{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WCUHMZ7QMY4OQGTHTFHZWOHAFX","short_pith_number":"pith:WCUHMZ7Q","canonical_record":{"source":{"id":"1812.03311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2018-12-08T12:35:39Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"0ec11f14161a7bc6531993a7d39af82626f67ac71130d7ef4dfc246f4044adff","abstract_canon_sha256":"6cbcdf7e6d3dd2ded794141e7e799632379a17793b3155318ed5942533bed689"},"schema_version":"1.0"},"canonical_sha256":"b0a87667f06638e81a67994f9b38e02dc6af00508a423dde05404d931cf1a113","source":{"kind":"arxiv","id":"1812.03311","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03311","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03311v1","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03311","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"pith_short_12","alias_value":"WCUHMZ7QMY4O","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WCUHMZ7QMY4OQGTH","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WCUHMZ7Q","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WCUHMZ7QMY4OQGTHTFHZWOHAFX","target":"record","payload":{"canonical_record":{"source":{"id":"1812.03311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2018-12-08T12:35:39Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"0ec11f14161a7bc6531993a7d39af82626f67ac71130d7ef4dfc246f4044adff","abstract_canon_sha256":"6cbcdf7e6d3dd2ded794141e7e799632379a17793b3155318ed5942533bed689"},"schema_version":"1.0"},"canonical_sha256":"b0a87667f06638e81a67994f9b38e02dc6af00508a423dde05404d931cf1a113","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:46.574889Z","signature_b64":"IfQjo/tb8ZN13SrfXJHmf3Xfzwmq/vpQE7PkAqgQqztnKG0lZuPFpsyj7Ia0ukPgnt0nda9UWBJgp/nAG6qECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0a87667f06638e81a67994f9b38e02dc6af00508a423dde05404d931cf1a113","last_reissued_at":"2026-05-17T23:58:46.574438Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:46.574438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.03311","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":"2026-05-17T23:58:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gZqnb0lCgH7DsD9AcS9IaIZZOW4rUdzOL6ZxQXy/pvC0Gpjw3VQAa/MhyARLsFTvDD+qiceG6KbY8tzdwBzfCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T08:31:06.305504Z"},"content_sha256":"0175e7b124d648507b1656eacdf8b0c4aad3e3ebf983ca05b03dbf1bd99e6341","schema_version":"1.0","event_id":"sha256:0175e7b124d648507b1656eacdf8b0c4aad3e3ebf983ca05b03dbf1bd99e6341"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WCUHMZ7QMY4OQGTHTFHZWOHAFX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalization of the pairwise stochastic precedence order to the sequence of random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"stat.AP","authors_text":"Maxim Finkelstein, Nil Kamal Hazra","submitted_at":"2018-12-08T12:35:39Z","abstract_excerpt":"We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence order that is defined for two random variables to the case $n>2$. All conventional stochastic orders are transitive, whereas the stochastic precedence order is not. Therefore, a new approach to compare the sequence of random variables had to be developed that resulted in the notion of the sequential precedence order. A sufficient condition for this order is derived and some examples are considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03311","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":"2026-05-17T23:58:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9rkK6VaZNCpPs727Zw5sGUZCPFcqK5JPru76VoRrmPierh5FbhOY3suvuOtpFHkdAd47ZhsGSKG5dPrDHcjJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T08:31:06.306169Z"},"content_sha256":"8e76c5fa5465ba4e76e4b1f078b5eac7a81cb7837594ab3b076d0f5b63fde62d","schema_version":"1.0","event_id":"sha256:8e76c5fa5465ba4e76e4b1f078b5eac7a81cb7837594ab3b076d0f5b63fde62d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WCUHMZ7QMY4OQGTHTFHZWOHAFX/bundle.json","state_url":"https://pith.science/pith/WCUHMZ7QMY4OQGTHTFHZWOHAFX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WCUHMZ7QMY4OQGTHTFHZWOHAFX/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":"2026-07-01T08:31:06Z","links":{"resolver":"https://pith.science/pith/WCUHMZ7QMY4OQGTHTFHZWOHAFX","bundle":"https://pith.science/pith/WCUHMZ7QMY4OQGTHTFHZWOHAFX/bundle.json","state":"https://pith.science/pith/WCUHMZ7QMY4OQGTHTFHZWOHAFX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WCUHMZ7QMY4OQGTHTFHZWOHAFX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WCUHMZ7QMY4OQGTHTFHZWOHAFX","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":"6cbcdf7e6d3dd2ded794141e7e799632379a17793b3155318ed5942533bed689","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2018-12-08T12:35:39Z","title_canon_sha256":"0ec11f14161a7bc6531993a7d39af82626f67ac71130d7ef4dfc246f4044adff"},"schema_version":"1.0","source":{"id":"1812.03311","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03311","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03311v1","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03311","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"pith_short_12","alias_value":"WCUHMZ7QMY4O","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WCUHMZ7QMY4OQGTH","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WCUHMZ7Q","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:8e76c5fa5465ba4e76e4b1f078b5eac7a81cb7837594ab3b076d0f5b63fde62d","target":"graph","created_at":"2026-05-17T23:58:46Z","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 discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence order that is defined for two random variables to the case $n>2$. All conventional stochastic orders are transitive, whereas the stochastic precedence order is not. Therefore, a new approach to compare the sequence of random variables had to be developed that resulted in the notion of the sequential precedence order. A sufficient condition for this order is derived and some examples are considered.","authors_text":"Maxim Finkelstein, Nil Kamal Hazra","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2018-12-08T12:35:39Z","title":"Generalization of the pairwise stochastic precedence order to the sequence of random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03311","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":"sha256:0175e7b124d648507b1656eacdf8b0c4aad3e3ebf983ca05b03dbf1bd99e6341","target":"record","created_at":"2026-05-17T23:58:46Z","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":"6cbcdf7e6d3dd2ded794141e7e799632379a17793b3155318ed5942533bed689","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2018-12-08T12:35:39Z","title_canon_sha256":"0ec11f14161a7bc6531993a7d39af82626f67ac71130d7ef4dfc246f4044adff"},"schema_version":"1.0","source":{"id":"1812.03311","kind":"arxiv","version":1}},"canonical_sha256":"b0a87667f06638e81a67994f9b38e02dc6af00508a423dde05404d931cf1a113","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0a87667f06638e81a67994f9b38e02dc6af00508a423dde05404d931cf1a113","first_computed_at":"2026-05-17T23:58:46.574438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:46.574438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IfQjo/tb8ZN13SrfXJHmf3Xfzwmq/vpQE7PkAqgQqztnKG0lZuPFpsyj7Ia0ukPgnt0nda9UWBJgp/nAG6qECg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:46.574889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.03311","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0175e7b124d648507b1656eacdf8b0c4aad3e3ebf983ca05b03dbf1bd99e6341","sha256:8e76c5fa5465ba4e76e4b1f078b5eac7a81cb7837594ab3b076d0f5b63fde62d"],"state_sha256":"07a2eef3cef26887ba4177c5d809a34e55c8f36547f034c1b17257848682c8fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xVPViShaLX/XMJDJf2ny/CGR26AZDqoV0ZFoGy7nnzy6E98A/1BL8KN7ms0psxTMVqaqMIaX5gj/6pbk0PNLDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T08:31:06.309736Z","bundle_sha256":"dd5b6b350f21bf3ee1c261b8a9d9aea1a2d23985047736453fcaa0773bd81df5"}}