{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:P3LBEOV4YJQD2YDJ57A3WO3VIS","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":"9ddee97657d276359a32f3cf974c398a846162ed77a678cdbdac4408811bf8e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-13T14:38:11Z","title_canon_sha256":"1c3f63d1ae9d3b66d12b583dca97bf182a1bb299c469bbe4ff97940404efa147"},"schema_version":"1.0","source":{"id":"1709.04355","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04355","created_at":"2026-07-05T00:59:09Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04355v3","created_at":"2026-07-05T00:59:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04355","created_at":"2026-07-05T00:59:09Z"},{"alias_kind":"pith_short_12","alias_value":"P3LBEOV4YJQD","created_at":"2026-07-05T00:59:09Z"},{"alias_kind":"pith_short_16","alias_value":"P3LBEOV4YJQD2YDJ","created_at":"2026-07-05T00:59:09Z"},{"alias_kind":"pith_short_8","alias_value":"P3LBEOV4","created_at":"2026-07-05T00:59:09Z"}],"graph_snapshots":[{"event_id":"sha256:862db2f84849af02ddd4b910f5e68823f36324ca85526ae2bc80b8d681f71f7c","target":"graph","created_at":"2026-07-05T00:59:09Z","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/1709.04355/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The aim of this review-style paper is to provide a concise, self-contained and unified presentation of the construction and main properties of Gaussian multiplicative chaos (GMC) measures for log-correlated fields in 2D in the subcritical regime. By considering the case of the 2D Gaussian free field, we review convergence, uniqueness and characterisations of the measures; revisit Kahane's convexity inequalities and existence and scaling of moments; discuss the measurability of the underlying field with respect to the GMC measure and present a KPZ relation for scaling exponents.","authors_text":"Juhan Aru","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-13T14:38:11Z","title":"Gaussian multiplicative chaos through the lens of the 2D Gaussian free field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04355","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:c7e29473c4b8d04d02d4c3cfbae3ca81ef0049e78c5fceca0bd8808e8cc94adb","target":"record","created_at":"2026-07-05T00:59:09Z","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":"9ddee97657d276359a32f3cf974c398a846162ed77a678cdbdac4408811bf8e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-13T14:38:11Z","title_canon_sha256":"1c3f63d1ae9d3b66d12b583dca97bf182a1bb299c469bbe4ff97940404efa147"},"schema_version":"1.0","source":{"id":"1709.04355","kind":"arxiv","version":3}},"canonical_sha256":"7ed6123abcc2603d6069efc1bb3b7544a52357920fa6b1b9afcf4e82a733be2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ed6123abcc2603d6069efc1bb3b7544a52357920fa6b1b9afcf4e82a733be2f","first_computed_at":"2026-07-05T00:59:09.885967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:59:09.885967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WsgObC/5LeAgNpSJ6V8vYo24fKnwl2Ka7voVG9j5s+N5mvzGbPj3t3jn7sIt2zZCmbTl7zzZXLgCyj1yMVZNBw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:59:09.886429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04355","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7e29473c4b8d04d02d4c3cfbae3ca81ef0049e78c5fceca0bd8808e8cc94adb","sha256:862db2f84849af02ddd4b910f5e68823f36324ca85526ae2bc80b8d681f71f7c"],"state_sha256":"3ddc8ceade0f468719e09bb79b64a92e139d988f9fbfe10e16cdab28cfe74f7e"}