{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:YVJYXVSLJEXIAACGA3QK23LPWM","short_pith_number":"pith:YVJYXVSL","canonical_record":{"source":{"id":"cond-mat/0609651","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-09-26T05:28:46Z","cross_cats_sorted":["cond-mat.dis-nn","hep-th","math-ph","math.MP"],"title_canon_sha256":"db0600c07024fd5fc1bfa80ea6c35abf6baae6fbfb6e4ba1df4c6605826a4fbe","abstract_canon_sha256":"0eac979f837a3e0cd90676594179149967fdf7da390f5a7378726c68a9f16cbe"},"schema_version":"1.0"},"canonical_sha256":"c5538bd64b492e80004606e0ad6d6fb31a83f9ac7e01fda1dcb0a41e0bac452d","source":{"kind":"arxiv","id":"cond-mat/0609651","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0609651","created_at":"2026-07-04T17:01:08Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0609651v2","created_at":"2026-07-04T17:01:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0609651","created_at":"2026-07-04T17:01:08Z"},{"alias_kind":"pith_short_12","alias_value":"YVJYXVSLJEXI","created_at":"2026-07-04T17:01:08Z"},{"alias_kind":"pith_short_16","alias_value":"YVJYXVSLJEXIAACG","created_at":"2026-07-04T17:01:08Z"},{"alias_kind":"pith_short_8","alias_value":"YVJYXVSL","created_at":"2026-07-04T17:01:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:YVJYXVSLJEXIAACGA3QK23LPWM","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0609651","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-09-26T05:28:46Z","cross_cats_sorted":["cond-mat.dis-nn","hep-th","math-ph","math.MP"],"title_canon_sha256":"db0600c07024fd5fc1bfa80ea6c35abf6baae6fbfb6e4ba1df4c6605826a4fbe","abstract_canon_sha256":"0eac979f837a3e0cd90676594179149967fdf7da390f5a7378726c68a9f16cbe"},"schema_version":"1.0"},"canonical_sha256":"c5538bd64b492e80004606e0ad6d6fb31a83f9ac7e01fda1dcb0a41e0bac452d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:01:08.492936Z","signature_b64":"kHkYFrqKCB6ZMggmHClrhoVKEZ57fOU29aW+5+VWTd3+v5GB5QDTOEjw1B0huWUQ45pVyyRVBKLsPcb/lsTqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5538bd64b492e80004606e0ad6d6fb31a83f9ac7e01fda1dcb0a41e0bac452d","last_reissued_at":"2026-07-04T17:01:08.492590Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:01:08.492590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0609651","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":"2026-07-04T17:01:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WPVa6yyRUxm+QJ+pOvPXbSUpxc6X5IG//1LSGSL+xXPnQSI6YzywjY8QJeNeYcX5lOOCsj4Gl5jZNzOGl2lDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T01:19:32.447738Z"},"content_sha256":"a756e4397f7d22e9d63f915cfe57971ba80f619ea2cf993a095ba3ec6f5b0260","schema_version":"1.0","event_id":"sha256:a756e4397f7d22e9d63f915cfe57971ba80f619ea2cf993a095ba3ec6f5b0260"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:YVJYXVSLJEXIAACGA3QK23LPWM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large Deviations of Extreme Eigenvalues of Random Matrices","license":"","headline":"","cross_cats":["cond-mat.dis-nn","hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"David S. Dean, Satya N. Majumdar","submitted_at":"2006-09-26T05:28:46Z","abstract_excerpt":"We calculate analytically the probability of large deviations from its mean of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we show that the probability that all the eigenvalues of an (N\\times N) random matrix are positive (negative) decreases for large N as \\exp[-\\beta \\theta(0) N^2] where the parameter \\beta characterizes the ensemble and the exponent \\theta(0)=(\\ln 3)/4=0.274653... is universal. We also calculate exactly the average density of states in matrices whose eigenvalues are restricted to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0609651","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cond-mat/0609651/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T17:01:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QXeQ3CrPh3UC9lWb+E/qY2+mI3hAO36fVg6Xweqoy+g8PAQwjQbOwzsVrcgAjJ4VJo3Tgw8ltygdmbZ0BamPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T01:19:32.448664Z"},"content_sha256":"249c70046a0e6fa0f1448caa56e7521a04e993ca17a9e0e850da26fec52443fc","schema_version":"1.0","event_id":"sha256:249c70046a0e6fa0f1448caa56e7521a04e993ca17a9e0e850da26fec52443fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YVJYXVSLJEXIAACGA3QK23LPWM/bundle.json","state_url":"https://pith.science/pith/YVJYXVSLJEXIAACGA3QK23LPWM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YVJYXVSLJEXIAACGA3QK23LPWM/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":"2026-08-06T01:19:32Z","links":{"resolver":"https://pith.science/pith/YVJYXVSLJEXIAACGA3QK23LPWM","bundle":"https://pith.science/pith/YVJYXVSLJEXIAACGA3QK23LPWM/bundle.json","state":"https://pith.science/pith/YVJYXVSLJEXIAACGA3QK23LPWM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YVJYXVSLJEXIAACGA3QK23LPWM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:YVJYXVSLJEXIAACGA3QK23LPWM","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":"0eac979f837a3e0cd90676594179149967fdf7da390f5a7378726c68a9f16cbe","cross_cats_sorted":["cond-mat.dis-nn","hep-th","math-ph","math.MP"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-09-26T05:28:46Z","title_canon_sha256":"db0600c07024fd5fc1bfa80ea6c35abf6baae6fbfb6e4ba1df4c6605826a4fbe"},"schema_version":"1.0","source":{"id":"cond-mat/0609651","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0609651","created_at":"2026-07-04T17:01:08Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0609651v2","created_at":"2026-07-04T17:01:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0609651","created_at":"2026-07-04T17:01:08Z"},{"alias_kind":"pith_short_12","alias_value":"YVJYXVSLJEXI","created_at":"2026-07-04T17:01:08Z"},{"alias_kind":"pith_short_16","alias_value":"YVJYXVSLJEXIAACG","created_at":"2026-07-04T17:01:08Z"},{"alias_kind":"pith_short_8","alias_value":"YVJYXVSL","created_at":"2026-07-04T17:01:08Z"}],"graph_snapshots":[{"event_id":"sha256:249c70046a0e6fa0f1448caa56e7521a04e993ca17a9e0e850da26fec52443fc","target":"graph","created_at":"2026-07-04T17:01:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cond-mat/0609651/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We calculate analytically the probability of large deviations from its mean of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we show that the probability that all the eigenvalues of an (N\\times N) random matrix are positive (negative) decreases for large N as \\exp[-\\beta \\theta(0) N^2] where the parameter \\beta characterizes the ensemble and the exponent \\theta(0)=(\\ln 3)/4=0.274653... is universal. We also calculate exactly the average density of states in matrices whose eigenvalues are restricted to","authors_text":"David S. Dean, Satya N. Majumdar","cross_cats":["cond-mat.dis-nn","hep-th","math-ph","math.MP"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-09-26T05:28:46Z","title":"Large Deviations of Extreme Eigenvalues of Random Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0609651","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:a756e4397f7d22e9d63f915cfe57971ba80f619ea2cf993a095ba3ec6f5b0260","target":"record","created_at":"2026-07-04T17:01:08Z","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":"0eac979f837a3e0cd90676594179149967fdf7da390f5a7378726c68a9f16cbe","cross_cats_sorted":["cond-mat.dis-nn","hep-th","math-ph","math.MP"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-09-26T05:28:46Z","title_canon_sha256":"db0600c07024fd5fc1bfa80ea6c35abf6baae6fbfb6e4ba1df4c6605826a4fbe"},"schema_version":"1.0","source":{"id":"cond-mat/0609651","kind":"arxiv","version":2}},"canonical_sha256":"c5538bd64b492e80004606e0ad6d6fb31a83f9ac7e01fda1dcb0a41e0bac452d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5538bd64b492e80004606e0ad6d6fb31a83f9ac7e01fda1dcb0a41e0bac452d","first_computed_at":"2026-07-04T17:01:08.492590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:01:08.492590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kHkYFrqKCB6ZMggmHClrhoVKEZ57fOU29aW+5+VWTd3+v5GB5QDTOEjw1B0huWUQ45pVyyRVBKLsPcb/lsTqAA==","signature_status":"signed_v1","signed_at":"2026-07-04T17:01:08.492936Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0609651","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a756e4397f7d22e9d63f915cfe57971ba80f619ea2cf993a095ba3ec6f5b0260","sha256:249c70046a0e6fa0f1448caa56e7521a04e993ca17a9e0e850da26fec52443fc"],"state_sha256":"fcf107fe422afd2aa24f8444c03b8cd81a5ec323ea43a7066fe87ff29be32119"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L7VK+SBr+/tD2RsGiyloqRn+h/g+yLXgHIvybmvIqWwVpFnjJ8hUsreQKOk2jhavv7cB1kdSDNoKwGpAvHKgDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T01:19:32.454964Z","bundle_sha256":"e674e01a6c3988a8c3a5cd48f1abb31d81c7ffe244c32e28bee6e5782fb97e0e"}}