{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:45M4M3OC3OAREZY73C6TFL4E6I","short_pith_number":"pith:45M4M3OC","canonical_record":{"source":{"id":"1303.4548","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-19T11:04:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"682ba79e15c9fd2d40a3e7ee9a53ed9d0e1810fd169f0e7cb7b5c41a4a8bf577","abstract_canon_sha256":"a29c6a02b0d6f022d72d91124cd41f0e23d348503e11ecb86ddc2621b928e71e"},"schema_version":"1.0"},"canonical_sha256":"e759c66dc2db8112671fd8bd32af84f2132b83f353967e2ee4cec02a27ecbfe6","source":{"kind":"arxiv","id":"1303.4548","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4548","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4548v4","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4548","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"pith_short_12","alias_value":"45M4M3OC3OAR","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"45M4M3OC3OAREZY7","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"45M4M3OC","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:45M4M3OC3OAREZY73C6TFL4E6I","target":"record","payload":{"canonical_record":{"source":{"id":"1303.4548","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-19T11:04:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"682ba79e15c9fd2d40a3e7ee9a53ed9d0e1810fd169f0e7cb7b5c41a4a8bf577","abstract_canon_sha256":"a29c6a02b0d6f022d72d91124cd41f0e23d348503e11ecb86ddc2621b928e71e"},"schema_version":"1.0"},"canonical_sha256":"e759c66dc2db8112671fd8bd32af84f2132b83f353967e2ee4cec02a27ecbfe6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:13.575670Z","signature_b64":"etNyGGf4YVOSyAItviifAxfnS6Svln+yn4YkGjQ7bzVKnKuSWI0+Q9hVhANV7HifhYjXY+lMWfDl3wi2uYkqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e759c66dc2db8112671fd8bd32af84f2132b83f353967e2ee4cec02a27ecbfe6","last_reissued_at":"2026-05-18T01:29:13.574992Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:13.574992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.4548","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:29:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Veg8k0zmChhT8tSshuoGFZ+GnSrpRgmajIN9nZhCvLT8Uc6Hc70bZBUc2h/2QF4Zj/lmNcx34tCaDgMxnbIKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:14:48.433090Z"},"content_sha256":"dd2d68a651898ab000262e81e6c1d662c857db8182a6025f5ba75746f6dbc3e6","schema_version":"1.0","event_id":"sha256:dd2d68a651898ab000262e81e6c1d662c857db8182a6025f5ba75746f6dbc3e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:45M4M3OC3OAREZY73C6TFL4E6I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Basic properties of critical lognormal multiplicative chaos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Antti Kupiainen, Christian Webb, Eero Saksman, Julien Barral, Miika Nikula","submitted_at":"2013-03-19T11:04:31Z","abstract_excerpt":"We study one-dimensional exact scaling lognormal multiplicative chaos measures at criticality. Our main results are the determination of the exact asymptotics of the right tail of the distribution of the total mass of the measure, and an almost sure upper bound for the modulus of continuity of the cumulative distribution function of the measure. We also find an almost sure lower bound for the increments of the measure almost everywhere with respect to the measure itself, strong enough to show that the measure is supported on a set of Hausdorff dimension $0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4548","kind":"arxiv","version":4},"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":"2026-05-18T01:29:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RObslUr+GN6VcAkg8fnc13h6tO1jvILzVvwrRc6a0K26f6e9+bcobYuR4t6HrDFLYineYrwebBQFqkNG8OFMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:14:48.433457Z"},"content_sha256":"2a77bb3b89af4842951ad1d69f364a72e5bfb771e137616d333c2fb6673ff846","schema_version":"1.0","event_id":"sha256:2a77bb3b89af4842951ad1d69f364a72e5bfb771e137616d333c2fb6673ff846"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/45M4M3OC3OAREZY73C6TFL4E6I/bundle.json","state_url":"https://pith.science/pith/45M4M3OC3OAREZY73C6TFL4E6I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/45M4M3OC3OAREZY73C6TFL4E6I/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":"2026-07-01T21:14:48Z","links":{"resolver":"https://pith.science/pith/45M4M3OC3OAREZY73C6TFL4E6I","bundle":"https://pith.science/pith/45M4M3OC3OAREZY73C6TFL4E6I/bundle.json","state":"https://pith.science/pith/45M4M3OC3OAREZY73C6TFL4E6I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/45M4M3OC3OAREZY73C6TFL4E6I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:45M4M3OC3OAREZY73C6TFL4E6I","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":"a29c6a02b0d6f022d72d91124cd41f0e23d348503e11ecb86ddc2621b928e71e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-19T11:04:31Z","title_canon_sha256":"682ba79e15c9fd2d40a3e7ee9a53ed9d0e1810fd169f0e7cb7b5c41a4a8bf577"},"schema_version":"1.0","source":{"id":"1303.4548","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4548","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4548v4","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4548","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"pith_short_12","alias_value":"45M4M3OC3OAR","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"45M4M3OC3OAREZY7","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"45M4M3OC","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:2a77bb3b89af4842951ad1d69f364a72e5bfb771e137616d333c2fb6673ff846","target":"graph","created_at":"2026-05-18T01:29:13Z","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 study one-dimensional exact scaling lognormal multiplicative chaos measures at criticality. Our main results are the determination of the exact asymptotics of the right tail of the distribution of the total mass of the measure, and an almost sure upper bound for the modulus of continuity of the cumulative distribution function of the measure. We also find an almost sure lower bound for the increments of the measure almost everywhere with respect to the measure itself, strong enough to show that the measure is supported on a set of Hausdorff dimension $0$.","authors_text":"Antti Kupiainen, Christian Webb, Eero Saksman, Julien Barral, Miika Nikula","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-19T11:04:31Z","title":"Basic properties of critical lognormal multiplicative chaos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4548","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:dd2d68a651898ab000262e81e6c1d662c857db8182a6025f5ba75746f6dbc3e6","target":"record","created_at":"2026-05-18T01:29:13Z","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":"a29c6a02b0d6f022d72d91124cd41f0e23d348503e11ecb86ddc2621b928e71e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-19T11:04:31Z","title_canon_sha256":"682ba79e15c9fd2d40a3e7ee9a53ed9d0e1810fd169f0e7cb7b5c41a4a8bf577"},"schema_version":"1.0","source":{"id":"1303.4548","kind":"arxiv","version":4}},"canonical_sha256":"e759c66dc2db8112671fd8bd32af84f2132b83f353967e2ee4cec02a27ecbfe6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e759c66dc2db8112671fd8bd32af84f2132b83f353967e2ee4cec02a27ecbfe6","first_computed_at":"2026-05-18T01:29:13.574992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:13.574992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"etNyGGf4YVOSyAItviifAxfnS6Svln+yn4YkGjQ7bzVKnKuSWI0+Q9hVhANV7HifhYjXY+lMWfDl3wi2uYkqBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:13.575670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4548","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd2d68a651898ab000262e81e6c1d662c857db8182a6025f5ba75746f6dbc3e6","sha256:2a77bb3b89af4842951ad1d69f364a72e5bfb771e137616d333c2fb6673ff846"],"state_sha256":"615ad320ee0b5e58e7790513a8051f7d46af59a82a2d229cfd72fb32a9b74328"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ti+Do0ajX3TNDjwU9Qmk/H7qQ7wz/zoQ9w0xL9I0Ig4/XsARrGrBhOa6PjrNfd0KMngnC+0H5yOR5R+9rEFCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T21:14:48.435424Z","bundle_sha256":"ad8afa8568bd6196e5c2b69a3f9d7c4ccb9550d6b0de11f7fcf845042e95deec"}}