{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TN2H5PC2SGG45R2Q2456JIIOJN","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":"d5b9b45b9cf4c3398738cb1657fee93d5c0c48a45beae5d5a19a99a45c0ef103","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-16T18:31:25Z","title_canon_sha256":"acde3cff8b8bfdb0a07b44fadcf707a6c4784c5c1dc0520f7ef81d3a374cd3b5"},"schema_version":"1.0","source":{"id":"1407.4418","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4418","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4418v4","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4418","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"pith_short_12","alias_value":"TN2H5PC2SGG4","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TN2H5PC2SGG45R2Q","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TN2H5PC2","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:4bc92c8eea854d09cf31bdf81ab3404d2d26a343c43cdc70f6c58c7be3bc3b18","target":"graph","created_at":"2026-05-18T01:13:31Z","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 propose a new definition of the Gaussian multiplicative chaos (GMC) and an approach based on the relation of subcritical GMC to randomized shifts of a Gaussian measure. Using this relation we prove general uniqueness and convergence results for subcritical GMC that hold for Gaussian fields with arbitrary covariance kernels.","authors_text":"Alexander Shamov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-16T18:31:25Z","title":"On Gaussian multiplicative chaos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4418","kind":"arxiv","version":4},"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":"sha256:3b09db830e849e66198ca81169bb77189d31fb8c8c3f7a3e630ad8c4e9387c46","target":"record","created_at":"2026-05-18T01:13:31Z","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":"d5b9b45b9cf4c3398738cb1657fee93d5c0c48a45beae5d5a19a99a45c0ef103","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-16T18:31:25Z","title_canon_sha256":"acde3cff8b8bfdb0a07b44fadcf707a6c4784c5c1dc0520f7ef81d3a374cd3b5"},"schema_version":"1.0","source":{"id":"1407.4418","kind":"arxiv","version":4}},"canonical_sha256":"9b747ebc5a918dcec750d73be4a10e4b7cc627f7f07b758437a20d74906f8caf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b747ebc5a918dcec750d73be4a10e4b7cc627f7f07b758437a20d74906f8caf","first_computed_at":"2026-05-18T01:13:31.174146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:31.174146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nSVNqxk13oWgqWM4tyFvCrh8EzjG2qK/dBdlsXRply2tHN+xI3lw6hdXejH6ezE8XHOk1XKdgonZ4t4F9n2RBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:31.174840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4418","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b09db830e849e66198ca81169bb77189d31fb8c8c3f7a3e630ad8c4e9387c46","sha256:4bc92c8eea854d09cf31bdf81ab3404d2d26a343c43cdc70f6c58c7be3bc3b18"],"state_sha256":"4838688c13a17001ab8e09df1d3f7b4e2d6e45bed8f1c4b813703b6346c341e4"}