{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QVDT7S4EGAGUTQGE3WT5GPA364","short_pith_number":"pith:QVDT7S4E","canonical_record":{"source":{"id":"1111.4591","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-19T22:29:05Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"bbe92fec77a5140d5f710ff4d098f546186ab60af5e761342ecf17524b847320","abstract_canon_sha256":"9a7b26a5d81748b72b7593a9d2e6870bac8711ac71621aacfe80496f231c8d4e"},"schema_version":"1.0"},"canonical_sha256":"85473fcb84300d49c0c4dda7d33c1bf73b1689c7d31c24e26e9fdb8d1450d515","source":{"kind":"arxiv","id":"1111.4591","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4591","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4591v1","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4591","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"pith_short_12","alias_value":"QVDT7S4EGAGU","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QVDT7S4EGAGUTQGE","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QVDT7S4E","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QVDT7S4EGAGUTQGE3WT5GPA364","target":"record","payload":{"canonical_record":{"source":{"id":"1111.4591","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-19T22:29:05Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"bbe92fec77a5140d5f710ff4d098f546186ab60af5e761342ecf17524b847320","abstract_canon_sha256":"9a7b26a5d81748b72b7593a9d2e6870bac8711ac71621aacfe80496f231c8d4e"},"schema_version":"1.0"},"canonical_sha256":"85473fcb84300d49c0c4dda7d33c1bf73b1689c7d31c24e26e9fdb8d1450d515","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:03.031349Z","signature_b64":"6f9bi1Ktfwxb6rA9v3RkC38Dr3/BjSQF0Di3iwSM0ewidYdr7VWXAnDWcgLmdlr8aFgEWX/Ou0+9L38q60lZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85473fcb84300d49c0c4dda7d33c1bf73b1689c7d31c24e26e9fdb8d1450d515","last_reissued_at":"2026-05-18T04:08:03.030893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:03.030893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.4591","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":"2026-05-18T04:08:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5kf+2kNJI7pbtiNg/PkG8+g9dw+aYNNDjlKg9irzsk3saEm16AddGM6fOeuxSJFs+0E42uF5JOS5+4e6rJviBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:59:48.248502Z"},"content_sha256":"08283b6867d4e5431107940338acf7e55ab776add065c49b847278d601ab5e0c","schema_version":"1.0","event_id":"sha256:08283b6867d4e5431107940338acf7e55ab776add065c49b847278d601ab5e0c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QVDT7S4EGAGUTQGE3WT5GPA364","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Empirical Quantile CLTs for Time Dependent Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"James Kuelbs, Joel Zinn","submitted_at":"2011-11-19T22:29:05Z","abstract_excerpt":"We establish empirical quantile process CLTs based on $n$ independent copies of a stochastic process $\\{X_t: t \\in E\\}$ that are uniform in $t \\in E$ and quantile levels $\\alpha \\in I$, where $I$ is a closed sub-interval of $(0,1)$. Typically $E=[0,T]$, or a finite product of such intervals. Also included are CLT's for the empirical process based on $\\{I_{X_t \\le y} - \\rm {Pr}(X_t \\le y): t \\in E, y \\in R \\}$ that are uniform in $t \\in E, y \\in R$. The process $\\{X_t: t \\in E\\}$ may be chosen from a broad collection of Gaussian processes, compound Poisson processes, stationary independent incr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4591","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":"2026-05-18T04:08:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CLIpGsUpwW0zZaJwVdhnAXlB3gNMEqV7TAogH7zz/C23ganHVX61roqiXj+5Fv+6k+H/+3IxrOQSV25ODo1uBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:59:48.249108Z"},"content_sha256":"dd7252b5969e3296d39e67ef867d5016ad16d190c5ca76a32371d3b1dcbd27f3","schema_version":"1.0","event_id":"sha256:dd7252b5969e3296d39e67ef867d5016ad16d190c5ca76a32371d3b1dcbd27f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVDT7S4EGAGUTQGE3WT5GPA364/bundle.json","state_url":"https://pith.science/pith/QVDT7S4EGAGUTQGE3WT5GPA364/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVDT7S4EGAGUTQGE3WT5GPA364/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":"2026-06-11T03:59:48Z","links":{"resolver":"https://pith.science/pith/QVDT7S4EGAGUTQGE3WT5GPA364","bundle":"https://pith.science/pith/QVDT7S4EGAGUTQGE3WT5GPA364/bundle.json","state":"https://pith.science/pith/QVDT7S4EGAGUTQGE3WT5GPA364/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVDT7S4EGAGUTQGE3WT5GPA364/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QVDT7S4EGAGUTQGE3WT5GPA364","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":"9a7b26a5d81748b72b7593a9d2e6870bac8711ac71621aacfe80496f231c8d4e","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-19T22:29:05Z","title_canon_sha256":"bbe92fec77a5140d5f710ff4d098f546186ab60af5e761342ecf17524b847320"},"schema_version":"1.0","source":{"id":"1111.4591","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4591","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4591v1","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4591","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"pith_short_12","alias_value":"QVDT7S4EGAGU","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QVDT7S4EGAGUTQGE","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QVDT7S4E","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:dd7252b5969e3296d39e67ef867d5016ad16d190c5ca76a32371d3b1dcbd27f3","target":"graph","created_at":"2026-05-18T04:08:03Z","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 establish empirical quantile process CLTs based on $n$ independent copies of a stochastic process $\\{X_t: t \\in E\\}$ that are uniform in $t \\in E$ and quantile levels $\\alpha \\in I$, where $I$ is a closed sub-interval of $(0,1)$. Typically $E=[0,T]$, or a finite product of such intervals. Also included are CLT's for the empirical process based on $\\{I_{X_t \\le y} - \\rm {Pr}(X_t \\le y): t \\in E, y \\in R \\}$ that are uniform in $t \\in E, y \\in R$. The process $\\{X_t: t \\in E\\}$ may be chosen from a broad collection of Gaussian processes, compound Poisson processes, stationary independent incr","authors_text":"James Kuelbs, Joel Zinn","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-19T22:29:05Z","title":"Empirical Quantile CLTs for Time Dependent Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4591","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":"sha256:08283b6867d4e5431107940338acf7e55ab776add065c49b847278d601ab5e0c","target":"record","created_at":"2026-05-18T04:08:03Z","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":"9a7b26a5d81748b72b7593a9d2e6870bac8711ac71621aacfe80496f231c8d4e","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-19T22:29:05Z","title_canon_sha256":"bbe92fec77a5140d5f710ff4d098f546186ab60af5e761342ecf17524b847320"},"schema_version":"1.0","source":{"id":"1111.4591","kind":"arxiv","version":1}},"canonical_sha256":"85473fcb84300d49c0c4dda7d33c1bf73b1689c7d31c24e26e9fdb8d1450d515","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85473fcb84300d49c0c4dda7d33c1bf73b1689c7d31c24e26e9fdb8d1450d515","first_computed_at":"2026-05-18T04:08:03.030893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:03.030893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6f9bi1Ktfwxb6rA9v3RkC38Dr3/BjSQF0Di3iwSM0ewidYdr7VWXAnDWcgLmdlr8aFgEWX/Ou0+9L38q60lZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:03.031349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4591","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08283b6867d4e5431107940338acf7e55ab776add065c49b847278d601ab5e0c","sha256:dd7252b5969e3296d39e67ef867d5016ad16d190c5ca76a32371d3b1dcbd27f3"],"state_sha256":"e27ae25a209703c6784592d8706816367f30437e3a3c411706496e6e7ceafbb3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cPgdJi5Bu7wEzp7VmPuUJ10e3Fqrd/cDFOj9a2AKL+bxlnplGFa2AuPlHAXQY6ohAsAlwt2ur4ZGIMKzflCsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:59:48.252805Z","bundle_sha256":"1760a10b8d9e3bee28aaef2eb8db7e484e217265c461d127f6b94d1ea3adfbb6"}}