{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:S5C2HGPGJ6ZKOZYLE4FIR6KSTM","short_pith_number":"pith:S5C2HGPG","canonical_record":{"source":{"id":"1611.05410","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-16T19:14:44Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"ab93a08b6e4aaddf47090486afe1d85d4b6089cda6534f085d04b99f38500d6f","abstract_canon_sha256":"7cb1d06830d2705d1b67594b0e0be28e088442b9f005129a2273b3df61fcc24a"},"schema_version":"1.0"},"canonical_sha256":"9745a399e64fb2a7670b270a88f9529b006c972efc02a0d69c9db82db799593f","source":{"kind":"arxiv","id":"1611.05410","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.05410","created_at":"2026-05-18T00:58:27Z"},{"alias_kind":"arxiv_version","alias_value":"1611.05410v1","created_at":"2026-05-18T00:58:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05410","created_at":"2026-05-18T00:58:27Z"},{"alias_kind":"pith_short_12","alias_value":"S5C2HGPGJ6ZK","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"S5C2HGPGJ6ZKOZYL","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"S5C2HGPG","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:S5C2HGPGJ6ZKOZYLE4FIR6KSTM","target":"record","payload":{"canonical_record":{"source":{"id":"1611.05410","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-16T19:14:44Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"ab93a08b6e4aaddf47090486afe1d85d4b6089cda6534f085d04b99f38500d6f","abstract_canon_sha256":"7cb1d06830d2705d1b67594b0e0be28e088442b9f005129a2273b3df61fcc24a"},"schema_version":"1.0"},"canonical_sha256":"9745a399e64fb2a7670b270a88f9529b006c972efc02a0d69c9db82db799593f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:27.149746Z","signature_b64":"nr0sXh62J8PlqD8skRoGkZxNutpqrPR8zbsGI0SHOAZgc9KECR/tS+TfyKyQfL81Y8aOvypynRgkrxw6AGGgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9745a399e64fb2a7670b270a88f9529b006c972efc02a0d69c9db82db799593f","last_reissued_at":"2026-05-18T00:58:27.149082Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:27.149082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.05410","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":"2026-05-18T00:58:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6DiS/yCzVk3VG8aENz0dp7Z1Vuds+VX67RFdhgEriwxzKeJxbktS8LfEOdrtfH3/FZV5/x7KTTcoMJW2R4vXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:22:31.812185Z"},"content_sha256":"0fde5d369bad6d049d5e128fef1b7ed39b843c6adc8c3e36613858893d0cff47","schema_version":"1.0","event_id":"sha256:0fde5d369bad6d049d5e128fef1b7ed39b843c6adc8c3e36613858893d0cff47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:S5C2HGPGJ6ZKOZYLE4FIR6KSTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Big Outliers Versus Heavy Tails: what to use?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Lev B. Klebanov","submitted_at":"2016-11-16T19:14:44Z","abstract_excerpt":"A possibility to give strong mathematical definitions of outliers and heavy tailed distributions or their modification is discussed. Some alternatives for the notion of tail index are proposed. Key words: outliers, heavy tails, tail index."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05410","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":"2026-05-18T00:58:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bE9J3RPYUrHFheSI3kVxDf4XcJDdVyEiLwQMwijsHNxcy7mSJTY26j9oLym+sDhwAjgmrM0HjT4OeCK+b17EAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:22:31.812538Z"},"content_sha256":"d74cc66df9e0af1fbf1f1046f1c53757a593fc35962cced4a8e86ee5fe2a1158","schema_version":"1.0","event_id":"sha256:d74cc66df9e0af1fbf1f1046f1c53757a593fc35962cced4a8e86ee5fe2a1158"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S5C2HGPGJ6ZKOZYLE4FIR6KSTM/bundle.json","state_url":"https://pith.science/pith/S5C2HGPGJ6ZKOZYLE4FIR6KSTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S5C2HGPGJ6ZKOZYLE4FIR6KSTM/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":"2026-06-26T08:22:31Z","links":{"resolver":"https://pith.science/pith/S5C2HGPGJ6ZKOZYLE4FIR6KSTM","bundle":"https://pith.science/pith/S5C2HGPGJ6ZKOZYLE4FIR6KSTM/bundle.json","state":"https://pith.science/pith/S5C2HGPGJ6ZKOZYLE4FIR6KSTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S5C2HGPGJ6ZKOZYLE4FIR6KSTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:S5C2HGPGJ6ZKOZYLE4FIR6KSTM","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":"7cb1d06830d2705d1b67594b0e0be28e088442b9f005129a2273b3df61fcc24a","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-16T19:14:44Z","title_canon_sha256":"ab93a08b6e4aaddf47090486afe1d85d4b6089cda6534f085d04b99f38500d6f"},"schema_version":"1.0","source":{"id":"1611.05410","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.05410","created_at":"2026-05-18T00:58:27Z"},{"alias_kind":"arxiv_version","alias_value":"1611.05410v1","created_at":"2026-05-18T00:58:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05410","created_at":"2026-05-18T00:58:27Z"},{"alias_kind":"pith_short_12","alias_value":"S5C2HGPGJ6ZK","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"S5C2HGPGJ6ZKOZYL","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"S5C2HGPG","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:d74cc66df9e0af1fbf1f1046f1c53757a593fc35962cced4a8e86ee5fe2a1158","target":"graph","created_at":"2026-05-18T00:58:27Z","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":"A possibility to give strong mathematical definitions of outliers and heavy tailed distributions or their modification is discussed. Some alternatives for the notion of tail index are proposed. Key words: outliers, heavy tails, tail index.","authors_text":"Lev B. Klebanov","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-16T19:14:44Z","title":"Big Outliers Versus Heavy Tails: what to use?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05410","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":"sha256:0fde5d369bad6d049d5e128fef1b7ed39b843c6adc8c3e36613858893d0cff47","target":"record","created_at":"2026-05-18T00:58:27Z","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":"7cb1d06830d2705d1b67594b0e0be28e088442b9f005129a2273b3df61fcc24a","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-16T19:14:44Z","title_canon_sha256":"ab93a08b6e4aaddf47090486afe1d85d4b6089cda6534f085d04b99f38500d6f"},"schema_version":"1.0","source":{"id":"1611.05410","kind":"arxiv","version":1}},"canonical_sha256":"9745a399e64fb2a7670b270a88f9529b006c972efc02a0d69c9db82db799593f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9745a399e64fb2a7670b270a88f9529b006c972efc02a0d69c9db82db799593f","first_computed_at":"2026-05-18T00:58:27.149082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:27.149082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nr0sXh62J8PlqD8skRoGkZxNutpqrPR8zbsGI0SHOAZgc9KECR/tS+TfyKyQfL81Y8aOvypynRgkrxw6AGGgAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:27.149746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.05410","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fde5d369bad6d049d5e128fef1b7ed39b843c6adc8c3e36613858893d0cff47","sha256:d74cc66df9e0af1fbf1f1046f1c53757a593fc35962cced4a8e86ee5fe2a1158"],"state_sha256":"1e6e351f25b36583e5619794e414c10e0ef8a901c65ad8762857a403c3f8d24f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"otw+eHWknycBplaKyADKllinUDanA8zQhkYd3FqWfe97SBrbD5rDGeCKySmaHr//4o0vKf6AKOE2Rb4iKB9hDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T08:22:31.814489Z","bundle_sha256":"a137425ca990f2828da94d31475f47312e218240c4f8f60a54b35316cc8f2f68"}}