{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:U5RCD4EMONTWQWAWVEIK5J2WMT","short_pith_number":"pith:U5RCD4EM","canonical_record":{"source":{"id":"1312.7769","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-30T16:29:48Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"2a9d8d5e7fa9e78f690f3c2062ac50b8e359d617b465d294b73fe785b6ed62d9","abstract_canon_sha256":"027d379e2b16f8ac033882e165ef156cb00b7fa010cb43fc4ad03c07a8ab23f2"},"schema_version":"1.0"},"canonical_sha256":"a76221f08c7367685816a910aea75664d4ada40f1b9b3e857a7823818c8bed70","source":{"kind":"arxiv","id":"1312.7769","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7769","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7769v2","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7769","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"pith_short_12","alias_value":"U5RCD4EMONTW","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U5RCD4EMONTWQWAW","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U5RCD4EM","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:U5RCD4EMONTWQWAWVEIK5J2WMT","target":"record","payload":{"canonical_record":{"source":{"id":"1312.7769","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-30T16:29:48Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"2a9d8d5e7fa9e78f690f3c2062ac50b8e359d617b465d294b73fe785b6ed62d9","abstract_canon_sha256":"027d379e2b16f8ac033882e165ef156cb00b7fa010cb43fc4ad03c07a8ab23f2"},"schema_version":"1.0"},"canonical_sha256":"a76221f08c7367685816a910aea75664d4ada40f1b9b3e857a7823818c8bed70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:44.592781Z","signature_b64":"FGh6YuUOEmYR7hjAzR+g7p89jkWGlJR2ZcueEWJnCR9UwXlfWZqUOEhbDFr60h9heJqbk8/ndz6b/rOtLb/wCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a76221f08c7367685816a910aea75664d4ada40f1b9b3e857a7823818c8bed70","last_reissued_at":"2026-05-18T00:35:44.592359Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:44.592359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.7769","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":"2026-05-18T00:35:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oFAI9kDqeYv6fKVEaW4kdvyf9NC77ls7pSibRkJEG6mSAdQftyek6upKZXhAZhv/JZdtLSeOf+rqJ77pssoEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T21:53:25.429734Z"},"content_sha256":"c1d51e72d839bbdebc4d53c5881ebaa4c149cff5a3f5a5a353400bee33523549","schema_version":"1.0","event_id":"sha256:c1d51e72d839bbdebc4d53c5881ebaa4c149cff5a3f5a5a353400bee33523549"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:U5RCD4EMONTWQWAWVEIK5J2WMT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the ubiquity of the Cauchy distribution in spectral problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Michael Aizenman, Simone Warzel","submitted_at":"2013-12-30T16:29:48Z","abstract_excerpt":"We consider the distribution of the values at real points of random functions which belong to the Herglotz-Pick (HP) class of analytic mappings of the upper half plane into itself. It is shown that under mild stationarity assumptions the individual values of HP functions with singular spectra have a Cauchy type distribution. The statement applies to the diagonal matrix elements of random operators, and holds regardless of the presence or not of level repulsion, i.e. applies to both random matrix and Poisson-type spectra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7769","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":"2026-05-18T00:35:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r8qu9KvSIr0+Ha42jveVsjiqrSuQfpwwT1a6RPIKSFXVJeteXyLf7tA9owJaeZ0GcW2foQx8MYDed5mqMPyiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T21:53:25.430447Z"},"content_sha256":"97e36c4a438073c2bf789fab3c5ba8ae40a4b130cda0e9863a29436124ac3667","schema_version":"1.0","event_id":"sha256:97e36c4a438073c2bf789fab3c5ba8ae40a4b130cda0e9863a29436124ac3667"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U5RCD4EMONTWQWAWVEIK5J2WMT/bundle.json","state_url":"https://pith.science/pith/U5RCD4EMONTWQWAWVEIK5J2WMT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U5RCD4EMONTWQWAWVEIK5J2WMT/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":"2026-05-22T21:53:25Z","links":{"resolver":"https://pith.science/pith/U5RCD4EMONTWQWAWVEIK5J2WMT","bundle":"https://pith.science/pith/U5RCD4EMONTWQWAWVEIK5J2WMT/bundle.json","state":"https://pith.science/pith/U5RCD4EMONTWQWAWVEIK5J2WMT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U5RCD4EMONTWQWAWVEIK5J2WMT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U5RCD4EMONTWQWAWVEIK5J2WMT","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":"027d379e2b16f8ac033882e165ef156cb00b7fa010cb43fc4ad03c07a8ab23f2","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-30T16:29:48Z","title_canon_sha256":"2a9d8d5e7fa9e78f690f3c2062ac50b8e359d617b465d294b73fe785b6ed62d9"},"schema_version":"1.0","source":{"id":"1312.7769","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7769","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7769v2","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7769","created_at":"2026-05-18T00:35:44Z"},{"alias_kind":"pith_short_12","alias_value":"U5RCD4EMONTW","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U5RCD4EMONTWQWAW","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U5RCD4EM","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:97e36c4a438073c2bf789fab3c5ba8ae40a4b130cda0e9863a29436124ac3667","target":"graph","created_at":"2026-05-18T00:35:44Z","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 consider the distribution of the values at real points of random functions which belong to the Herglotz-Pick (HP) class of analytic mappings of the upper half plane into itself. It is shown that under mild stationarity assumptions the individual values of HP functions with singular spectra have a Cauchy type distribution. The statement applies to the diagonal matrix elements of random operators, and holds regardless of the presence or not of level repulsion, i.e. applies to both random matrix and Poisson-type spectra.","authors_text":"Michael Aizenman, Simone Warzel","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-30T16:29:48Z","title":"On the ubiquity of the Cauchy distribution in spectral problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7769","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:c1d51e72d839bbdebc4d53c5881ebaa4c149cff5a3f5a5a353400bee33523549","target":"record","created_at":"2026-05-18T00:35:44Z","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":"027d379e2b16f8ac033882e165ef156cb00b7fa010cb43fc4ad03c07a8ab23f2","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-30T16:29:48Z","title_canon_sha256":"2a9d8d5e7fa9e78f690f3c2062ac50b8e359d617b465d294b73fe785b6ed62d9"},"schema_version":"1.0","source":{"id":"1312.7769","kind":"arxiv","version":2}},"canonical_sha256":"a76221f08c7367685816a910aea75664d4ada40f1b9b3e857a7823818c8bed70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a76221f08c7367685816a910aea75664d4ada40f1b9b3e857a7823818c8bed70","first_computed_at":"2026-05-18T00:35:44.592359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:44.592359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FGh6YuUOEmYR7hjAzR+g7p89jkWGlJR2ZcueEWJnCR9UwXlfWZqUOEhbDFr60h9heJqbk8/ndz6b/rOtLb/wCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:44.592781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7769","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1d51e72d839bbdebc4d53c5881ebaa4c149cff5a3f5a5a353400bee33523549","sha256:97e36c4a438073c2bf789fab3c5ba8ae40a4b130cda0e9863a29436124ac3667"],"state_sha256":"abff43f455fa06c12cda24f5a5922af302853829545a53a22de70144728f6c46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FIzrs+OogD4V5cwiiZ6gmtcdp2RGYP53LWXO2tr4TobnOpCza3IvRkFMolX6ut0dCrZ7A+GlZMb0wCHEbr9OBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T21:53:25.434184Z","bundle_sha256":"26c7cf83ffd1fe73ed4ce51c50ecab46de9a7a397f8f835aa4a4e429d556cc4e"}}