{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AOFWIDED5EQ2R34JG7H5MQ5ZPW","short_pith_number":"pith:AOFWIDED","canonical_record":{"source":{"id":"1612.02367","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-07T18:54:20Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"eee0977258233e79b6d9b4fd6bf3b3d7ed8ab6a7b2859bd5776f95868236c6e5","abstract_canon_sha256":"7b338849fdc91c3c3be358e4197997c0c9d9507b4bb9ce3976ed87c822dc3d65"},"schema_version":"1.0"},"canonical_sha256":"038b640c83e921a8ef8937cfd643b97d877403974d253947c12b623aea4b5766","source":{"kind":"arxiv","id":"1612.02367","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02367","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02367v2","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02367","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"AOFWIDED5EQ2","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AOFWIDED5EQ2R34J","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AOFWIDED","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AOFWIDED5EQ2R34JG7H5MQ5ZPW","target":"record","payload":{"canonical_record":{"source":{"id":"1612.02367","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-07T18:54:20Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"eee0977258233e79b6d9b4fd6bf3b3d7ed8ab6a7b2859bd5776f95868236c6e5","abstract_canon_sha256":"7b338849fdc91c3c3be358e4197997c0c9d9507b4bb9ce3976ed87c822dc3d65"},"schema_version":"1.0"},"canonical_sha256":"038b640c83e921a8ef8937cfd643b97d877403974d253947c12b623aea4b5766","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:05.430061Z","signature_b64":"kwPhjD5asqbrbtsH82VipGLVnKij/PxXKScC68G+F6pnP1Ym+2OfW04I01TKqgu4Ln8otFlmLGj87BUe3BVgBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"038b640c83e921a8ef8937cfd643b97d877403974d253947c12b623aea4b5766","last_reissued_at":"2026-05-18T00:18:05.429404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:05.429404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.02367","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":"2026-05-18T00:18:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HBfqOk1R4yJf22i+x9U8792enuklkGSSKMwdjUj0vgFbOL+HcSmkWj8unHYJB/DZ8b/KZDvcxe1YHqRj/qZDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:06:38.387019Z"},"content_sha256":"c0117a3bd37859c2f000239dbea0683778249b12f8932080202ce38096c918bf","schema_version":"1.0","event_id":"sha256:c0117a3bd37859c2f000239dbea0683778249b12f8932080202ce38096c918bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AOFWIDED5EQ2R34JG7H5MQ5ZPW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subcritical multiplicative chaos for regularized counting statistics from random matrix theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Dmitry Ostrovsky, Gaultier Lambert, Nick Simm","submitted_at":"2016-12-07T18:54:20Z","abstract_excerpt":"For an $N \\times N$ random unitary matrix $U_N$, we consider the random field defined by counting the number of eigenvalues of $U_N$ in a mesoscopic arc of the unit circle, regularized at an $N$-dependent scale $\\epsilon_N>0$. We prove that the renormalized exponential of this field converges as $N \\to \\infty$ to a Gaussian multiplicative chaos measure in the whole subcritical phase. In addition, we show that the moments of the total mass converge to a Selberg-like integral and by taking a further limit as the size of the arc diverges, we establish part of the conjectures in \\cite{Ost16}. By a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02367","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":""},"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":"2026-05-18T00:18:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LVItu9kAyjew4ZdphYSnAaepQJM3dJh6bSe7poF9pOWzC7XHHtOHkQCl9zSDTNcBYq+vAniv5lKIEiZDOxS7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:06:38.387687Z"},"content_sha256":"88cd8991e9c4cea8f6b8632ecdcd4dec1806369a06f18ebab3aaa325cef70bc9","schema_version":"1.0","event_id":"sha256:88cd8991e9c4cea8f6b8632ecdcd4dec1806369a06f18ebab3aaa325cef70bc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AOFWIDED5EQ2R34JG7H5MQ5ZPW/bundle.json","state_url":"https://pith.science/pith/AOFWIDED5EQ2R34JG7H5MQ5ZPW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AOFWIDED5EQ2R34JG7H5MQ5ZPW/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":"2026-05-30T05:06:38Z","links":{"resolver":"https://pith.science/pith/AOFWIDED5EQ2R34JG7H5MQ5ZPW","bundle":"https://pith.science/pith/AOFWIDED5EQ2R34JG7H5MQ5ZPW/bundle.json","state":"https://pith.science/pith/AOFWIDED5EQ2R34JG7H5MQ5ZPW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AOFWIDED5EQ2R34JG7H5MQ5ZPW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AOFWIDED5EQ2R34JG7H5MQ5ZPW","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":"7b338849fdc91c3c3be358e4197997c0c9d9507b4bb9ce3976ed87c822dc3d65","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-07T18:54:20Z","title_canon_sha256":"eee0977258233e79b6d9b4fd6bf3b3d7ed8ab6a7b2859bd5776f95868236c6e5"},"schema_version":"1.0","source":{"id":"1612.02367","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02367","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02367v2","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02367","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"AOFWIDED5EQ2","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AOFWIDED5EQ2R34J","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AOFWIDED","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:88cd8991e9c4cea8f6b8632ecdcd4dec1806369a06f18ebab3aaa325cef70bc9","target":"graph","created_at":"2026-05-18T00:18:05Z","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":"For an $N \\times N$ random unitary matrix $U_N$, we consider the random field defined by counting the number of eigenvalues of $U_N$ in a mesoscopic arc of the unit circle, regularized at an $N$-dependent scale $\\epsilon_N>0$. We prove that the renormalized exponential of this field converges as $N \\to \\infty$ to a Gaussian multiplicative chaos measure in the whole subcritical phase. In addition, we show that the moments of the total mass converge to a Selberg-like integral and by taking a further limit as the size of the arc diverges, we establish part of the conjectures in \\cite{Ost16}. By a","authors_text":"Dmitry Ostrovsky, Gaultier Lambert, Nick Simm","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-07T18:54:20Z","title":"Subcritical multiplicative chaos for regularized counting statistics from random matrix theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02367","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:c0117a3bd37859c2f000239dbea0683778249b12f8932080202ce38096c918bf","target":"record","created_at":"2026-05-18T00:18:05Z","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":"7b338849fdc91c3c3be358e4197997c0c9d9507b4bb9ce3976ed87c822dc3d65","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-07T18:54:20Z","title_canon_sha256":"eee0977258233e79b6d9b4fd6bf3b3d7ed8ab6a7b2859bd5776f95868236c6e5"},"schema_version":"1.0","source":{"id":"1612.02367","kind":"arxiv","version":2}},"canonical_sha256":"038b640c83e921a8ef8937cfd643b97d877403974d253947c12b623aea4b5766","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"038b640c83e921a8ef8937cfd643b97d877403974d253947c12b623aea4b5766","first_computed_at":"2026-05-18T00:18:05.429404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:05.429404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kwPhjD5asqbrbtsH82VipGLVnKij/PxXKScC68G+F6pnP1Ym+2OfW04I01TKqgu4Ln8otFlmLGj87BUe3BVgBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:05.430061Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02367","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0117a3bd37859c2f000239dbea0683778249b12f8932080202ce38096c918bf","sha256:88cd8991e9c4cea8f6b8632ecdcd4dec1806369a06f18ebab3aaa325cef70bc9"],"state_sha256":"166af223d91b0766faaf48c503c3d4350c10b1ab43a31f4be8aa72aa41080805"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MmR8mrJV9n4Mn41LKSGXnZWwz4J5/XTo78D9TUxsv+Qa2MBElgpY55mNnUjawBfPaYbpjWIJgK5Y2YRmxEvrAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:06:38.390615Z","bundle_sha256":"97e59f091b3b3faeff535dbe86616ad01e247c4359566b69d4e5c78d0bf4fcfd"}}