{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YTIDBJQHIMKWTD7DZN2JEMULBW","short_pith_number":"pith:YTIDBJQH","canonical_record":{"source":{"id":"1510.03641","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-13T12:12:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3adce919888e540f3398a9c8b4ebd04988c81e9869a76277632d2e2286448e47","abstract_canon_sha256":"a28edfe0d121a07465f29211b35c19f3d2e313f06538fc88906b8b69025c4bc5"},"schema_version":"1.0"},"canonical_sha256":"c4d030a6074315698fe3cb7492328b0d812af807c7afcf4fe4278a3d4e870590","source":{"kind":"arxiv","id":"1510.03641","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03641","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03641v3","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03641","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"YTIDBJQHIMKW","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YTIDBJQHIMKWTD7D","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YTIDBJQH","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YTIDBJQHIMKWTD7DZN2JEMULBW","target":"record","payload":{"canonical_record":{"source":{"id":"1510.03641","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-13T12:12:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3adce919888e540f3398a9c8b4ebd04988c81e9869a76277632d2e2286448e47","abstract_canon_sha256":"a28edfe0d121a07465f29211b35c19f3d2e313f06538fc88906b8b69025c4bc5"},"schema_version":"1.0"},"canonical_sha256":"c4d030a6074315698fe3cb7492328b0d812af807c7afcf4fe4278a3d4e870590","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:50.409864Z","signature_b64":"aHdJMPls7Pd1QUTE8vOb8Rk6tOn79wsmxT72J18ftQaHWjkfg2YJV/kxo1Orhq52czlQ3By4YQT6djlmLFgxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4d030a6074315698fe3cb7492328b0d812af807c7afcf4fe4278a3d4e870590","last_reissued_at":"2026-05-18T01:04:50.409451Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:50.409451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.03641","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":"2026-05-18T01:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/rO5G8jXb33eOKjxobJ438LgGy8MugdXyC28dYLhIup0sKxM+8brCkgj5XJJrEjJrdPC0gsrW0XLLuanzK7wCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:13:46.180276Z"},"content_sha256":"08edf3c3b04ad0d2fe6c36fdd59104e3516ac05f953f74d09c94fbdbb6b29e45","schema_version":"1.0","event_id":"sha256:08edf3c3b04ad0d2fe6c36fdd59104e3516ac05f953f74d09c94fbdbb6b29e45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YTIDBJQHIMKWTD7DZN2JEMULBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mesoscopic fluctuations for unitary invariant ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Gaultier Lambert","submitted_at":"2015-10-13T12:12:32Z","abstract_excerpt":"Considering a determinantal point process on the real line, we establish a connection between the sine-kernel asymptotics for the correlation kernel and the CLT for mesoscopic linear statistics. This implies universality of mesoscopic fluctuations for a large class of unitary invariant Hermitian ensembles. In particular, this shows that the support of the equilibrium measure need not be connected in order to see Gaussian fluctuations at mesoscopic scales. Our proof is based on the cumulants computations introduced in [48] for the CUE and the sine process and the asymptotics formulae derived by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03641","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":"2026-05-18T01:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vZ+YK475fc8TkFAB4Um0CU5ybzDkoLMzgv7wXP1cQ6U2ix71Fn953o7cuQeT+eiazWZukuyrZFp7jWGaJUWZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:13:46.180706Z"},"content_sha256":"ae63e2b8f173f038ad683604bfadf88ccfec8c43ce4ee1c9bfdb847ab9c3f795","schema_version":"1.0","event_id":"sha256:ae63e2b8f173f038ad683604bfadf88ccfec8c43ce4ee1c9bfdb847ab9c3f795"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YTIDBJQHIMKWTD7DZN2JEMULBW/bundle.json","state_url":"https://pith.science/pith/YTIDBJQHIMKWTD7DZN2JEMULBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YTIDBJQHIMKWTD7DZN2JEMULBW/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":"2026-05-30T08:13:46Z","links":{"resolver":"https://pith.science/pith/YTIDBJQHIMKWTD7DZN2JEMULBW","bundle":"https://pith.science/pith/YTIDBJQHIMKWTD7DZN2JEMULBW/bundle.json","state":"https://pith.science/pith/YTIDBJQHIMKWTD7DZN2JEMULBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YTIDBJQHIMKWTD7DZN2JEMULBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YTIDBJQHIMKWTD7DZN2JEMULBW","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":"a28edfe0d121a07465f29211b35c19f3d2e313f06538fc88906b8b69025c4bc5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-13T12:12:32Z","title_canon_sha256":"3adce919888e540f3398a9c8b4ebd04988c81e9869a76277632d2e2286448e47"},"schema_version":"1.0","source":{"id":"1510.03641","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03641","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03641v3","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03641","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"YTIDBJQHIMKW","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YTIDBJQHIMKWTD7D","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YTIDBJQH","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:ae63e2b8f173f038ad683604bfadf88ccfec8c43ce4ee1c9bfdb847ab9c3f795","target":"graph","created_at":"2026-05-18T01:04:50Z","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":"Considering a determinantal point process on the real line, we establish a connection between the sine-kernel asymptotics for the correlation kernel and the CLT for mesoscopic linear statistics. This implies universality of mesoscopic fluctuations for a large class of unitary invariant Hermitian ensembles. In particular, this shows that the support of the equilibrium measure need not be connected in order to see Gaussian fluctuations at mesoscopic scales. Our proof is based on the cumulants computations introduced in [48] for the CUE and the sine process and the asymptotics formulae derived by","authors_text":"Gaultier Lambert","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-13T12:12:32Z","title":"Mesoscopic fluctuations for unitary invariant ensembles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03641","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":"sha256:08edf3c3b04ad0d2fe6c36fdd59104e3516ac05f953f74d09c94fbdbb6b29e45","target":"record","created_at":"2026-05-18T01:04:50Z","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":"a28edfe0d121a07465f29211b35c19f3d2e313f06538fc88906b8b69025c4bc5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-13T12:12:32Z","title_canon_sha256":"3adce919888e540f3398a9c8b4ebd04988c81e9869a76277632d2e2286448e47"},"schema_version":"1.0","source":{"id":"1510.03641","kind":"arxiv","version":3}},"canonical_sha256":"c4d030a6074315698fe3cb7492328b0d812af807c7afcf4fe4278a3d4e870590","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4d030a6074315698fe3cb7492328b0d812af807c7afcf4fe4278a3d4e870590","first_computed_at":"2026-05-18T01:04:50.409451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:50.409451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aHdJMPls7Pd1QUTE8vOb8Rk6tOn79wsmxT72J18ftQaHWjkfg2YJV/kxo1Orhq52czlQ3By4YQT6djlmLFgxBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:50.409864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03641","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08edf3c3b04ad0d2fe6c36fdd59104e3516ac05f953f74d09c94fbdbb6b29e45","sha256:ae63e2b8f173f038ad683604bfadf88ccfec8c43ce4ee1c9bfdb847ab9c3f795"],"state_sha256":"ea76645d4e8f8029211db34b882a1b3aeb4d62d5457fe8a2708b9b8e8128aa0e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9vXtoKBqTHk/QFVs7jStQLABaB0LL4aH70PbsZtV2Ic5Dm7xNJcrLGbmQDimtt3hzxDwlPMpWD47lJADbRpXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:13:46.183089Z","bundle_sha256":"1b4d1111b92c9312965054a488bc1c450f5c02a0f7d999cf9a4854f2d4a64391"}}