{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IKLDK5JIL4X4ZN2AQ7HMVBFC47","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":"aba623d86220651e6da7ddb67ea750180260a705b3a5ecdc5ef082337280022f","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-29T19:46:57Z","title_canon_sha256":"2993e9152bce31cdff332aabece607af4fc1c060f1d75a91c3f7bc65b243edac"},"schema_version":"1.0","source":{"id":"1612.09265","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09265","created_at":"2026-05-18T00:53:46Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09265v1","created_at":"2026-05-18T00:53:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09265","created_at":"2026-05-18T00:53:46Z"},{"alias_kind":"pith_short_12","alias_value":"IKLDK5JIL4X4","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IKLDK5JIL4X4ZN2A","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IKLDK5JI","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:7cfb50b8755aba36ee4355e047b661bd616b808dbfc4d261aef1ebed42f491fe","target":"graph","created_at":"2026-05-18T00:53:46Z","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 are trying to give a mathematically correct definition of outliers. Our approach is based on the distance between two last order statistics and appears to be connected to the law of large numbers. Key words: outliers, law of large numbers, heavy tails, stability index.","authors_text":"Andrea Karlova, Ashot V. Kakosyan, Lev B. Klebanov","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-29T19:46:57Z","title":"Outliers, the Law of Large Numbers, Index of Stability and Heavy Tails"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09265","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":"sha256:56bf178b1e78d6adfb3a4c26af527e023e57daab2b036fcbf03fffdcbd1ad839","target":"record","created_at":"2026-05-18T00:53:46Z","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":"aba623d86220651e6da7ddb67ea750180260a705b3a5ecdc5ef082337280022f","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-29T19:46:57Z","title_canon_sha256":"2993e9152bce31cdff332aabece607af4fc1c060f1d75a91c3f7bc65b243edac"},"schema_version":"1.0","source":{"id":"1612.09265","kind":"arxiv","version":1}},"canonical_sha256":"42963575285f2fccb74087ceca84a2e7f5fa4bc55c1f911f6a0d8660af5f7a25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42963575285f2fccb74087ceca84a2e7f5fa4bc55c1f911f6a0d8660af5f7a25","first_computed_at":"2026-05-18T00:53:46.130671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:46.130671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FAZfN6rfBwyAyJjgw1WUgAXOK3TELPrMsVUi1zaxNxF+5s7rI84XRH704331jT+Rsir6ZqEXBqVUpqxA55i5Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:46.131141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09265","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56bf178b1e78d6adfb3a4c26af527e023e57daab2b036fcbf03fffdcbd1ad839","sha256:7cfb50b8755aba36ee4355e047b661bd616b808dbfc4d261aef1ebed42f491fe"],"state_sha256":"c790e83aa1a546cfb3f094e63d2b57f8fcad103539d1869bee96de3b7eb6ffc8"}