{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:USZ3ZUFE44EX6QWNAF7TF7UZJV","short_pith_number":"pith:USZ3ZUFE","canonical_record":{"source":{"id":"1902.06800","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-18T20:59:34Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c4fd605adfddc281c5cf10da3f38cf84a456d7b4599d7810448aa777d3e007c9","abstract_canon_sha256":"775d44029e699602d52774a768b3bf9fd5e386ff995564ece85bc1ef84989783"},"schema_version":"1.0"},"canonical_sha256":"a4b3bcd0a4e7097f42cd017f32fe994d755a7b9c5f29250e1ce8869981eb6a59","source":{"kind":"arxiv","id":"1902.06800","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.06800","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1902.06800v1","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06800","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"USZ3ZUFE44EX","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"USZ3ZUFE44EX6QWN","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"USZ3ZUFE","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:USZ3ZUFE44EX6QWNAF7TF7UZJV","target":"record","payload":{"canonical_record":{"source":{"id":"1902.06800","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-18T20:59:34Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c4fd605adfddc281c5cf10da3f38cf84a456d7b4599d7810448aa777d3e007c9","abstract_canon_sha256":"775d44029e699602d52774a768b3bf9fd5e386ff995564ece85bc1ef84989783"},"schema_version":"1.0"},"canonical_sha256":"a4b3bcd0a4e7097f42cd017f32fe994d755a7b9c5f29250e1ce8869981eb6a59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:40.775364Z","signature_b64":"fKCvnFI/lh/zovK5GiYUFfHIfbgS75bhMkc561GUayEJynnEsx1lhGB/k/Z3DxDxXXEaQF2jGkw8kFfd9PnfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4b3bcd0a4e7097f42cd017f32fe994d755a7b9c5f29250e1ce8869981eb6a59","last_reissued_at":"2026-05-17T23:53:40.774913Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:40.774913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.06800","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":"2026-05-17T23:53:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EpiUSir0/s92xv6610KjigXrmerO+NotNRaEU3By6IORoiJX6bfM8FMT4xjMniTDDDL/pjkclp1UMBWQNSQcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:11:37.775135Z"},"content_sha256":"d046f994d51c9ed7eb7add8f9c1cb9b588a6b7c750775be2b7cbcf29f07241e1","schema_version":"1.0","event_id":"sha256:d046f994d51c9ed7eb7add8f9c1cb9b588a6b7c750775be2b7cbcf29f07241e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:USZ3ZUFE44EX6QWNAF7TF7UZJV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The KLR-theorem revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Abram M. Kagan","submitted_at":"2019-02-18T20:59:34Z","abstract_excerpt":"For independent random variables $X_1,\\ldots, X_n;Y_1,\\ldots, Y_n$ with all $X_i$ identically distributed and same for $Y_j$, we study the relation \\[E\\{a\\bar X + b\\bar Y|X_1 -\\bar X +Y_1 -\\bar Y,\\ldots,X_n -\\bar X +Y_n -\\bar Y\\}={\\rm const}\\] with $a, b$ some constants. It is proved that for $n\\geq 3$ and $ab>0$ the relation holds iff $X_i$ and $Y_j$ are Gaussian.\\\\ A new characterization arises in case of $a=1, b= -1$. In this case either $X_i$ or $Y_j$ or both have a Gaussian component. It is the first (at least known to the author) case when presence of a Gaussian component is a characteri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06800","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":"2026-05-17T23:53:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HMHSjfB4/DfjLmCfj2aItkz3kSnDk0daVN9AWmHjOGGS2yxsWv1jS5U43wPciM1y7pBIKrG1WCFzIMHD/fO2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:11:37.775778Z"},"content_sha256":"f33c86556a6aa118573a6ca2937161a9c53e1007e7f8aa5673339b3f6395c694","schema_version":"1.0","event_id":"sha256:f33c86556a6aa118573a6ca2937161a9c53e1007e7f8aa5673339b3f6395c694"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/USZ3ZUFE44EX6QWNAF7TF7UZJV/bundle.json","state_url":"https://pith.science/pith/USZ3ZUFE44EX6QWNAF7TF7UZJV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/USZ3ZUFE44EX6QWNAF7TF7UZJV/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":"2026-05-27T06:11:37Z","links":{"resolver":"https://pith.science/pith/USZ3ZUFE44EX6QWNAF7TF7UZJV","bundle":"https://pith.science/pith/USZ3ZUFE44EX6QWNAF7TF7UZJV/bundle.json","state":"https://pith.science/pith/USZ3ZUFE44EX6QWNAF7TF7UZJV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/USZ3ZUFE44EX6QWNAF7TF7UZJV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:USZ3ZUFE44EX6QWNAF7TF7UZJV","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":"775d44029e699602d52774a768b3bf9fd5e386ff995564ece85bc1ef84989783","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-18T20:59:34Z","title_canon_sha256":"c4fd605adfddc281c5cf10da3f38cf84a456d7b4599d7810448aa777d3e007c9"},"schema_version":"1.0","source":{"id":"1902.06800","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.06800","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1902.06800v1","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06800","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"USZ3ZUFE44EX","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"USZ3ZUFE44EX6QWN","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"USZ3ZUFE","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:f33c86556a6aa118573a6ca2937161a9c53e1007e7f8aa5673339b3f6395c694","target":"graph","created_at":"2026-05-17T23:53:40Z","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":"For independent random variables $X_1,\\ldots, X_n;Y_1,\\ldots, Y_n$ with all $X_i$ identically distributed and same for $Y_j$, we study the relation \\[E\\{a\\bar X + b\\bar Y|X_1 -\\bar X +Y_1 -\\bar Y,\\ldots,X_n -\\bar X +Y_n -\\bar Y\\}={\\rm const}\\] with $a, b$ some constants. It is proved that for $n\\geq 3$ and $ab>0$ the relation holds iff $X_i$ and $Y_j$ are Gaussian.\\\\ A new characterization arises in case of $a=1, b= -1$. In this case either $X_i$ or $Y_j$ or both have a Gaussian component. It is the first (at least known to the author) case when presence of a Gaussian component is a characteri","authors_text":"Abram M. Kagan","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-18T20:59:34Z","title":"The KLR-theorem revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06800","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:d046f994d51c9ed7eb7add8f9c1cb9b588a6b7c750775be2b7cbcf29f07241e1","target":"record","created_at":"2026-05-17T23:53:40Z","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":"775d44029e699602d52774a768b3bf9fd5e386ff995564ece85bc1ef84989783","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-18T20:59:34Z","title_canon_sha256":"c4fd605adfddc281c5cf10da3f38cf84a456d7b4599d7810448aa777d3e007c9"},"schema_version":"1.0","source":{"id":"1902.06800","kind":"arxiv","version":1}},"canonical_sha256":"a4b3bcd0a4e7097f42cd017f32fe994d755a7b9c5f29250e1ce8869981eb6a59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4b3bcd0a4e7097f42cd017f32fe994d755a7b9c5f29250e1ce8869981eb6a59","first_computed_at":"2026-05-17T23:53:40.774913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:40.774913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fKCvnFI/lh/zovK5GiYUFfHIfbgS75bhMkc561GUayEJynnEsx1lhGB/k/Z3DxDxXXEaQF2jGkw8kFfd9PnfDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:40.775364Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.06800","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d046f994d51c9ed7eb7add8f9c1cb9b588a6b7c750775be2b7cbcf29f07241e1","sha256:f33c86556a6aa118573a6ca2937161a9c53e1007e7f8aa5673339b3f6395c694"],"state_sha256":"486aaa4a3de4b19c7ab1050a8648f1b0869b4cb04d753c73e4257627d65094b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c8RmdvhsmAsjSXi4VGjFuDJpmeYbIWKhcI+4HdbFPeqmL8QeYcqfXx4UL6Tm6r6wnrb+xogNI7fg+exRxc3lAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:11:37.779155Z","bundle_sha256":"57f4dc107b4ec62fe6c786e14485c1c0be5f48fd28348a480123293af6318e6b"}}