d1a045340e3b9f422b6cf7e7f9c53d2b8b2","target":"graph","created_at":"2026-05-18T04:36:50Z","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":"Consider random symmetric Toeplitz matrices $T_{n}=(a_{i-j})_{i,j=1}^{n}$ with matrix entries $a_{j}, j=0,1,2,...,$ being independent real random variables such that\n  \\be \\mathbb{E}[a_{j}]=0, \\ \\ \\mathbb{E}[|a_{j}|^{2}]=1 \\ \\ \\textrm{for}\\,\\ \\ j=0,1,2,...,\\ee (homogeneity of 4-th moments) \\be{\\kappa=\\mathbb{E}[|a_{j}|^{4}],}\\ee\n  \\noindent and further (uniform boundedness)\\be\\sup\\limits_{j\\geq 0} \\mathbb{E}[|a_{j}|^{k}]=C_{k}<\\iy\\ \\ \\ \\textrm{for} \\ \\ \\ k\\geq 3.\\ee\n  Under the assumption of $a_{0}\\equiv 0$, we prove a central limit theorem for linear statistics of eigenvalues for a fixed poly","authors_text":"Dang-Zheng Liu, Xin Sun, Zheng-Dong Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-10-17T04:04:29Z","title":"Fluctuation of Eigenvalues for Random Toeplitz and Related Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3394","kind":"arxiv","version":2},"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:d3ea68fbb563a13a4541a646988a5c1b218184ecde65c7a966a85af3ecb60a8f","target":"record","created_at":"2026-05-18T04:36:50Z","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":"7c33a3791e436b15f76ddfe4ed217ed045d3bbf9649d02bdd4a604be5f44bcbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-10-17T04:04:29Z","title_canon_sha256":"57a1c4e6b7d71fd72a7f8e665e68073fbcfd51f898cf31edb24f38934ba6a272"},"schema_version":"1.0","source":{"id":"1010.3394","kind":"arxiv","version":2}},"canonical_sha256":"257c2d16ce6c0c2c29e1a688664f4fd713038cba45718fd9eb42a5db884c03a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"257c2d16ce6c0c2c29e1a688664f4fd713038cba45718fd9eb42a5db884c03a0","first_computed_at":"2026-05-18T04:36:50.036880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:50.036880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wzw9QwUwh+kOTN0roXg90bgNVjglh12qAx/dy0Fbfb3Q/MMg7uH834TxUmMrrRCFFWqgN/fYwkRFQNylHso6Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:50.037399Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3394","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3ea68fbb563a13a4541a646988a5c1b218184ecde65c7a966a85af3ecb60a8f","sha256:3db5d421b83bad1e442ddc35b5a14d1a045340e3b9f422b6cf7e7f9c53d2b8b2"],"state_sha256":"979384a5f8e7642360db7e2246c11421154f4b2b176ebe826cb811caa48c8974"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ktpzEPVyaDUaXYu0pUayMgnUjxXx5nywHZI6b0PSTfHjYfku13p99VpdSPlgPOoGUm9L5ev+tFaH7mJxvkJ0Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:42:24.347298Z","bundle_sha256":"f69a1118e8247acdf20239280203a7409e390b347b427707331eb098165e52c1"}}