{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:OB7MGP3PQTORBCJJVUNUMPJ6XW","short_pith_number":"pith:OB7MGP3P","canonical_record":{"source":{"id":"2311.04027","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-11-07T14:26:22Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"648e716d3968a363df57e83fbbbf415ab3cd4850dc2a02d25ca8b8245de0871f","abstract_canon_sha256":"a69446415a0b8ca66cd0ad9782d41ad55c98f66cb947841f1c78946545f0b637"},"schema_version":"1.0"},"canonical_sha256":"707ec33f6f84dd108929ad1b463d3ebdbcb18636c472306e36147647b32a03d3","source":{"kind":"arxiv","id":"2311.04027","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.04027","created_at":"2026-07-05T07:50:21Z"},{"alias_kind":"arxiv_version","alias_value":"2311.04027v2","created_at":"2026-07-05T07:50:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.04027","created_at":"2026-07-05T07:50:21Z"},{"alias_kind":"pith_short_12","alias_value":"OB7MGP3PQTOR","created_at":"2026-07-05T07:50:21Z"},{"alias_kind":"pith_short_16","alias_value":"OB7MGP3PQTORBCJJ","created_at":"2026-07-05T07:50:21Z"},{"alias_kind":"pith_short_8","alias_value":"OB7MGP3P","created_at":"2026-07-05T07:50:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:OB7MGP3PQTORBCJJVUNUMPJ6XW","target":"record","payload":{"canonical_record":{"source":{"id":"2311.04027","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-11-07T14:26:22Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"648e716d3968a363df57e83fbbbf415ab3cd4850dc2a02d25ca8b8245de0871f","abstract_canon_sha256":"a69446415a0b8ca66cd0ad9782d41ad55c98f66cb947841f1c78946545f0b637"},"schema_version":"1.0"},"canonical_sha256":"707ec33f6f84dd108929ad1b463d3ebdbcb18636c472306e36147647b32a03d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:50:21.448138Z","signature_b64":"Woc+3kYM0MOqq2J+blMTd22B/acXLuuJbcdWOY7Re0GnxInHLOaPNW/vRzQjrTYmUZG8sVHYlC4L0IAXcsAAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"707ec33f6f84dd108929ad1b463d3ebdbcb18636c472306e36147647b32a03d3","last_reissued_at":"2026-07-05T07:50:21.447662Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:50:21.447662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.04027","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:50:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WnS8kf9QMhYjccHRTRloelYEnkycMeVpz35/XTNdiVqRnENDkYyTGlNw9QavGBpnfsxQUh+twwFWIgyrVeESBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T14:04:22.000691Z"},"content_sha256":"c69cb021ed5e5adfc59c27024d4e817647e9dee98eda349a406eff27998143bc","schema_version":"1.0","event_id":"sha256:c69cb021ed5e5adfc59c27024d4e817647e9dee98eda349a406eff27998143bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:OB7MGP3PQTORBCJJVUNUMPJ6XW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Harmonic analysis of Gaussian multiplicative chaos on the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.PR","authors_text":"Christophe Garban, Vincent Vargas","submitted_at":"2023-11-07T14:26:22Z","abstract_excerpt":"In this paper, we initiate the harmonic analysis of Gaussian multiplicative chaos (GMC) on the circle, i.e. the study of its Fourier coefficients. In particular, we show that almost surely GMC is a so-called Rajchman measure which means that its Fourier coefficients converge to $0$ when the frequency goes to infinity. We supplement this result with a convergence in law result for the rescaled Fourier coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.04027","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.04027/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:50:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hulnbcNIlUCgjyt2cDcRpmtVnMC+KJO/NaUt8usUCZWNL9JxxSlwlQsY+qNtq5oH0EQMuLLzZ+MZg9wWnn/8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T14:04:22.001635Z"},"content_sha256":"a9f7a2bed598a20127e1b6ee9e62b5abf1e123b38b1dc97f82b815a083b23393","schema_version":"1.0","event_id":"sha256:a9f7a2bed598a20127e1b6ee9e62b5abf1e123b38b1dc97f82b815a083b23393"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OB7MGP3PQTORBCJJVUNUMPJ6XW/bundle.json","state_url":"https://pith.science/pith/OB7MGP3PQTORBCJJVUNUMPJ6XW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OB7MGP3PQTORBCJJVUNUMPJ6XW/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":"2026-08-10T14:04:22Z","links":{"resolver":"https://pith.science/pith/OB7MGP3PQTORBCJJVUNUMPJ6XW","bundle":"https://pith.science/pith/OB7MGP3PQTORBCJJVUNUMPJ6XW/bundle.json","state":"https://pith.science/pith/OB7MGP3PQTORBCJJVUNUMPJ6XW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OB7MGP3PQTORBCJJVUNUMPJ6XW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:OB7MGP3PQTORBCJJVUNUMPJ6XW","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":"a69446415a0b8ca66cd0ad9782d41ad55c98f66cb947841f1c78946545f0b637","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-11-07T14:26:22Z","title_canon_sha256":"648e716d3968a363df57e83fbbbf415ab3cd4850dc2a02d25ca8b8245de0871f"},"schema_version":"1.0","source":{"id":"2311.04027","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.04027","created_at":"2026-07-05T07:50:21Z"},{"alias_kind":"arxiv_version","alias_value":"2311.04027v2","created_at":"2026-07-05T07:50:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.04027","created_at":"2026-07-05T07:50:21Z"},{"alias_kind":"pith_short_12","alias_value":"OB7MGP3PQTOR","created_at":"2026-07-05T07:50:21Z"},{"alias_kind":"pith_short_16","alias_value":"OB7MGP3PQTORBCJJ","created_at":"2026-07-05T07:50:21Z"},{"alias_kind":"pith_short_8","alias_value":"OB7MGP3P","created_at":"2026-07-05T07:50:21Z"}],"graph_snapshots":[{"event_id":"sha256:a9f7a2bed598a20127e1b6ee9e62b5abf1e123b38b1dc97f82b815a083b23393","target":"graph","created_at":"2026-07-05T07:50:21Z","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/2311.04027/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we initiate the harmonic analysis of Gaussian multiplicative chaos (GMC) on the circle, i.e. the study of its Fourier coefficients. In particular, we show that almost surely GMC is a so-called Rajchman measure which means that its Fourier coefficients converge to $0$ when the frequency goes to infinity. We supplement this result with a convergence in law result for the rescaled Fourier coefficients.","authors_text":"Christophe Garban, Vincent Vargas","cross_cats":["math-ph","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-11-07T14:26:22Z","title":"Harmonic analysis of Gaussian multiplicative chaos on the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.04027","kind":"arxiv","version":2},"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:c69cb021ed5e5adfc59c27024d4e817647e9dee98eda349a406eff27998143bc","target":"record","created_at":"2026-07-05T07:50:21Z","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":"a69446415a0b8ca66cd0ad9782d41ad55c98f66cb947841f1c78946545f0b637","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-11-07T14:26:22Z","title_canon_sha256":"648e716d3968a363df57e83fbbbf415ab3cd4850dc2a02d25ca8b8245de0871f"},"schema_version":"1.0","source":{"id":"2311.04027","kind":"arxiv","version":2}},"canonical_sha256":"707ec33f6f84dd108929ad1b463d3ebdbcb18636c472306e36147647b32a03d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"707ec33f6f84dd108929ad1b463d3ebdbcb18636c472306e36147647b32a03d3","first_computed_at":"2026-07-05T07:50:21.447662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:50:21.447662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Woc+3kYM0MOqq2J+blMTd22B/acXLuuJbcdWOY7Re0GnxInHLOaPNW/vRzQjrTYmUZG8sVHYlC4L0IAXcsAAAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:50:21.448138Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.04027","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c69cb021ed5e5adfc59c27024d4e817647e9dee98eda349a406eff27998143bc","sha256:a9f7a2bed598a20127e1b6ee9e62b5abf1e123b38b1dc97f82b815a083b23393"],"state_sha256":"432c72b0a03476ee5e97dbb44a097291446c06a1e4922eea8c16211d7f3b4bbf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tVOxZUt7ckiwESUrHOC/Hwwo6rVPSSAhQX0x0a5fRdMU6TvNkKbdibvahpWOL0a2ZtLAlf3oBCnMF73Z1io/CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T14:04:22.008682Z","bundle_sha256":"68057229d71c16fb60fb450004c3490cf07a6860234f057f195310e62ddced2d"}}