{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KRH5FGMB6KG6UWSGQTQP5TEVGE","short_pith_number":"pith:KRH5FGMB","canonical_record":{"source":{"id":"1509.01836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-06T17:43:44Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"3bf98eb8cb0254061d69f99d0ef7e9967787aeeafd8076799d28c2052d3978a6","abstract_canon_sha256":"9947ea0a568c6a829ef4ba6af1c0698db5cacd191a8e9682ef68c0cf99822d9b"},"schema_version":"1.0"},"canonical_sha256":"544fd29981f28dea5a4684e0fecc95310821405fd962e33b9a8896686c6c482a","source":{"kind":"arxiv","id":"1509.01836","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01836","created_at":"2026-05-18T01:00:53Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01836v1","created_at":"2026-05-18T01:00:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01836","created_at":"2026-05-18T01:00:53Z"},{"alias_kind":"pith_short_12","alias_value":"KRH5FGMB6KG6","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KRH5FGMB6KG6UWSG","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KRH5FGMB","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KRH5FGMB6KG6UWSGQTQP5TEVGE","target":"record","payload":{"canonical_record":{"source":{"id":"1509.01836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-06T17:43:44Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"3bf98eb8cb0254061d69f99d0ef7e9967787aeeafd8076799d28c2052d3978a6","abstract_canon_sha256":"9947ea0a568c6a829ef4ba6af1c0698db5cacd191a8e9682ef68c0cf99822d9b"},"schema_version":"1.0"},"canonical_sha256":"544fd29981f28dea5a4684e0fecc95310821405fd962e33b9a8896686c6c482a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:53.765140Z","signature_b64":"Ng439viWXoZXD4wDwXDP3cn29CadbDs0P2XH9Gv6DAY02iXma0MWJBLa8bBDCxUBI9Na5gaHmrXtjcX+t7X/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"544fd29981f28dea5a4684e0fecc95310821405fd962e33b9a8896686c6c482a","last_reissued_at":"2026-05-18T01:00:53.764579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:53.764579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.01836","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":"2026-05-18T01:00:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sZW+SbUa0R1dNTSsyW/so29ZODM63xtaOTg9j511BGBz90uNr6+qunszEUYDya5+lG8nrnPuE10LgjVeUERQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:25:02.785001Z"},"content_sha256":"d74d77ab8e93181e3d248b8dc2dbac5751818fbb6184237e33f72cad1d18f192","schema_version":"1.0","event_id":"sha256:d74d77ab8e93181e3d248b8dc2dbac5751818fbb6184237e33f72cad1d18f192"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KRH5FGMB6KG6UWSGQTQP5TEVGE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From convergence in distribution to uniform convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Albrecht Boettcher, Egor A. Maximenko, Johan Manuel Bogoya","submitted_at":"2015-09-06T17:43:44Z","abstract_excerpt":"We present conditions that allow us to pass from the convergence of probability measures in distribution to the uniform convergence of the associated quantile functions. Under these conditions, one can in particular pass from the asymptotic distribution of collections of real numbers, such as the eigenvalues of a family of $n$-by-$n$ matrices as $n$ goes to infinity, to their uniform approximation by the values of the quantile function at equidistant points. For Hermitian Toeplitz-like matrices, convergence in distribution is ensured by theorems of the Szeg\\H{o} type. Our results transfer thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01836","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":"2026-05-18T01:00:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hzQpA5dt/BzxDar5jKl1+Z/ySDI0GQbnvX/oUZF0BVhrKETiyGuFOEGhO6xRVw6o+pxipBGCDFEZA3qUV3KqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:25:02.785706Z"},"content_sha256":"ad60f1920b2a586bfae44e9ed7d436954817f487d974540e027ce1a0d4033a94","schema_version":"1.0","event_id":"sha256:ad60f1920b2a586bfae44e9ed7d436954817f487d974540e027ce1a0d4033a94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KRH5FGMB6KG6UWSGQTQP5TEVGE/bundle.json","state_url":"https://pith.science/pith/KRH5FGMB6KG6UWSGQTQP5TEVGE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KRH5FGMB6KG6UWSGQTQP5TEVGE/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":"2026-06-07T23:25:02Z","links":{"resolver":"https://pith.science/pith/KRH5FGMB6KG6UWSGQTQP5TEVGE","bundle":"https://pith.science/pith/KRH5FGMB6KG6UWSGQTQP5TEVGE/bundle.json","state":"https://pith.science/pith/KRH5FGMB6KG6UWSGQTQP5TEVGE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KRH5FGMB6KG6UWSGQTQP5TEVGE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KRH5FGMB6KG6UWSGQTQP5TEVGE","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":"9947ea0a568c6a829ef4ba6af1c0698db5cacd191a8e9682ef68c0cf99822d9b","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-06T17:43:44Z","title_canon_sha256":"3bf98eb8cb0254061d69f99d0ef7e9967787aeeafd8076799d28c2052d3978a6"},"schema_version":"1.0","source":{"id":"1509.01836","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01836","created_at":"2026-05-18T01:00:53Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01836v1","created_at":"2026-05-18T01:00:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01836","created_at":"2026-05-18T01:00:53Z"},{"alias_kind":"pith_short_12","alias_value":"KRH5FGMB6KG6","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KRH5FGMB6KG6UWSG","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KRH5FGMB","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:ad60f1920b2a586bfae44e9ed7d436954817f487d974540e027ce1a0d4033a94","target":"graph","created_at":"2026-05-18T01:00:53Z","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 present conditions that allow us to pass from the convergence of probability measures in distribution to the uniform convergence of the associated quantile functions. Under these conditions, one can in particular pass from the asymptotic distribution of collections of real numbers, such as the eigenvalues of a family of $n$-by-$n$ matrices as $n$ goes to infinity, to their uniform approximation by the values of the quantile function at equidistant points. For Hermitian Toeplitz-like matrices, convergence in distribution is ensured by theorems of the Szeg\\H{o} type. Our results transfer thes","authors_text":"Albrecht Boettcher, Egor A. Maximenko, Johan Manuel Bogoya","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-06T17:43:44Z","title":"From convergence in distribution to uniform convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01836","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:d74d77ab8e93181e3d248b8dc2dbac5751818fbb6184237e33f72cad1d18f192","target":"record","created_at":"2026-05-18T01:00:53Z","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":"9947ea0a568c6a829ef4ba6af1c0698db5cacd191a8e9682ef68c0cf99822d9b","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-06T17:43:44Z","title_canon_sha256":"3bf98eb8cb0254061d69f99d0ef7e9967787aeeafd8076799d28c2052d3978a6"},"schema_version":"1.0","source":{"id":"1509.01836","kind":"arxiv","version":1}},"canonical_sha256":"544fd29981f28dea5a4684e0fecc95310821405fd962e33b9a8896686c6c482a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"544fd29981f28dea5a4684e0fecc95310821405fd962e33b9a8896686c6c482a","first_computed_at":"2026-05-18T01:00:53.764579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:53.764579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ng439viWXoZXD4wDwXDP3cn29CadbDs0P2XH9Gv6DAY02iXma0MWJBLa8bBDCxUBI9Na5gaHmrXtjcX+t7X/DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:53.765140Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01836","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d74d77ab8e93181e3d248b8dc2dbac5751818fbb6184237e33f72cad1d18f192","sha256:ad60f1920b2a586bfae44e9ed7d436954817f487d974540e027ce1a0d4033a94"],"state_sha256":"768f264863bfb389500e5327e93364bba011372d92bf5f5c991a9b42db55c772"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ZfYIqVP4agy/G9+ic/PmxbjMniGFPVNWRzcRUgRxA2IcTEk4XL5VQbZELjZ/UqcPUPdvfrYzEOFlsRG8GxlBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T23:25:02.789655Z","bundle_sha256":"cf81713f15076ddc8dc8f0bb5c4020ac3e863b2a319437d74d266b27fed5fa92"}}