{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:A7HY2KB5V2DCIVJ2BJ52XEJW26","short_pith_number":"pith:A7HY2KB5","canonical_record":{"source":{"id":"1701.06642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-23T21:42:31Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"9dd08e5fd136b57285b63de611206d925562fb17daba2746517e565521c2d53a","abstract_canon_sha256":"089d899a8ec4747349ee6f3331779705c4044fbb4f3557c075b23ef6adfb5d46"},"schema_version":"1.0"},"canonical_sha256":"07cf8d283dae8624553a0a7bab9136d7877f5456591efa05a509e5ca56549aec","source":{"kind":"arxiv","id":"1701.06642","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06642","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06642v1","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06642","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"A7HY2KB5V2DC","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"A7HY2KB5V2DCIVJ2","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"A7HY2KB5","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:A7HY2KB5V2DCIVJ2BJ52XEJW26","target":"record","payload":{"canonical_record":{"source":{"id":"1701.06642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-23T21:42:31Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"9dd08e5fd136b57285b63de611206d925562fb17daba2746517e565521c2d53a","abstract_canon_sha256":"089d899a8ec4747349ee6f3331779705c4044fbb4f3557c075b23ef6adfb5d46"},"schema_version":"1.0"},"canonical_sha256":"07cf8d283dae8624553a0a7bab9136d7877f5456591efa05a509e5ca56549aec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:12.487394Z","signature_b64":"Q5rY4M3UnLiungizsAjDQ8BL0ieBwpfvH6V/KHTEF5hx65g+ZpaaKqduelBw/X0EgWhcr2kDBrhKAQgubzUVBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07cf8d283dae8624553a0a7bab9136d7877f5456591efa05a509e5ca56549aec","last_reissued_at":"2026-05-18T00:52:12.486957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:12.486957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.06642","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":"2026-05-18T00:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VHz4TdqvExXVHwgFhLY1Y+gRYZUmJ2fudB5RRzEr7VK/JMcP1F2bufjmBxYYJ29etQ8d+6fzAusbr9hoZfm3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:05:01.390068Z"},"content_sha256":"52b1a039e936030681833dca93564299ac9c75d9fed41fe348fe7e1d80e10d8e","schema_version":"1.0","event_id":"sha256:52b1a039e936030681833dca93564299ac9c75d9fed41fe348fe7e1d80e10d8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:A7HY2KB5V2DCIVJ2BJ52XEJW26","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Outliers and related problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Andrea Karlova, Ashot V. Kakosyan, Jaromir Antoch, Lev B. Klebanov","submitted_at":"2017-01-23T21:42:31Z","abstract_excerpt":"We define outliers as a set of observations which contradicts the proposed mathematical (statistical) model and we discuss the frequently observed types of the outliers. Further we explore what changes in the model have to be made in order to avoid the occurance of the outliers. We observe that some variants of the outliers lead to classical results in probability, such as the law of large numbers and the concept of heavy tailed distributions.\n  Key words: outlier; the law of large numbers; heavy tailed distributions; model rejection."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06642","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":"2026-05-18T00:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KSSBtm7DBqSs/tjEQ5+bKoCYUfeVkFcxP791e/kyepZOuGycwEgPsAKk9hyMIJUFnWHK4RIQ2UBM/+lQeplFBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:05:01.390446Z"},"content_sha256":"e79c76c06f2f651774118e2747f597aea1172793ef4a0c410a2eacfd6f08b107","schema_version":"1.0","event_id":"sha256:e79c76c06f2f651774118e2747f597aea1172793ef4a0c410a2eacfd6f08b107"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A7HY2KB5V2DCIVJ2BJ52XEJW26/bundle.json","state_url":"https://pith.science/pith/A7HY2KB5V2DCIVJ2BJ52XEJW26/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A7HY2KB5V2DCIVJ2BJ52XEJW26/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":"2026-06-26T11:05:01Z","links":{"resolver":"https://pith.science/pith/A7HY2KB5V2DCIVJ2BJ52XEJW26","bundle":"https://pith.science/pith/A7HY2KB5V2DCIVJ2BJ52XEJW26/bundle.json","state":"https://pith.science/pith/A7HY2KB5V2DCIVJ2BJ52XEJW26/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A7HY2KB5V2DCIVJ2BJ52XEJW26/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:A7HY2KB5V2DCIVJ2BJ52XEJW26","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":"089d899a8ec4747349ee6f3331779705c4044fbb4f3557c075b23ef6adfb5d46","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-23T21:42:31Z","title_canon_sha256":"9dd08e5fd136b57285b63de611206d925562fb17daba2746517e565521c2d53a"},"schema_version":"1.0","source":{"id":"1701.06642","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06642","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06642v1","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06642","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"A7HY2KB5V2DC","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"A7HY2KB5V2DCIVJ2","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"A7HY2KB5","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:e79c76c06f2f651774118e2747f597aea1172793ef4a0c410a2eacfd6f08b107","target":"graph","created_at":"2026-05-18T00:52:12Z","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 define outliers as a set of observations which contradicts the proposed mathematical (statistical) model and we discuss the frequently observed types of the outliers. Further we explore what changes in the model have to be made in order to avoid the occurance of the outliers. We observe that some variants of the outliers lead to classical results in probability, such as the law of large numbers and the concept of heavy tailed distributions.\n  Key words: outlier; the law of large numbers; heavy tailed distributions; model rejection.","authors_text":"Andrea Karlova, Ashot V. Kakosyan, Jaromir Antoch, 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":"2017-01-23T21:42:31Z","title":"Outliers and related problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06642","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":"sha256:52b1a039e936030681833dca93564299ac9c75d9fed41fe348fe7e1d80e10d8e","target":"record","created_at":"2026-05-18T00:52:12Z","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":"089d899a8ec4747349ee6f3331779705c4044fbb4f3557c075b23ef6adfb5d46","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-23T21:42:31Z","title_canon_sha256":"9dd08e5fd136b57285b63de611206d925562fb17daba2746517e565521c2d53a"},"schema_version":"1.0","source":{"id":"1701.06642","kind":"arxiv","version":1}},"canonical_sha256":"07cf8d283dae8624553a0a7bab9136d7877f5456591efa05a509e5ca56549aec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07cf8d283dae8624553a0a7bab9136d7877f5456591efa05a509e5ca56549aec","first_computed_at":"2026-05-18T00:52:12.486957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:12.486957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q5rY4M3UnLiungizsAjDQ8BL0ieBwpfvH6V/KHTEF5hx65g+ZpaaKqduelBw/X0EgWhcr2kDBrhKAQgubzUVBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:12.487394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06642","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52b1a039e936030681833dca93564299ac9c75d9fed41fe348fe7e1d80e10d8e","sha256:e79c76c06f2f651774118e2747f597aea1172793ef4a0c410a2eacfd6f08b107"],"state_sha256":"fc606952ae9315c9eda246791aebb3155edc20510f7e63e6422adbd1d4a9f9ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5V7ehXdi4SJlpLLskSuhIB1OIo0mhtzOZ0b65OEIkTmkDggvXQvh28h2SIZTqry1VnpbgOfMTxNC2x/Mb3kjCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:05:01.392449Z","bundle_sha256":"16ae951b2e9f98b24d32699e4876882de9cb5b13376e12de4e76c85167edf2df"}}