{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:F6UQS5HRVX6J6EGM4O7WPVAEIO","short_pith_number":"pith:F6UQS5HR","canonical_record":{"source":{"id":"1803.10544","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-28T11:47:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8e3d25bac35cd2287d79075e968dda1678a3311fa5507acfa7f3b74b2a77ecad","abstract_canon_sha256":"74eae2eea137a57060228b46a49ed0f4499199e0f570d46735badc1a3e2064bc"},"schema_version":"1.0"},"canonical_sha256":"2fa90974f1adfc9f10cce3bf67d40443b9d4614abb4cb0be5bdeab1650480685","source":{"kind":"arxiv","id":"1803.10544","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10544","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10544v3","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10544","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"F6UQS5HRVX6J","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"F6UQS5HRVX6J6EGM","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"F6UQS5HR","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:F6UQS5HRVX6J6EGM4O7WPVAEIO","target":"record","payload":{"canonical_record":{"source":{"id":"1803.10544","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-28T11:47:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8e3d25bac35cd2287d79075e968dda1678a3311fa5507acfa7f3b74b2a77ecad","abstract_canon_sha256":"74eae2eea137a57060228b46a49ed0f4499199e0f570d46735badc1a3e2064bc"},"schema_version":"1.0"},"canonical_sha256":"2fa90974f1adfc9f10cce3bf67d40443b9d4614abb4cb0be5bdeab1650480685","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:13.882947Z","signature_b64":"kllpoZTJTJjllw6iCi0GiO9xCphNri1Bhu+0w94HzzkPWK74gaviHmK4vIcMfMTYxfVMq59B9V5jDZXdLpZZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fa90974f1adfc9f10cce3bf67d40443b9d4614abb4cb0be5bdeab1650480685","last_reissued_at":"2026-05-17T23:50:13.882226Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:13.882226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.10544","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":"2026-05-17T23:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VoIyxm4U+UM2pex6NNSWkJimItqxMifeezg+NhAzvtQo0BBEZ2vlU9GAzlzHjpvMLUb1xg/TPASljzSe7mv+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T18:43:10.172288Z"},"content_sha256":"4434b275c9b5c150e844e6a656c1c1100494894f843fabced2bb6ca99ff80f5e","schema_version":"1.0","event_id":"sha256:4434b275c9b5c150e844e6a656c1c1100494894f843fabced2bb6ca99ff80f5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:F6UQS5HRVX6J6EGM4O7WPVAEIO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mesoscopic linear statistics of Wigner matrices of mixed symmetry class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Yukun He","submitted_at":"2018-03-28T11:47:34Z","abstract_excerpt":"We prove a central limit theorem for the mesoscopic linear statistics of $N\\times N$ Wigner matrices $H$ satisfying $\\mathbb{E}|H_{ij}|^2=1/N$ and $\\mathbb{E} H_{ij}^2= \\sigma /N$, where $\\sigma \\in [-1,1]$. We show that on all mesoscopic scales $\\eta$ ($1/N \\ll \\eta \\ll 1$), the linear statistics of $H$ have a sharp transition at $1-\\sigma \\sim \\eta$. As an application, we identify the mesoscopic linear statistics of Dyson's Brownian motion $H_t$ started from a real symmetric Wigner matrix $H_0$ at any nonnegative time $t \\in [0,\\infty]$. In particular, we obtain the transition from the centr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10544","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":"2026-05-17T23:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VohRAbPWzG9RE1LjI7mSYRzFFOCUXazy0UdD6zYCEeIBwAotRdFcsrsPaEfNXWXGNtUbaO5yW0GjeiQ97WRHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T18:43:10.173071Z"},"content_sha256":"0c07e5901ce554acb567fbf0ae0e0b604a90e81098dcc2433efd14173a4c9067","schema_version":"1.0","event_id":"sha256:0c07e5901ce554acb567fbf0ae0e0b604a90e81098dcc2433efd14173a4c9067"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F6UQS5HRVX6J6EGM4O7WPVAEIO/bundle.json","state_url":"https://pith.science/pith/F6UQS5HRVX6J6EGM4O7WPVAEIO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F6UQS5HRVX6J6EGM4O7WPVAEIO/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":"2026-06-11T18:43:10Z","links":{"resolver":"https://pith.science/pith/F6UQS5HRVX6J6EGM4O7WPVAEIO","bundle":"https://pith.science/pith/F6UQS5HRVX6J6EGM4O7WPVAEIO/bundle.json","state":"https://pith.science/pith/F6UQS5HRVX6J6EGM4O7WPVAEIO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F6UQS5HRVX6J6EGM4O7WPVAEIO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:F6UQS5HRVX6J6EGM4O7WPVAEIO","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":"74eae2eea137a57060228b46a49ed0f4499199e0f570d46735badc1a3e2064bc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-28T11:47:34Z","title_canon_sha256":"8e3d25bac35cd2287d79075e968dda1678a3311fa5507acfa7f3b74b2a77ecad"},"schema_version":"1.0","source":{"id":"1803.10544","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10544","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10544v3","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10544","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"F6UQS5HRVX6J","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"F6UQS5HRVX6J6EGM","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"F6UQS5HR","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:0c07e5901ce554acb567fbf0ae0e0b604a90e81098dcc2433efd14173a4c9067","target":"graph","created_at":"2026-05-17T23:50:13Z","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 prove a central limit theorem for the mesoscopic linear statistics of $N\\times N$ Wigner matrices $H$ satisfying $\\mathbb{E}|H_{ij}|^2=1/N$ and $\\mathbb{E} H_{ij}^2= \\sigma /N$, where $\\sigma \\in [-1,1]$. We show that on all mesoscopic scales $\\eta$ ($1/N \\ll \\eta \\ll 1$), the linear statistics of $H$ have a sharp transition at $1-\\sigma \\sim \\eta$. As an application, we identify the mesoscopic linear statistics of Dyson's Brownian motion $H_t$ started from a real symmetric Wigner matrix $H_0$ at any nonnegative time $t \\in [0,\\infty]$. In particular, we obtain the transition from the centr","authors_text":"Yukun He","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-28T11:47:34Z","title":"Mesoscopic linear statistics of Wigner matrices of mixed symmetry class"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10544","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":"sha256:4434b275c9b5c150e844e6a656c1c1100494894f843fabced2bb6ca99ff80f5e","target":"record","created_at":"2026-05-17T23:50:13Z","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":"74eae2eea137a57060228b46a49ed0f4499199e0f570d46735badc1a3e2064bc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-28T11:47:34Z","title_canon_sha256":"8e3d25bac35cd2287d79075e968dda1678a3311fa5507acfa7f3b74b2a77ecad"},"schema_version":"1.0","source":{"id":"1803.10544","kind":"arxiv","version":3}},"canonical_sha256":"2fa90974f1adfc9f10cce3bf67d40443b9d4614abb4cb0be5bdeab1650480685","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fa90974f1adfc9f10cce3bf67d40443b9d4614abb4cb0be5bdeab1650480685","first_computed_at":"2026-05-17T23:50:13.882226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:13.882226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kllpoZTJTJjllw6iCi0GiO9xCphNri1Bhu+0w94HzzkPWK74gaviHmK4vIcMfMTYxfVMq59B9V5jDZXdLpZZDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:13.882947Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.10544","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4434b275c9b5c150e844e6a656c1c1100494894f843fabced2bb6ca99ff80f5e","sha256:0c07e5901ce554acb567fbf0ae0e0b604a90e81098dcc2433efd14173a4c9067"],"state_sha256":"aee08d1fce03c559e4369006906c1c2fc12cb3984d358b5fb20ffdd6c42dadfe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pe0etcDjkBPyB0/qNQB8xE+0jRWrDwtSqou8LEqqWFe0zNALT1zuHfgaQ3vTmTI6FxCYdCoNfeMLldw4zfh9Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T18:43:10.178226Z","bundle_sha256":"24092d000d5f3c6ead333f210207b14a6a76600e259251081b652c8fb15b4cae"}}