{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7AXTO77D52RO6PNRTXC3DH5Z6D","short_pith_number":"pith:7AXTO77D","canonical_record":{"source":{"id":"1605.07244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-05-24T00:35:55Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"335c4f25216fc0aac50a81e777141cd0df55326cd00eaf1983b479425fcf7641","abstract_canon_sha256":"22b6879f4dbab6de4e6bce7f197974ee0eb8bec4055b5ad7314e035f81b866ec"},"schema_version":"1.0"},"canonical_sha256":"f82f377fe3eea2ef3db19dc5b19fb9f0d1d3bf6c8e985df3fd30bfb12ddfb414","source":{"kind":"arxiv","id":"1605.07244","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07244","created_at":"2026-05-18T01:13:46Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07244v1","created_at":"2026-05-18T01:13:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07244","created_at":"2026-05-18T01:13:46Z"},{"alias_kind":"pith_short_12","alias_value":"7AXTO77D52RO","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7AXTO77D52RO6PNR","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7AXTO77D","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7AXTO77D52RO6PNRTXC3DH5Z6D","target":"record","payload":{"canonical_record":{"source":{"id":"1605.07244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-05-24T00:35:55Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"335c4f25216fc0aac50a81e777141cd0df55326cd00eaf1983b479425fcf7641","abstract_canon_sha256":"22b6879f4dbab6de4e6bce7f197974ee0eb8bec4055b5ad7314e035f81b866ec"},"schema_version":"1.0"},"canonical_sha256":"f82f377fe3eea2ef3db19dc5b19fb9f0d1d3bf6c8e985df3fd30bfb12ddfb414","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:46.568736Z","signature_b64":"709F4RMUtEcQ2sEBGip+Ua4WTuT8FSIn6vsisAUdiU/U2vQGb+g18zhYueBVZKLWXqROLXsIaPZmDHzLkQqNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f82f377fe3eea2ef3db19dc5b19fb9f0d1d3bf6c8e985df3fd30bfb12ddfb414","last_reissued_at":"2026-05-18T01:13:46.568186Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:46.568186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.07244","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":"2026-05-18T01:13:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d2EpikaCtJRShVdyIPHcP/muIX6Q7KMWEunIT0cOkMVS4LmZHZ0Xj5mYblCi20uh9G8aIjmuxUouHXzAbUBvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:43:30.335147Z"},"content_sha256":"b50cefa1f09d998c06655adbdcb9100fc83c6b062937f04bb0d2903dded714e6","schema_version":"1.0","event_id":"sha256:b50cefa1f09d998c06655adbdcb9100fc83c6b062937f04bb0d2903dded714e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7AXTO77D52RO6PNRTXC3DH5Z6D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Estimation of Co-heritability in High-dimensional Linear Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Hongzhe Li, T. Tony Cai, Wanjie Wang, Zijian Guo","submitted_at":"2016-05-24T00:35:55Z","abstract_excerpt":"Co-heritability is an important concept that characterizes the genetic associations within pairs of quantitative traits. There has been significant recent interest in estimating the co-heritability based on data from the genome-wide association studies (GWAS). This paper introduces two measures of co-heritability in the high-dimensional linear model framework, including the inner product of the two regression vectors and a normalized inner product by their lengths. Functional de-biased estimators (FDEs) are developed to estimate these two co-heritability measures. In addition, estimators of qu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07244","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":"2026-05-18T01:13:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MMshTdr8RP5d5/1sAOplNu6ExmezEjtEuvpTMhpM7zkzFQ1cB+FE9SPy8bdJBI1TzjR4RAAbQo2YVM1iGuuBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:43:30.335864Z"},"content_sha256":"013e1ef361ff5300228f814c8a1e7b1edf838bc4eee9d56ef73606554b92b77f","schema_version":"1.0","event_id":"sha256:013e1ef361ff5300228f814c8a1e7b1edf838bc4eee9d56ef73606554b92b77f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7AXTO77D52RO6PNRTXC3DH5Z6D/bundle.json","state_url":"https://pith.science/pith/7AXTO77D52RO6PNRTXC3DH5Z6D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7AXTO77D52RO6PNRTXC3DH5Z6D/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":"2026-05-25T22:43:30Z","links":{"resolver":"https://pith.science/pith/7AXTO77D52RO6PNRTXC3DH5Z6D","bundle":"https://pith.science/pith/7AXTO77D52RO6PNRTXC3DH5Z6D/bundle.json","state":"https://pith.science/pith/7AXTO77D52RO6PNRTXC3DH5Z6D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7AXTO77D52RO6PNRTXC3DH5Z6D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7AXTO77D52RO6PNRTXC3DH5Z6D","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":"22b6879f4dbab6de4e6bce7f197974ee0eb8bec4055b5ad7314e035f81b866ec","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-05-24T00:35:55Z","title_canon_sha256":"335c4f25216fc0aac50a81e777141cd0df55326cd00eaf1983b479425fcf7641"},"schema_version":"1.0","source":{"id":"1605.07244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07244","created_at":"2026-05-18T01:13:46Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07244v1","created_at":"2026-05-18T01:13:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07244","created_at":"2026-05-18T01:13:46Z"},{"alias_kind":"pith_short_12","alias_value":"7AXTO77D52RO","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7AXTO77D52RO6PNR","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7AXTO77D","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:013e1ef361ff5300228f814c8a1e7b1edf838bc4eee9d56ef73606554b92b77f","target":"graph","created_at":"2026-05-18T01:13:46Z","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":"Co-heritability is an important concept that characterizes the genetic associations within pairs of quantitative traits. There has been significant recent interest in estimating the co-heritability based on data from the genome-wide association studies (GWAS). This paper introduces two measures of co-heritability in the high-dimensional linear model framework, including the inner product of the two regression vectors and a normalized inner product by their lengths. Functional de-biased estimators (FDEs) are developed to estimate these two co-heritability measures. In addition, estimators of qu","authors_text":"Hongzhe Li, T. Tony Cai, Wanjie Wang, Zijian Guo","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-05-24T00:35:55Z","title":"Optimal Estimation of Co-heritability in High-dimensional Linear Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07244","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:b50cefa1f09d998c06655adbdcb9100fc83c6b062937f04bb0d2903dded714e6","target":"record","created_at":"2026-05-18T01:13:46Z","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":"22b6879f4dbab6de4e6bce7f197974ee0eb8bec4055b5ad7314e035f81b866ec","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-05-24T00:35:55Z","title_canon_sha256":"335c4f25216fc0aac50a81e777141cd0df55326cd00eaf1983b479425fcf7641"},"schema_version":"1.0","source":{"id":"1605.07244","kind":"arxiv","version":1}},"canonical_sha256":"f82f377fe3eea2ef3db19dc5b19fb9f0d1d3bf6c8e985df3fd30bfb12ddfb414","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f82f377fe3eea2ef3db19dc5b19fb9f0d1d3bf6c8e985df3fd30bfb12ddfb414","first_computed_at":"2026-05-18T01:13:46.568186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:46.568186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"709F4RMUtEcQ2sEBGip+Ua4WTuT8FSIn6vsisAUdiU/U2vQGb+g18zhYueBVZKLWXqROLXsIaPZmDHzLkQqNDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:46.568736Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.07244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b50cefa1f09d998c06655adbdcb9100fc83c6b062937f04bb0d2903dded714e6","sha256:013e1ef361ff5300228f814c8a1e7b1edf838bc4eee9d56ef73606554b92b77f"],"state_sha256":"8af264db2235e0b2404acf9635c59942a0c92acc46bc569a98d0be0712e17f68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P8LnYL1+uLcTFHq/HIduacW+BJSLGqcGh1hOF5CXZrEdJVNF1UsRnPW6Ob7B3kV13JWYwOsY6imnzSp61KdMDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:43:30.339581Z","bundle_sha256":"4b6a9ec8b6245e2b46d1ee6f3f64bf8beeef0f0d18df9bef7e441e1955a2c6b3"}}