{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GFLA2YRSMWGBAAVOT7DQACLJUI","short_pith_number":"pith:GFLA2YRS","canonical_record":{"source":{"id":"1710.06566","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-18T02:47:56Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"ae06955826e60f187e4659c27e945bf179f5a4ce31f7a3fcc01ba029145dca62","abstract_canon_sha256":"dc7195e07734ac26657205a457ddca78bd82ff2be695cd858b14742699778402"},"schema_version":"1.0"},"canonical_sha256":"31560d6232658c1002ae9fc7000969a211263606e2b165dc5a26d0bd4caca530","source":{"kind":"arxiv","id":"1710.06566","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06566","created_at":"2026-05-18T00:09:00Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06566v1","created_at":"2026-05-18T00:09:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06566","created_at":"2026-05-18T00:09:00Z"},{"alias_kind":"pith_short_12","alias_value":"GFLA2YRSMWGB","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GFLA2YRSMWGBAAVO","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GFLA2YRS","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GFLA2YRSMWGBAAVOT7DQACLJUI","target":"record","payload":{"canonical_record":{"source":{"id":"1710.06566","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-18T02:47:56Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"ae06955826e60f187e4659c27e945bf179f5a4ce31f7a3fcc01ba029145dca62","abstract_canon_sha256":"dc7195e07734ac26657205a457ddca78bd82ff2be695cd858b14742699778402"},"schema_version":"1.0"},"canonical_sha256":"31560d6232658c1002ae9fc7000969a211263606e2b165dc5a26d0bd4caca530","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:00.396844Z","signature_b64":"Mnespqu+xT3oe0ZGzUJHO0B6Mx6wP/zvOQKbiaj4Qc7xlHS3oCVonlJ1pZV4+4o5MqNUbfbRbX0wsdBIAFVrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31560d6232658c1002ae9fc7000969a211263606e2b165dc5a26d0bd4caca530","last_reissued_at":"2026-05-18T00:09:00.396188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:00.396188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.06566","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":"2026-05-18T00:09:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TmQaMV6Q/D5ghW7k19bHrKc4z9WlfrlppyQn+MkkqmXV78OIqw7llc19RUMWl/9Lddx1Z5/WwLm2Je7rhEU9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:14:46.238119Z"},"content_sha256":"acb2dcc116473a3fdb67b7d52c4c5426480dc10ba4a7edc6f8733a59a303d416","schema_version":"1.0","event_id":"sha256:acb2dcc116473a3fdb67b7d52c4c5426480dc10ba4a7edc6f8733a59a303d416"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GFLA2YRSMWGBAAVOT7DQACLJUI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Least Squares Linear Regression Without Second Moment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Rajeshwari Majumdar","submitted_at":"2017-10-18T02:47:56Z","abstract_excerpt":"If X and Y are real valued random variables such that the first moments of X, Y, and XY exist and the conditional expectation of Y given X is an affine function of X, then the intercept and slope of the conditional expectation equal the intercept and slope of the least squares linear regression function, even though Y may not have a finite second moment. As a consequence, the affine in X form of the conditional expectation and zero covariance imply mean independence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06566","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":"2026-05-18T00:09:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WeIIAftUOhdPgfGB0q0ttdOedOPMBBBFS5/r61+e+W5jCWU5UABwwEAbUHpWglKG+IITkuGT4l7SrWyCiJwpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:14:46.238485Z"},"content_sha256":"dc4504e531093c47a759c9c41cc2bf09a955a2d106608afd29689fa86f624e06","schema_version":"1.0","event_id":"sha256:dc4504e531093c47a759c9c41cc2bf09a955a2d106608afd29689fa86f624e06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFLA2YRSMWGBAAVOT7DQACLJUI/bundle.json","state_url":"https://pith.science/pith/GFLA2YRSMWGBAAVOT7DQACLJUI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFLA2YRSMWGBAAVOT7DQACLJUI/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":"2026-06-25T11:14:46Z","links":{"resolver":"https://pith.science/pith/GFLA2YRSMWGBAAVOT7DQACLJUI","bundle":"https://pith.science/pith/GFLA2YRSMWGBAAVOT7DQACLJUI/bundle.json","state":"https://pith.science/pith/GFLA2YRSMWGBAAVOT7DQACLJUI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFLA2YRSMWGBAAVOT7DQACLJUI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GFLA2YRSMWGBAAVOT7DQACLJUI","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":"dc7195e07734ac26657205a457ddca78bd82ff2be695cd858b14742699778402","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-18T02:47:56Z","title_canon_sha256":"ae06955826e60f187e4659c27e945bf179f5a4ce31f7a3fcc01ba029145dca62"},"schema_version":"1.0","source":{"id":"1710.06566","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06566","created_at":"2026-05-18T00:09:00Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06566v1","created_at":"2026-05-18T00:09:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06566","created_at":"2026-05-18T00:09:00Z"},{"alias_kind":"pith_short_12","alias_value":"GFLA2YRSMWGB","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GFLA2YRSMWGBAAVO","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GFLA2YRS","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:dc4504e531093c47a759c9c41cc2bf09a955a2d106608afd29689fa86f624e06","target":"graph","created_at":"2026-05-18T00:09:00Z","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":"If X and Y are real valued random variables such that the first moments of X, Y, and XY exist and the conditional expectation of Y given X is an affine function of X, then the intercept and slope of the conditional expectation equal the intercept and slope of the least squares linear regression function, even though Y may not have a finite second moment. As a consequence, the affine in X form of the conditional expectation and zero covariance imply mean independence.","authors_text":"Rajeshwari Majumdar","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-18T02:47:56Z","title":"On Least Squares Linear Regression Without Second Moment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06566","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:acb2dcc116473a3fdb67b7d52c4c5426480dc10ba4a7edc6f8733a59a303d416","target":"record","created_at":"2026-05-18T00:09:00Z","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":"dc7195e07734ac26657205a457ddca78bd82ff2be695cd858b14742699778402","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-10-18T02:47:56Z","title_canon_sha256":"ae06955826e60f187e4659c27e945bf179f5a4ce31f7a3fcc01ba029145dca62"},"schema_version":"1.0","source":{"id":"1710.06566","kind":"arxiv","version":1}},"canonical_sha256":"31560d6232658c1002ae9fc7000969a211263606e2b165dc5a26d0bd4caca530","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31560d6232658c1002ae9fc7000969a211263606e2b165dc5a26d0bd4caca530","first_computed_at":"2026-05-18T00:09:00.396188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:00.396188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mnespqu+xT3oe0ZGzUJHO0B6Mx6wP/zvOQKbiaj4Qc7xlHS3oCVonlJ1pZV4+4o5MqNUbfbRbX0wsdBIAFVrDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:00.396844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.06566","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acb2dcc116473a3fdb67b7d52c4c5426480dc10ba4a7edc6f8733a59a303d416","sha256:dc4504e531093c47a759c9c41cc2bf09a955a2d106608afd29689fa86f624e06"],"state_sha256":"3a5063bcf7843deb0ab4eb337ab7f52ebf085c0723f38f802183524c9bea462e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rODIOtUmZ9RfLIPilCb5ZcPwLrGOoEstbbjh3JYTUwvCXRjiO8T1hQ5MHpk0PrRRJJcp2cCgqiO40Wm/Vi2ADw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:14:46.240403Z","bundle_sha256":"1b24d9fe9c75bddbe138ce340a530ac525e93d4c14f1a81a68aed171abdc0631"}}