{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PDU44I5EH7DCCB452ZAB6WRKZC","short_pith_number":"pith:PDU44I5E","canonical_record":{"source":{"id":"1309.1407","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-05T17:09:49Z","cross_cats_sorted":[],"title_canon_sha256":"78900ccc3c92b93feb3a8aa061198d4e496fd83bc03f31ce4d85680517458ce6","abstract_canon_sha256":"d09ae3dbf70b2b4a8519e826f74aa25e34ab558a4b441a783ba9ed9179a6bd61"},"schema_version":"1.0"},"canonical_sha256":"78e9ce23a43fc621079dd6401f5a2ac89ec9a1d7c7fd57962e8c3222403e80f5","source":{"kind":"arxiv","id":"1309.1407","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1407","created_at":"2026-05-18T02:50:00Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1407v2","created_at":"2026-05-18T02:50:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1407","created_at":"2026-05-18T02:50:00Z"},{"alias_kind":"pith_short_12","alias_value":"PDU44I5EH7DC","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PDU44I5EH7DCCB45","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PDU44I5E","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PDU44I5EH7DCCB452ZAB6WRKZC","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1407","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-05T17:09:49Z","cross_cats_sorted":[],"title_canon_sha256":"78900ccc3c92b93feb3a8aa061198d4e496fd83bc03f31ce4d85680517458ce6","abstract_canon_sha256":"d09ae3dbf70b2b4a8519e826f74aa25e34ab558a4b441a783ba9ed9179a6bd61"},"schema_version":"1.0"},"canonical_sha256":"78e9ce23a43fc621079dd6401f5a2ac89ec9a1d7c7fd57962e8c3222403e80f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:00.816257Z","signature_b64":"Y75X6dIMwZsWfAuB8tvD0hZ9qnhlBxH9cwephh+fUvu81+ToI3Qtyzx0qYR4GjMytAnm12PIM5eQEmQOM0GODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78e9ce23a43fc621079dd6401f5a2ac89ec9a1d7c7fd57962e8c3222403e80f5","last_reissued_at":"2026-05-18T02:50:00.815512Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:00.815512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1407","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":"2026-05-18T02:50:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zw8/LiaK/Ctmlh718dQQFiBLMsMF+wsGPZ6qS5OBebnoDlgoYHWVLoPZEDzoy0LE4/ren2CkUulAohy7r+0hBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:34:00.914738Z"},"content_sha256":"40368bc06a95822a57530418012c4b9d2a49738099b9a2a7dedef2c3a2c4c986","schema_version":"1.0","event_id":"sha256:40368bc06a95822a57530418012c4b9d2a49738099b9a2a7dedef2c3a2c4c986"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PDU44I5EH7DCCB452ZAB6WRKZC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximum eigenvalue of symmetric random matrices with dependent heavy tailed entries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arijit Chakrabarty, Parthanil Roy, Rajat Subhra Hazra","submitted_at":"2013-09-05T17:09:49Z","abstract_excerpt":"This paper deals with symmetric random matrices whose upper diagonal entries are obtained from a linear random field with heavy tailed noise. It is shown that the maximum eigenvalue and the spectral radius of such a random matrix with dependent entries converge to the Frech\\'et distribution after appropriate scaling. This extends a seminal result of Soshnikov(2004) when the tail index is strictly less than one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1407","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":"2026-05-18T02:50:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w4q8WnspYLDl+Erh2rslpj6GOG9rw9XIouAbG5hllJo//ugImIl23300VAOu2f14dwczFlPnJUcD8FU2mQE/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:34:00.915072Z"},"content_sha256":"ef101fea33e68e46f4122afa649d9e5a82912da454a1d8fd124c818621c426e7","schema_version":"1.0","event_id":"sha256:ef101fea33e68e46f4122afa649d9e5a82912da454a1d8fd124c818621c426e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PDU44I5EH7DCCB452ZAB6WRKZC/bundle.json","state_url":"https://pith.science/pith/PDU44I5EH7DCCB452ZAB6WRKZC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PDU44I5EH7DCCB452ZAB6WRKZC/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":"2026-06-20T05:34:00Z","links":{"resolver":"https://pith.science/pith/PDU44I5EH7DCCB452ZAB6WRKZC","bundle":"https://pith.science/pith/PDU44I5EH7DCCB452ZAB6WRKZC/bundle.json","state":"https://pith.science/pith/PDU44I5EH7DCCB452ZAB6WRKZC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PDU44I5EH7DCCB452ZAB6WRKZC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PDU44I5EH7DCCB452ZAB6WRKZC","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":"d09ae3dbf70b2b4a8519e826f74aa25e34ab558a4b441a783ba9ed9179a6bd61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-05T17:09:49Z","title_canon_sha256":"78900ccc3c92b93feb3a8aa061198d4e496fd83bc03f31ce4d85680517458ce6"},"schema_version":"1.0","source":{"id":"1309.1407","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1407","created_at":"2026-05-18T02:50:00Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1407v2","created_at":"2026-05-18T02:50:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1407","created_at":"2026-05-18T02:50:00Z"},{"alias_kind":"pith_short_12","alias_value":"PDU44I5EH7DC","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PDU44I5EH7DCCB45","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PDU44I5E","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:ef101fea33e68e46f4122afa649d9e5a82912da454a1d8fd124c818621c426e7","target":"graph","created_at":"2026-05-18T02:50:00Z","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":"This paper deals with symmetric random matrices whose upper diagonal entries are obtained from a linear random field with heavy tailed noise. It is shown that the maximum eigenvalue and the spectral radius of such a random matrix with dependent entries converge to the Frech\\'et distribution after appropriate scaling. This extends a seminal result of Soshnikov(2004) when the tail index is strictly less than one.","authors_text":"Arijit Chakrabarty, Parthanil Roy, Rajat Subhra Hazra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-05T17:09:49Z","title":"Maximum eigenvalue of symmetric random matrices with dependent heavy tailed entries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1407","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":"sha256:40368bc06a95822a57530418012c4b9d2a49738099b9a2a7dedef2c3a2c4c986","target":"record","created_at":"2026-05-18T02:50:00Z","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":"d09ae3dbf70b2b4a8519e826f74aa25e34ab558a4b441a783ba9ed9179a6bd61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-05T17:09:49Z","title_canon_sha256":"78900ccc3c92b93feb3a8aa061198d4e496fd83bc03f31ce4d85680517458ce6"},"schema_version":"1.0","source":{"id":"1309.1407","kind":"arxiv","version":2}},"canonical_sha256":"78e9ce23a43fc621079dd6401f5a2ac89ec9a1d7c7fd57962e8c3222403e80f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78e9ce23a43fc621079dd6401f5a2ac89ec9a1d7c7fd57962e8c3222403e80f5","first_computed_at":"2026-05-18T02:50:00.815512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:00.815512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y75X6dIMwZsWfAuB8tvD0hZ9qnhlBxH9cwephh+fUvu81+ToI3Qtyzx0qYR4GjMytAnm12PIM5eQEmQOM0GODw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:00.816257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1407","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40368bc06a95822a57530418012c4b9d2a49738099b9a2a7dedef2c3a2c4c986","sha256:ef101fea33e68e46f4122afa649d9e5a82912da454a1d8fd124c818621c426e7"],"state_sha256":"1b616ba432db0e8fda970321212bd332c9646c62c3856cfb2a9d2a32d32f43cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RXFWupzaabqeHIxDvytWIVIfmC6VXBkVYZsd77Qp+JJDVyF3TyVzcPTvVhAAbIcXGW8gOxG6+lQ5OsHrFADODg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:34:00.916967Z","bundle_sha256":"e758a7ff37a09dcf7d0a954c497926011c2b17e1ae498aaf460a6a9e270f4f9a"}}