{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HAEVFDGT4FU6WISUZV6CSWT6NU","short_pith_number":"pith:HAEVFDGT","canonical_record":{"source":{"id":"1803.06677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-18T15:33:52Z","cross_cats_sorted":[],"title_canon_sha256":"c62a4101444ad5a190ebc63b9737cc5afb415cebfd2740988ab8e46985274bbf","abstract_canon_sha256":"e2f8a7af7bfb6321b82758d9f0e649921bc91111ba494a21d39fac0e4fabb9f2"},"schema_version":"1.0"},"canonical_sha256":"3809528cd3e169eb2254cd7c295a7e6d0baaf855b6a6c7444aa8f133e1bf696c","source":{"kind":"arxiv","id":"1803.06677","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06677","created_at":"2026-05-18T00:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06677v1","created_at":"2026-05-18T00:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06677","created_at":"2026-05-18T00:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"HAEVFDGT4FU6","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HAEVFDGT4FU6WISU","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HAEVFDGT","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HAEVFDGT4FU6WISUZV6CSWT6NU","target":"record","payload":{"canonical_record":{"source":{"id":"1803.06677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-18T15:33:52Z","cross_cats_sorted":[],"title_canon_sha256":"c62a4101444ad5a190ebc63b9737cc5afb415cebfd2740988ab8e46985274bbf","abstract_canon_sha256":"e2f8a7af7bfb6321b82758d9f0e649921bc91111ba494a21d39fac0e4fabb9f2"},"schema_version":"1.0"},"canonical_sha256":"3809528cd3e169eb2254cd7c295a7e6d0baaf855b6a6c7444aa8f133e1bf696c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:12.646500Z","signature_b64":"VmCdL/MzQ80/AN5NtleMwx1KrpZ/ZMiZ8pKrMSF3Am3KrBClLsRhUJi5Y7xO/STpFd+Vh7ePpklgrcyZ2XxLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3809528cd3e169eb2254cd7c295a7e6d0baaf855b6a6c7444aa8f133e1bf696c","last_reissued_at":"2026-05-18T00:02:12.645834Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:12.645834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.06677","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UwiEosS723NULlh/EdkSR//7a5AmweSPpx9wqXSV6/cp5Hu/5J0wN3kF6ivmJ83PElxk4JvUgynbk2OkmR01Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:24:11.107533Z"},"content_sha256":"47e64d61605dcfb950ead13d6db4ce82f113edc55935f9a06a0ec7b1c4d016d2","schema_version":"1.0","event_id":"sha256:47e64d61605dcfb950ead13d6db4ce82f113edc55935f9a06a0ec7b1c4d016d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HAEVFDGT4FU6WISUZV6CSWT6NU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Review of Conjectured Laws of Total Mass of Bacry-Muzy GMC Measures on the Interval and Circle and Their Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dmitry Ostrovsky","submitted_at":"2018-03-18T15:33:52Z","abstract_excerpt":"Selberg and Morris integral probability distributions are long conjectured to be distributions of the total mass of the Bacry-Muzy Gaussian Multiplicative Chaos measures with non-random logarithmic potentials on the unit interval and circle, respectively. The construction and properties of these distributions are reviewed from three perspectives: analytic based on several representations of the Mellin transform, asymptotic based on low intermittency expansions, and probabilistic based on the theory of Barnes beta probability distributions. In particular, positive and negative integer moments, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06677","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:02:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bCeyfRB4f2glD30IlHDhiWLpi6XgxXZoPAnCiV9y4P83WTjIrHapOJpeCNj1qZZmFRYKb0EXHnslZ3aojE96BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:24:11.107888Z"},"content_sha256":"7cc31159348ed23707678dd6e59aedc92845c31edf42db408a4071d79aa17663","schema_version":"1.0","event_id":"sha256:7cc31159348ed23707678dd6e59aedc92845c31edf42db408a4071d79aa17663"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HAEVFDGT4FU6WISUZV6CSWT6NU/bundle.json","state_url":"https://pith.science/pith/HAEVFDGT4FU6WISUZV6CSWT6NU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HAEVFDGT4FU6WISUZV6CSWT6NU/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":"2026-05-30T20:24:11Z","links":{"resolver":"https://pith.science/pith/HAEVFDGT4FU6WISUZV6CSWT6NU","bundle":"https://pith.science/pith/HAEVFDGT4FU6WISUZV6CSWT6NU/bundle.json","state":"https://pith.science/pith/HAEVFDGT4FU6WISUZV6CSWT6NU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HAEVFDGT4FU6WISUZV6CSWT6NU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HAEVFDGT4FU6WISUZV6CSWT6NU","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":"e2f8a7af7bfb6321b82758d9f0e649921bc91111ba494a21d39fac0e4fabb9f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-18T15:33:52Z","title_canon_sha256":"c62a4101444ad5a190ebc63b9737cc5afb415cebfd2740988ab8e46985274bbf"},"schema_version":"1.0","source":{"id":"1803.06677","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06677","created_at":"2026-05-18T00:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06677v1","created_at":"2026-05-18T00:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06677","created_at":"2026-05-18T00:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"HAEVFDGT4FU6","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HAEVFDGT4FU6WISU","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HAEVFDGT","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:7cc31159348ed23707678dd6e59aedc92845c31edf42db408a4071d79aa17663","target":"graph","created_at":"2026-05-18T00:02:12Z","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":"Selberg and Morris integral probability distributions are long conjectured to be distributions of the total mass of the Bacry-Muzy Gaussian Multiplicative Chaos measures with non-random logarithmic potentials on the unit interval and circle, respectively. The construction and properties of these distributions are reviewed from three perspectives: analytic based on several representations of the Mellin transform, asymptotic based on low intermittency expansions, and probabilistic based on the theory of Barnes beta probability distributions. In particular, positive and negative integer moments, ","authors_text":"Dmitry Ostrovsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-18T15:33:52Z","title":"A Review of Conjectured Laws of Total Mass of Bacry-Muzy GMC Measures on the Interval and Circle and Their Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06677","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":"sha256:47e64d61605dcfb950ead13d6db4ce82f113edc55935f9a06a0ec7b1c4d016d2","target":"record","created_at":"2026-05-18T00:02:12Z","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":"e2f8a7af7bfb6321b82758d9f0e649921bc91111ba494a21d39fac0e4fabb9f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-18T15:33:52Z","title_canon_sha256":"c62a4101444ad5a190ebc63b9737cc5afb415cebfd2740988ab8e46985274bbf"},"schema_version":"1.0","source":{"id":"1803.06677","kind":"arxiv","version":1}},"canonical_sha256":"3809528cd3e169eb2254cd7c295a7e6d0baaf855b6a6c7444aa8f133e1bf696c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3809528cd3e169eb2254cd7c295a7e6d0baaf855b6a6c7444aa8f133e1bf696c","first_computed_at":"2026-05-18T00:02:12.645834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:12.645834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VmCdL/MzQ80/AN5NtleMwx1KrpZ/ZMiZ8pKrMSF3Am3KrBClLsRhUJi5Y7xO/STpFd+Vh7ePpklgrcyZ2XxLBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:12.646500Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.06677","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47e64d61605dcfb950ead13d6db4ce82f113edc55935f9a06a0ec7b1c4d016d2","sha256:7cc31159348ed23707678dd6e59aedc92845c31edf42db408a4071d79aa17663"],"state_sha256":"709bbfa45a55a06fb4a5eaec489e7c76dbb7d7445ee4edc47399886114f8ed9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bL+CFZl7q7A98BvsfUoHQrcJG2kWflgZkPmvPgPSUHEYWcw+iwFXCCfOlZ4Uso09fwET1j54XwHADxebYIUEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:24:11.110180Z","bundle_sha256":"09ab9a0416a2fafb5306deafb419d3d6fbd651056c0504d0a9092e7a6ebe0fbe"}}