{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3KZJ6CX7ETDCRLGU5RGUY5CV3R","short_pith_number":"pith:3KZJ6CX7","canonical_record":{"source":{"id":"1607.06564","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-22T06:08:28Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"660cff10d33f2aabb676f6eaa90098b62ba5fe652d26d8f83f6e360c7eebcb2d","abstract_canon_sha256":"f910214a6ec4d86522b167f8dd59eae9ed4808fdbc2693a4b8569ef763070533"},"schema_version":"1.0"},"canonical_sha256":"dab29f0aff24c628acd4ec4d4c7455dc47706e011b9477417c06ea6d890f2a4c","source":{"kind":"arxiv","id":"1607.06564","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06564","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06564v1","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06564","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"pith_short_12","alias_value":"3KZJ6CX7ETDC","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3KZJ6CX7ETDCRLGU","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3KZJ6CX7","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3KZJ6CX7ETDCRLGU5RGUY5CV3R","target":"record","payload":{"canonical_record":{"source":{"id":"1607.06564","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-22T06:08:28Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"660cff10d33f2aabb676f6eaa90098b62ba5fe652d26d8f83f6e360c7eebcb2d","abstract_canon_sha256":"f910214a6ec4d86522b167f8dd59eae9ed4808fdbc2693a4b8569ef763070533"},"schema_version":"1.0"},"canonical_sha256":"dab29f0aff24c628acd4ec4d4c7455dc47706e011b9477417c06ea6d890f2a4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:39.539705Z","signature_b64":"0LOAZpqA9oQGWXMUtOtQe0NsCs+Yf1Bg7UHs3wnJpJFqqvpvtPLSkET2bCoXD3vZArKgs1QSaK//w25yW6OqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dab29f0aff24c628acd4ec4d4c7455dc47706e011b9477417c06ea6d890f2a4c","last_reissued_at":"2026-05-18T01:10:39.539261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:39.539261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.06564","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":"2026-05-18T01:10:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3SASf5EgICp5FrGVPVT1pkFH00fNbYSW2gjq1HLLW/en6SAGfNv+uYf7X37Kz/Y7tLSopD33Sou27zrcHQl/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:15:32.254758Z"},"content_sha256":"065fc0c979be92fbb9ef110aa15e2dc5c0f4fb5f9317bb1525013c951b14f058","schema_version":"1.0","event_id":"sha256:065fc0c979be92fbb9ef110aa15e2dc5c0f4fb5f9317bb1525013c951b14f058"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3KZJ6CX7ETDCRLGU5RGUY5CV3R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Stochastic Comparisons of Order Statistics from Heterogeneous Exponential Samples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Yaming Yu","submitted_at":"2016-07-22T06:08:28Z","abstract_excerpt":"We show that the $k$th order statistic from a heterogeneous sample of $n\\geq k$ exponential random variables is larger than that from a homogeneous exponential sample in the sense of star ordering, as conjectured by Xu and Balakrishnan (2012). As a consequence, we establish hazard rate ordering for order statistics between heterogeneous and homogeneous exponential samples, resolving an open problem of P\\v{a}lt\\v{a}nea (2008). Extensions to general spacings are also presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06564","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":"2026-05-18T01:10:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l7CheuLueK9C9gT8SP1ntwn3Mfk0tFEnK8lOpHe+6Il9dz3zsS4DvkmCbhEeLk7p2OLzooFqAKYr5bzRoQwyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:15:32.255101Z"},"content_sha256":"22f441d05800381f81fa3035c75c60d72ef51f1df96a0b5857e2abd766963b3d","schema_version":"1.0","event_id":"sha256:22f441d05800381f81fa3035c75c60d72ef51f1df96a0b5857e2abd766963b3d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3KZJ6CX7ETDCRLGU5RGUY5CV3R/bundle.json","state_url":"https://pith.science/pith/3KZJ6CX7ETDCRLGU5RGUY5CV3R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3KZJ6CX7ETDCRLGU5RGUY5CV3R/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":"2026-06-20T06:15:32Z","links":{"resolver":"https://pith.science/pith/3KZJ6CX7ETDCRLGU5RGUY5CV3R","bundle":"https://pith.science/pith/3KZJ6CX7ETDCRLGU5RGUY5CV3R/bundle.json","state":"https://pith.science/pith/3KZJ6CX7ETDCRLGU5RGUY5CV3R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3KZJ6CX7ETDCRLGU5RGUY5CV3R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3KZJ6CX7ETDCRLGU5RGUY5CV3R","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":"f910214a6ec4d86522b167f8dd59eae9ed4808fdbc2693a4b8569ef763070533","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-22T06:08:28Z","title_canon_sha256":"660cff10d33f2aabb676f6eaa90098b62ba5fe652d26d8f83f6e360c7eebcb2d"},"schema_version":"1.0","source":{"id":"1607.06564","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06564","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06564v1","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06564","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"pith_short_12","alias_value":"3KZJ6CX7ETDC","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3KZJ6CX7ETDCRLGU","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3KZJ6CX7","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:22f441d05800381f81fa3035c75c60d72ef51f1df96a0b5857e2abd766963b3d","target":"graph","created_at":"2026-05-18T01:10:39Z","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 show that the $k$th order statistic from a heterogeneous sample of $n\\geq k$ exponential random variables is larger than that from a homogeneous exponential sample in the sense of star ordering, as conjectured by Xu and Balakrishnan (2012). As a consequence, we establish hazard rate ordering for order statistics between heterogeneous and homogeneous exponential samples, resolving an open problem of P\\v{a}lt\\v{a}nea (2008). Extensions to general spacings are also presented.","authors_text":"Yaming Yu","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-22T06:08:28Z","title":"On Stochastic Comparisons of Order Statistics from Heterogeneous Exponential Samples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06564","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":"sha256:065fc0c979be92fbb9ef110aa15e2dc5c0f4fb5f9317bb1525013c951b14f058","target":"record","created_at":"2026-05-18T01:10:39Z","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":"f910214a6ec4d86522b167f8dd59eae9ed4808fdbc2693a4b8569ef763070533","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-07-22T06:08:28Z","title_canon_sha256":"660cff10d33f2aabb676f6eaa90098b62ba5fe652d26d8f83f6e360c7eebcb2d"},"schema_version":"1.0","source":{"id":"1607.06564","kind":"arxiv","version":1}},"canonical_sha256":"dab29f0aff24c628acd4ec4d4c7455dc47706e011b9477417c06ea6d890f2a4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dab29f0aff24c628acd4ec4d4c7455dc47706e011b9477417c06ea6d890f2a4c","first_computed_at":"2026-05-18T01:10:39.539261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:39.539261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0LOAZpqA9oQGWXMUtOtQe0NsCs+Yf1Bg7UHs3wnJpJFqqvpvtPLSkET2bCoXD3vZArKgs1QSaK//w25yW6OqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:39.539705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06564","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:065fc0c979be92fbb9ef110aa15e2dc5c0f4fb5f9317bb1525013c951b14f058","sha256:22f441d05800381f81fa3035c75c60d72ef51f1df96a0b5857e2abd766963b3d"],"state_sha256":"3428db6394443dcb983ab5f5d693015fc0f778e1cfe28af368590a10b9fa1852"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YZxyoOxkmHkBUwxxUfcGvlAnTFjbYn0lMDj8E13jhbAQlzWJGMqMVQ/yCBU7rO1ffcVF5z5Mg1Qb14WZPpo6AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:15:32.257042Z","bundle_sha256":"a61740f094d04c3abf56970173bcfb6b4910c594a3ad4f393d51da4e3b286fc7"}}