{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FSDUW5MZX6OPVCGQYVYLHBMAMB","short_pith_number":"pith:FSDUW5MZ","canonical_record":{"source":{"id":"1403.7814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-30T21:22:49Z","cross_cats_sorted":[],"title_canon_sha256":"5efddd10694579b62ef05d5a10e2828155f1a9f075a1eefb5ae57bb41e3126b2","abstract_canon_sha256":"43606bbd2b72d991e693ede43cdd31adb01af6efd118e5b7d8fc5445c0e121a8"},"schema_version":"1.0"},"canonical_sha256":"2c874b7599bf9cfa88d0c570b38580607e821612949799e4bed12cbbcb4f1e52","source":{"kind":"arxiv","id":"1403.7814","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7814","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7814v1","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7814","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"FSDUW5MZX6OP","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FSDUW5MZX6OPVCGQ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FSDUW5MZ","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FSDUW5MZX6OPVCGQYVYLHBMAMB","target":"record","payload":{"canonical_record":{"source":{"id":"1403.7814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-30T21:22:49Z","cross_cats_sorted":[],"title_canon_sha256":"5efddd10694579b62ef05d5a10e2828155f1a9f075a1eefb5ae57bb41e3126b2","abstract_canon_sha256":"43606bbd2b72d991e693ede43cdd31adb01af6efd118e5b7d8fc5445c0e121a8"},"schema_version":"1.0"},"canonical_sha256":"2c874b7599bf9cfa88d0c570b38580607e821612949799e4bed12cbbcb4f1e52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:12.331786Z","signature_b64":"Qgh1nkQrFKC2OPPZRZcFpug3zWlHLqNQKQKOIN9AB17Mc4Y5lAlS0c3alodR04ev21WuHU+rfV/w9LJtxu2iCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c874b7599bf9cfa88d0c570b38580607e821612949799e4bed12cbbcb4f1e52","last_reissued_at":"2026-05-18T02:55:12.331423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:12.331423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.7814","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:55:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aTsYh/B1r2nBLxMlIfTEXbNYTIIH1wTjYlhUWFV9VgCk4agx4Id4sZ9uvcRfzyhtpd1GPDTQimXwqhwRj7qgAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:26:37.971662Z"},"content_sha256":"4b9546950d110e9732eb6c3cd603cd19c57932a94295b497388313f726f31e65","schema_version":"1.0","event_id":"sha256:4b9546950d110e9732eb6c3cd603cd19c57932a94295b497388313f726f31e65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FSDUW5MZX6OPVCGQYVYLHBMAMB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A limiting random analytic function related to the CUE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ashkan Nikeghbali, Joseph Najnudel, Reda Chhaibi","submitted_at":"2014-03-30T21:22:49Z","abstract_excerpt":"We show in this paper that, when properly rescaled in time and in space, the characteristic polynomial of a random unitary matrix converges almost surely to a random analytic function whose zeros, which are on the real line, form a determinantal point process with sine kernel. We prove this result in the framework of virtual isometries to circumvent the fact that the rescaled characteristic polynomial does not even have a moment of order one, hence making the classical techniques of random matrix theory difficult to apply."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7814","kind":"arxiv","version":1},"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":"2026-05-18T02:55:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"miGyQ1xOJUbIi08CKg5IyOxvvFoMRdNeYY/8LigbTnJedGputmTeO9mGBNbgv3bPPuJrnggMIyk6mbBWijPMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:26:37.972012Z"},"content_sha256":"4337910850c44c75e458026c04126570894a99ea8ba246584fdcc22d5c5383d6","schema_version":"1.0","event_id":"sha256:4337910850c44c75e458026c04126570894a99ea8ba246584fdcc22d5c5383d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FSDUW5MZX6OPVCGQYVYLHBMAMB/bundle.json","state_url":"https://pith.science/pith/FSDUW5MZX6OPVCGQYVYLHBMAMB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FSDUW5MZX6OPVCGQYVYLHBMAMB/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":"2026-06-03T01:26:37Z","links":{"resolver":"https://pith.science/pith/FSDUW5MZX6OPVCGQYVYLHBMAMB","bundle":"https://pith.science/pith/FSDUW5MZX6OPVCGQYVYLHBMAMB/bundle.json","state":"https://pith.science/pith/FSDUW5MZX6OPVCGQYVYLHBMAMB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FSDUW5MZX6OPVCGQYVYLHBMAMB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FSDUW5MZX6OPVCGQYVYLHBMAMB","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":"43606bbd2b72d991e693ede43cdd31adb01af6efd118e5b7d8fc5445c0e121a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-30T21:22:49Z","title_canon_sha256":"5efddd10694579b62ef05d5a10e2828155f1a9f075a1eefb5ae57bb41e3126b2"},"schema_version":"1.0","source":{"id":"1403.7814","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7814","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7814v1","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7814","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"FSDUW5MZX6OP","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FSDUW5MZX6OPVCGQ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FSDUW5MZ","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:4337910850c44c75e458026c04126570894a99ea8ba246584fdcc22d5c5383d6","target":"graph","created_at":"2026-05-18T02:55:12Z","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 show in this paper that, when properly rescaled in time and in space, the characteristic polynomial of a random unitary matrix converges almost surely to a random analytic function whose zeros, which are on the real line, form a determinantal point process with sine kernel. We prove this result in the framework of virtual isometries to circumvent the fact that the rescaled characteristic polynomial does not even have a moment of order one, hence making the classical techniques of random matrix theory difficult to apply.","authors_text":"Ashkan Nikeghbali, Joseph Najnudel, Reda Chhaibi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-30T21:22:49Z","title":"A limiting random analytic function related to the CUE"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7814","kind":"arxiv","version":1},"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":"sha256:4b9546950d110e9732eb6c3cd603cd19c57932a94295b497388313f726f31e65","target":"record","created_at":"2026-05-18T02:55:12Z","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":"43606bbd2b72d991e693ede43cdd31adb01af6efd118e5b7d8fc5445c0e121a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-30T21:22:49Z","title_canon_sha256":"5efddd10694579b62ef05d5a10e2828155f1a9f075a1eefb5ae57bb41e3126b2"},"schema_version":"1.0","source":{"id":"1403.7814","kind":"arxiv","version":1}},"canonical_sha256":"2c874b7599bf9cfa88d0c570b38580607e821612949799e4bed12cbbcb4f1e52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c874b7599bf9cfa88d0c570b38580607e821612949799e4bed12cbbcb4f1e52","first_computed_at":"2026-05-18T02:55:12.331423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:12.331423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qgh1nkQrFKC2OPPZRZcFpug3zWlHLqNQKQKOIN9AB17Mc4Y5lAlS0c3alodR04ev21WuHU+rfV/w9LJtxu2iCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:12.331786Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.7814","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b9546950d110e9732eb6c3cd603cd19c57932a94295b497388313f726f31e65","sha256:4337910850c44c75e458026c04126570894a99ea8ba246584fdcc22d5c5383d6"],"state_sha256":"d3315b444dd338a9f9d4bb8017ea313862709a2801a787f8eb4a5102e9a5ab4a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0cO7y/F6NX0LU/s+JPvuJLupZYUCBjT/1gSReTB5ZPZRWvFUSkvl7yX8kFFKGCeLYim8Ycj/SdhVJTrNeqF+Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:26:37.974205Z","bundle_sha256":"49e74156087568d18ec9b76d4ede5361ab3a0f51e66fabe651229d0fc9fb124a"}}