{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5AQFU6RB572CVWLZR7S3RFHE3I","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":"8a7a983985c2b3d5bc25a4cf78a6f86a3c6fb9b3e2e459809c7af5fb98e9ca82","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-05T17:39:49Z","title_canon_sha256":"a105d93c611a26b37aa388ba29b5142939cdc109a21615ad1ee9a4cb46005ce3"},"schema_version":"1.0","source":{"id":"1806.01831","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.01831","created_at":"2026-05-18T00:14:11Z"},{"alias_kind":"arxiv_version","alias_value":"1806.01831v1","created_at":"2026-05-18T00:14:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.01831","created_at":"2026-05-18T00:14:11Z"},{"alias_kind":"pith_short_12","alias_value":"5AQFU6RB572C","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5AQFU6RB572CVWLZ","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5AQFU6RB","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:b84ed9f311a00e9b4139a8848a76e53f2c223fb9e5c42a321ddebd62b0a3aea7","target":"graph","created_at":"2026-05-18T00:14:11Z","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":"In this note we prove that suitable positive powers of the absolute value of the characteristic polynomial of a Haar distributed random unitary matrix converge in law, as the size of the matrix tends to infinity, to a Gaussian multiplicative chaos measure once correctly normalized. We prove this in the whole $L^1$- or subcritical phase of the chaos measure.","authors_text":"Christian Webb, Eero Saksman, Miika Nikula","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-05T17:39:49Z","title":"Multiplicative chaos and the characteristic polynomial of the CUE: the $L^1$-phase"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01831","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":"sha256:0d6b23f24ce07ba63d6b3ceb0c787348df63f61b208bc669c999360126a0a10b","target":"record","created_at":"2026-05-18T00:14:11Z","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":"8a7a983985c2b3d5bc25a4cf78a6f86a3c6fb9b3e2e459809c7af5fb98e9ca82","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-05T17:39:49Z","title_canon_sha256":"a105d93c611a26b37aa388ba29b5142939cdc109a21615ad1ee9a4cb46005ce3"},"schema_version":"1.0","source":{"id":"1806.01831","kind":"arxiv","version":1}},"canonical_sha256":"e8205a7a21eff42ad9798fe5b894e4da1a7999f95ffefaad6fc5a29fb4691cdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8205a7a21eff42ad9798fe5b894e4da1a7999f95ffefaad6fc5a29fb4691cdf","first_computed_at":"2026-05-18T00:14:11.726238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:11.726238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8MpllwtwzIiWtO/74y7FRB+KjZJJa0gRcJAGfxErZ2oRVP4Y1+H9FypWHM79FDyXudbmD2MkqaarTTshuKidCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:11.726875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.01831","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d6b23f24ce07ba63d6b3ceb0c787348df63f61b208bc669c999360126a0a10b","sha256:b84ed9f311a00e9b4139a8848a76e53f2c223fb9e5c42a321ddebd62b0a3aea7"],"state_sha256":"5930846b67bfea0062db01a60b369f9e4ff41371098352666a4f6ac9a55ba843"}