{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JKTFIK57J6AFVAIRWXQ6PTP7XL","short_pith_number":"pith:JKTFIK57","canonical_record":{"source":{"id":"1611.09476","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-29T03:47:16Z","cross_cats_sorted":[],"title_canon_sha256":"319097142c94e91fcb6999f846ab34c57967ed30986c57cba76f9e71f11dc1b2","abstract_canon_sha256":"908ba87278d258593b9b0a88a66919a351cdff2c391c51f8f325f131d682d9b1"},"schema_version":"1.0"},"canonical_sha256":"4aa6542bbf4f805a8111b5e1e7cdffbafec91284d6306e25d3d6b038dba68086","source":{"kind":"arxiv","id":"1611.09476","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09476","created_at":"2026-05-18T00:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09476v2","created_at":"2026-05-18T00:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09476","created_at":"2026-05-18T00:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"JKTFIK57J6AF","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JKTFIK57J6AFVAIR","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JKTFIK57","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JKTFIK57J6AFVAIRWXQ6PTP7XL","target":"record","payload":{"canonical_record":{"source":{"id":"1611.09476","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-29T03:47:16Z","cross_cats_sorted":[],"title_canon_sha256":"319097142c94e91fcb6999f846ab34c57967ed30986c57cba76f9e71f11dc1b2","abstract_canon_sha256":"908ba87278d258593b9b0a88a66919a351cdff2c391c51f8f325f131d682d9b1"},"schema_version":"1.0"},"canonical_sha256":"4aa6542bbf4f805a8111b5e1e7cdffbafec91284d6306e25d3d6b038dba68086","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:35.226106Z","signature_b64":"k67/VRxlPcdH+2LDHLTWSRXyUsps8KWK0RYubEv0D+FdDowcWjnO2UOxuetjcFktnbJpYhvdXoZUve9vH3RrCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4aa6542bbf4f805a8111b5e1e7cdffbafec91284d6306e25d3d6b038dba68086","last_reissued_at":"2026-05-18T00:34:35.225715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:35.225715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.09476","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":"2026-05-18T00:34:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oT8lIBNVGStVoXHJWZk4PAG6E+U+jzEsG0HXqiYyYySzjviSOoH4PPO4jYhhwOjHFq3IBiQXoJJGTMUhw1fHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T08:32:57.575827Z"},"content_sha256":"4931f1146391e7af4c8a6e900bcc5bc0a48946cd27d178d9f49f825264e3524f","schema_version":"1.0","event_id":"sha256:4931f1146391e7af4c8a6e900bcc5bc0a48946cd27d178d9f49f825264e3524f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JKTFIK57J6AFVAIRWXQ6PTP7XL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fumihiko Nakano, Trinh Khanh Duy","submitted_at":"2016-11-29T03:47:16Z","abstract_excerpt":"We study the limiting behavior of Gaussian beta ensembles in the regime where $\\beta n = const$ as $n \\to \\infty$. The results are (1) Gaussian fluctuations for linear statistics of the eigenvalues, and (2) Poisson convergence of the bulk statistics. (2) is an alternative proof of the result by F.~Benaych-Georges and S.~P\\'ech\\'e (2015) with the explicit form of the intensity measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09476","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":"2026-05-18T00:34:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ptFExp8pfd3cEMQQl75lXE4J94r5KKuFtSZsgDd4Mh6zauSTp16OBtlu0bZToIO707rlFKIY75MaeLgnghPBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T08:32:57.576176Z"},"content_sha256":"069e9183be6603d774863b3b992e26dfc793b8611ed5d7731f0bed1be03b4cbe","schema_version":"1.0","event_id":"sha256:069e9183be6603d774863b3b992e26dfc793b8611ed5d7731f0bed1be03b4cbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JKTFIK57J6AFVAIRWXQ6PTP7XL/bundle.json","state_url":"https://pith.science/pith/JKTFIK57J6AFVAIRWXQ6PTP7XL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JKTFIK57J6AFVAIRWXQ6PTP7XL/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":"2026-06-27T08:32:57Z","links":{"resolver":"https://pith.science/pith/JKTFIK57J6AFVAIRWXQ6PTP7XL","bundle":"https://pith.science/pith/JKTFIK57J6AFVAIRWXQ6PTP7XL/bundle.json","state":"https://pith.science/pith/JKTFIK57J6AFVAIRWXQ6PTP7XL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JKTFIK57J6AFVAIRWXQ6PTP7XL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JKTFIK57J6AFVAIRWXQ6PTP7XL","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":"908ba87278d258593b9b0a88a66919a351cdff2c391c51f8f325f131d682d9b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-29T03:47:16Z","title_canon_sha256":"319097142c94e91fcb6999f846ab34c57967ed30986c57cba76f9e71f11dc1b2"},"schema_version":"1.0","source":{"id":"1611.09476","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09476","created_at":"2026-05-18T00:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09476v2","created_at":"2026-05-18T00:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09476","created_at":"2026-05-18T00:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"JKTFIK57J6AF","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JKTFIK57J6AFVAIR","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JKTFIK57","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:069e9183be6603d774863b3b992e26dfc793b8611ed5d7731f0bed1be03b4cbe","target":"graph","created_at":"2026-05-18T00:34:35Z","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 study the limiting behavior of Gaussian beta ensembles in the regime where $\\beta n = const$ as $n \\to \\infty$. The results are (1) Gaussian fluctuations for linear statistics of the eigenvalues, and (2) Poisson convergence of the bulk statistics. (2) is an alternative proof of the result by F.~Benaych-Georges and S.~P\\'ech\\'e (2015) with the explicit form of the intensity measure.","authors_text":"Fumihiko Nakano, Trinh Khanh Duy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-29T03:47:16Z","title":"Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09476","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":"sha256:4931f1146391e7af4c8a6e900bcc5bc0a48946cd27d178d9f49f825264e3524f","target":"record","created_at":"2026-05-18T00:34:35Z","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":"908ba87278d258593b9b0a88a66919a351cdff2c391c51f8f325f131d682d9b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-29T03:47:16Z","title_canon_sha256":"319097142c94e91fcb6999f846ab34c57967ed30986c57cba76f9e71f11dc1b2"},"schema_version":"1.0","source":{"id":"1611.09476","kind":"arxiv","version":2}},"canonical_sha256":"4aa6542bbf4f805a8111b5e1e7cdffbafec91284d6306e25d3d6b038dba68086","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4aa6542bbf4f805a8111b5e1e7cdffbafec91284d6306e25d3d6b038dba68086","first_computed_at":"2026-05-18T00:34:35.225715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:35.225715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k67/VRxlPcdH+2LDHLTWSRXyUsps8KWK0RYubEv0D+FdDowcWjnO2UOxuetjcFktnbJpYhvdXoZUve9vH3RrCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:35.226106Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.09476","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4931f1146391e7af4c8a6e900bcc5bc0a48946cd27d178d9f49f825264e3524f","sha256:069e9183be6603d774863b3b992e26dfc793b8611ed5d7731f0bed1be03b4cbe"],"state_sha256":"54d1de2e4de8fa737d185736308452cb2305771d1f8a8a17fa9f66742a6b42c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0vBaF4ilXtM469k5iqBvwpCFk8R2tNHQbFO5Pn44lbfcXSThMwqozDTJ5CKutw8Rjf7shxgXF0QPdAmGZIX0Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T08:32:57.578066Z","bundle_sha256":"a306e2f4d8e04d09a0926ccec03b2c19e04adf88e73eeb0fba33cf6658264e14"}}