{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:VOIXXTM4JGNES3FDSXPMZROR7F","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":"201a8eb25e57ac1d50ee7fe16fb94a7965753c58070c2603717246349161314a","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-06-13T12:38:23Z","title_canon_sha256":"a77a0ac871e869d90e13fe105abdb9f3227c9994dd32032a855e3fb9f784250b"},"schema_version":"1.0","source":{"id":"2306.07732","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.07732","created_at":"2026-07-05T06:20:08Z"},{"alias_kind":"arxiv_version","alias_value":"2306.07732v1","created_at":"2026-07-05T06:20:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.07732","created_at":"2026-07-05T06:20:08Z"},{"alias_kind":"pith_short_12","alias_value":"VOIXXTM4JGNE","created_at":"2026-07-05T06:20:08Z"},{"alias_kind":"pith_short_16","alias_value":"VOIXXTM4JGNES3FD","created_at":"2026-07-05T06:20:08Z"},{"alias_kind":"pith_short_8","alias_value":"VOIXXTM4","created_at":"2026-07-05T06:20:08Z"}],"graph_snapshots":[{"event_id":"sha256:244f0bdd8d7b995b3ca63db0275a22cf674fee9ffc35f9f3983f9d5425b98157","target":"graph","created_at":"2026-07-05T06:20:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2306.07732/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define a random analytic function $\\varphi$ on the unit disc by letting a Gaussian multiplicative measure to be one of its Clark measures. We show that $\\varphi$ is almost surely a Blaschke product and we provide rather sharp estimates for the density of its zeroes.","authors_text":"Eero Saksman, Yichao Huang","cross_cats":["math.CV"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-06-13T12:38:23Z","title":"Random analytic functions via Gaussian multiplicative chaos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.07732","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":"sha256:81c954e50a6c993b20fe1a67c2bf5c5613f0aaa42f9e79ea780cd24a9abe59d0","target":"record","created_at":"2026-07-05T06:20:08Z","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":"201a8eb25e57ac1d50ee7fe16fb94a7965753c58070c2603717246349161314a","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-06-13T12:38:23Z","title_canon_sha256":"a77a0ac871e869d90e13fe105abdb9f3227c9994dd32032a855e3fb9f784250b"},"schema_version":"1.0","source":{"id":"2306.07732","kind":"arxiv","version":1}},"canonical_sha256":"ab917bcd9c499a496ca395deccc5d1f94510e1e04eacb7da41af5f7f1fdd4f0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab917bcd9c499a496ca395deccc5d1f94510e1e04eacb7da41af5f7f1fdd4f0d","first_computed_at":"2026-07-05T06:20:08.142957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:20:08.142957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IE+heIWtC16SMbmXp06OYZHTZcmtYt3Rjt3LN+A1w96VtSHZ8xMHO8r0aAibVUglpoYnKyQIuggpCJZXHL/GAA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:20:08.143353Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.07732","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81c954e50a6c993b20fe1a67c2bf5c5613f0aaa42f9e79ea780cd24a9abe59d0","sha256:244f0bdd8d7b995b3ca63db0275a22cf674fee9ffc35f9f3983f9d5425b98157"],"state_sha256":"499ebfcf0633e008549d856a4cde6b7a776ed524b2d8faab80887eb9fafea39d"}