{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ET45ASIWXDU6ZVIBAYQGROESH2","short_pith_number":"pith:ET45ASIW","canonical_record":{"source":{"id":"1410.8167","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-10-29T21:14:15Z","cross_cats_sorted":[],"title_canon_sha256":"a61ea937808f4320dc121dc672148b1cde8ca42974db3b8ec23a434aea4c6c17","abstract_canon_sha256":"792488f501a40ec81ed4b29265711c0e22cce6c3e2166889871aa9d078afe38c"},"schema_version":"1.0"},"canonical_sha256":"24f9d04916b8e9ecd501062068b8923eb5ed21c7d3ef18623c69c74e2443b24f","source":{"kind":"arxiv","id":"1410.8167","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8167","created_at":"2026-05-18T02:39:00Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8167v1","created_at":"2026-05-18T02:39:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8167","created_at":"2026-05-18T02:39:00Z"},{"alias_kind":"pith_short_12","alias_value":"ET45ASIWXDU6","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"ET45ASIWXDU6ZVIB","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"ET45ASIW","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ET45ASIWXDU6ZVIBAYQGROESH2","target":"record","payload":{"canonical_record":{"source":{"id":"1410.8167","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-10-29T21:14:15Z","cross_cats_sorted":[],"title_canon_sha256":"a61ea937808f4320dc121dc672148b1cde8ca42974db3b8ec23a434aea4c6c17","abstract_canon_sha256":"792488f501a40ec81ed4b29265711c0e22cce6c3e2166889871aa9d078afe38c"},"schema_version":"1.0"},"canonical_sha256":"24f9d04916b8e9ecd501062068b8923eb5ed21c7d3ef18623c69c74e2443b24f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:00.494428Z","signature_b64":"1vnbS/SeNSobx6x/25SSzQbaszteTVGOIJtyyGo98Ak44MyBhT6PTAUitgBFDzU8rKPSJq2b14sp4MQTfWr1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24f9d04916b8e9ecd501062068b8923eb5ed21c7d3ef18623c69c74e2443b24f","last_reissued_at":"2026-05-18T02:39:00.493960Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:00.493960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.8167","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":"2026-05-18T02:39:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2bEv52Yr7p7F8KxxB3dU5E+f3av/X5JVmPv2kpryPd3Qk8z8y0ECw9y5gKOWLrc88TvTo+vOAc5S6JN+Duj7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:30:51.499260Z"},"content_sha256":"dc08da5d7c18b12f72566e3da2bc602db870fa5635e1f210f20f42499cbb1adb","schema_version":"1.0","event_id":"sha256:dc08da5d7c18b12f72566e3da2bc602db870fa5635e1f210f20f42499cbb1adb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ET45ASIWXDU6ZVIBAYQGROESH2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization of Order Statistics in Two Runs Using Conditional Expectation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Ali Akbar Jafari, Mohammad Reza Kazemi","submitted_at":"2014-10-29T21:14:15Z","abstract_excerpt":"The runs test is a well-known test that is used for checking independence between elements of a sample data sequence. Some of runs tests are based on the longest run and others based on the total runs. In this paper, we consider order statistics of two runs statistics, and obtain their probability mass functions. In addition, the means and variances of the order statistics are derived using traditional conditional expectation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8167","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":"2026-05-18T02:39:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wkuGMjlYvFhLOS7ejFqWH9ZtvbY4HSNNv+/iTr+gUNqcT+U2Xs80hulEnrKmO87pWMB0/ba8fKmeinUw3sXrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:30:51.499615Z"},"content_sha256":"4a2a6d59c04264f16dc96bb46311b09470f9fbfc84e44723078a2889876a8682","schema_version":"1.0","event_id":"sha256:4a2a6d59c04264f16dc96bb46311b09470f9fbfc84e44723078a2889876a8682"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ET45ASIWXDU6ZVIBAYQGROESH2/bundle.json","state_url":"https://pith.science/pith/ET45ASIWXDU6ZVIBAYQGROESH2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ET45ASIWXDU6ZVIBAYQGROESH2/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":"2026-06-01T07:30:51Z","links":{"resolver":"https://pith.science/pith/ET45ASIWXDU6ZVIBAYQGROESH2","bundle":"https://pith.science/pith/ET45ASIWXDU6ZVIBAYQGROESH2/bundle.json","state":"https://pith.science/pith/ET45ASIWXDU6ZVIBAYQGROESH2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ET45ASIWXDU6ZVIBAYQGROESH2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ET45ASIWXDU6ZVIBAYQGROESH2","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":"792488f501a40ec81ed4b29265711c0e22cce6c3e2166889871aa9d078afe38c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-10-29T21:14:15Z","title_canon_sha256":"a61ea937808f4320dc121dc672148b1cde8ca42974db3b8ec23a434aea4c6c17"},"schema_version":"1.0","source":{"id":"1410.8167","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8167","created_at":"2026-05-18T02:39:00Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8167v1","created_at":"2026-05-18T02:39:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8167","created_at":"2026-05-18T02:39:00Z"},{"alias_kind":"pith_short_12","alias_value":"ET45ASIWXDU6","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"ET45ASIWXDU6ZVIB","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"ET45ASIW","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:4a2a6d59c04264f16dc96bb46311b09470f9fbfc84e44723078a2889876a8682","target":"graph","created_at":"2026-05-18T02:39:00Z","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":"The runs test is a well-known test that is used for checking independence between elements of a sample data sequence. Some of runs tests are based on the longest run and others based on the total runs. In this paper, we consider order statistics of two runs statistics, and obtain their probability mass functions. In addition, the means and variances of the order statistics are derived using traditional conditional expectation.","authors_text":"Ali Akbar Jafari, Mohammad Reza Kazemi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-10-29T21:14:15Z","title":"Characterization of Order Statistics in Two Runs Using Conditional Expectation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8167","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:dc08da5d7c18b12f72566e3da2bc602db870fa5635e1f210f20f42499cbb1adb","target":"record","created_at":"2026-05-18T02:39:00Z","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":"792488f501a40ec81ed4b29265711c0e22cce6c3e2166889871aa9d078afe38c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-10-29T21:14:15Z","title_canon_sha256":"a61ea937808f4320dc121dc672148b1cde8ca42974db3b8ec23a434aea4c6c17"},"schema_version":"1.0","source":{"id":"1410.8167","kind":"arxiv","version":1}},"canonical_sha256":"24f9d04916b8e9ecd501062068b8923eb5ed21c7d3ef18623c69c74e2443b24f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24f9d04916b8e9ecd501062068b8923eb5ed21c7d3ef18623c69c74e2443b24f","first_computed_at":"2026-05-18T02:39:00.493960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:00.493960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1vnbS/SeNSobx6x/25SSzQbaszteTVGOIJtyyGo98Ak44MyBhT6PTAUitgBFDzU8rKPSJq2b14sp4MQTfWr1Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:00.494428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.8167","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc08da5d7c18b12f72566e3da2bc602db870fa5635e1f210f20f42499cbb1adb","sha256:4a2a6d59c04264f16dc96bb46311b09470f9fbfc84e44723078a2889876a8682"],"state_sha256":"b3b113516e7bbdd9a1043b10969980609e7a8294776e150dd6da4e73659afdc9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BGW/dw0nMRByuBPLar6+p1xzqLB90qY59/n18v9bS4Ps6wBSIl/rz+ay2EdGhSfEEcggb5cmWBjJQT1YeYUoAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:30:51.501433Z","bundle_sha256":"9d3e7f5f56bc56f4a6c12de3e0dbfe896376506d50510d59cf1383c6aba6f57b"}}