{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UAU4WL73ZPV43JVEU6RU32X5ZX","short_pith_number":"pith:UAU4WL73","canonical_record":{"source":{"id":"1605.02332","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2016-05-08T16:42:08Z","cross_cats_sorted":[],"title_canon_sha256":"6bf4e0040a58e6af809afba94d2691ea7a0342902d350d6729a26ebdf98898a8","abstract_canon_sha256":"7c20ba3e79bb8d39c9fa1feb27d91d82bbea0ba479563a4ff5fc540ac5051e63"},"schema_version":"1.0"},"canonical_sha256":"a029cb2ffbcbebcda6a4a7a34deafdcdf20a7393383b69e4f975ad629917161c","source":{"kind":"arxiv","id":"1605.02332","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02332","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02332v1","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02332","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"UAU4WL73ZPV4","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UAU4WL73ZPV43JVE","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UAU4WL73","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UAU4WL73ZPV43JVEU6RU32X5ZX","target":"record","payload":{"canonical_record":{"source":{"id":"1605.02332","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2016-05-08T16:42:08Z","cross_cats_sorted":[],"title_canon_sha256":"6bf4e0040a58e6af809afba94d2691ea7a0342902d350d6729a26ebdf98898a8","abstract_canon_sha256":"7c20ba3e79bb8d39c9fa1feb27d91d82bbea0ba479563a4ff5fc540ac5051e63"},"schema_version":"1.0"},"canonical_sha256":"a029cb2ffbcbebcda6a4a7a34deafdcdf20a7393383b69e4f975ad629917161c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:21.267798Z","signature_b64":"j25BXQBZzutF+wIcFxqr9vB61dQVjQkMTXE0Dw0S0ZYxlmcs9xRHkm9o3B2juzBhRa5+VPmU/Q5WxIlTsNuHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a029cb2ffbcbebcda6a4a7a34deafdcdf20a7393383b69e4f975ad629917161c","last_reissued_at":"2026-05-18T01:15:21.267088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:21.267088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.02332","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":"2026-05-18T01:15:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YPiLYygkreLjWLZqk8Ch7+0+vg5dblntDhQ2cr03oJAyOuqaJjBdkqNp6d3oWaS3HL45+pmHzJaH6UyvtyyKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:00:29.230793Z"},"content_sha256":"2639fb10c24e5eeeea847d337c6099865c9fb1ac9434ef3c7d40cb99cf170d09","schema_version":"1.0","event_id":"sha256:2639fb10c24e5eeeea847d337c6099865c9fb1ac9434ef3c7d40cb99cf170d09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UAU4WL73ZPV43JVEU6RU32X5ZX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetric Gini Covariance and Correlation","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Hailin Sang, Xin Dang, Yongli Sang","submitted_at":"2016-05-08T16:42:08Z","abstract_excerpt":"Standard Gini covariance and Gini correlation play important roles in measuring the dependence of random variables with heavy tails. However, the asymmetry brings a substantial difficulty in interpretation. In this paper, we propose a symmetric Gini-type covariance and a symmetric Gini correlation ($\\rho_g$) based on the joint rank function. The proposed correlation $\\rho_g$ is more robust than the Pearson correlation but less robust than the Kendall's $\\tau$ correlation. We establish the relationship between $\\rho_g$ and the linear correlation $\\rho$ for a class of random vectors in the famil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02332","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":"2026-05-18T01:15:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pQVZILp8taBjwWxOTbMjzNJWOmJ3bm4dnHBU/qcvRdtd9my6XznqZio7FP/QV9PbqM2r54ZR43xiU/7LzYLSAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:00:29.231138Z"},"content_sha256":"ffd9a02a037302d614815e8ac5f97f3c8d8f967b3e20a120893140d598350c51","schema_version":"1.0","event_id":"sha256:ffd9a02a037302d614815e8ac5f97f3c8d8f967b3e20a120893140d598350c51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UAU4WL73ZPV43JVEU6RU32X5ZX/bundle.json","state_url":"https://pith.science/pith/UAU4WL73ZPV43JVEU6RU32X5ZX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UAU4WL73ZPV43JVEU6RU32X5ZX/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":"2026-06-02T08:00:29Z","links":{"resolver":"https://pith.science/pith/UAU4WL73ZPV43JVEU6RU32X5ZX","bundle":"https://pith.science/pith/UAU4WL73ZPV43JVEU6RU32X5ZX/bundle.json","state":"https://pith.science/pith/UAU4WL73ZPV43JVEU6RU32X5ZX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UAU4WL73ZPV43JVEU6RU32X5ZX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UAU4WL73ZPV43JVEU6RU32X5ZX","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":"7c20ba3e79bb8d39c9fa1feb27d91d82bbea0ba479563a4ff5fc540ac5051e63","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2016-05-08T16:42:08Z","title_canon_sha256":"6bf4e0040a58e6af809afba94d2691ea7a0342902d350d6729a26ebdf98898a8"},"schema_version":"1.0","source":{"id":"1605.02332","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02332","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02332v1","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02332","created_at":"2026-05-18T01:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"UAU4WL73ZPV4","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UAU4WL73ZPV43JVE","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UAU4WL73","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:ffd9a02a037302d614815e8ac5f97f3c8d8f967b3e20a120893140d598350c51","target":"graph","created_at":"2026-05-18T01:15:21Z","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":"Standard Gini covariance and Gini correlation play important roles in measuring the dependence of random variables with heavy tails. However, the asymmetry brings a substantial difficulty in interpretation. In this paper, we propose a symmetric Gini-type covariance and a symmetric Gini correlation ($\\rho_g$) based on the joint rank function. The proposed correlation $\\rho_g$ is more robust than the Pearson correlation but less robust than the Kendall's $\\tau$ correlation. We establish the relationship between $\\rho_g$ and the linear correlation $\\rho$ for a class of random vectors in the famil","authors_text":"Hailin Sang, Xin Dang, Yongli Sang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2016-05-08T16:42:08Z","title":"Symmetric Gini Covariance and Correlation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02332","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":"sha256:2639fb10c24e5eeeea847d337c6099865c9fb1ac9434ef3c7d40cb99cf170d09","target":"record","created_at":"2026-05-18T01:15:21Z","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":"7c20ba3e79bb8d39c9fa1feb27d91d82bbea0ba479563a4ff5fc540ac5051e63","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2016-05-08T16:42:08Z","title_canon_sha256":"6bf4e0040a58e6af809afba94d2691ea7a0342902d350d6729a26ebdf98898a8"},"schema_version":"1.0","source":{"id":"1605.02332","kind":"arxiv","version":1}},"canonical_sha256":"a029cb2ffbcbebcda6a4a7a34deafdcdf20a7393383b69e4f975ad629917161c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a029cb2ffbcbebcda6a4a7a34deafdcdf20a7393383b69e4f975ad629917161c","first_computed_at":"2026-05-18T01:15:21.267088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:21.267088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j25BXQBZzutF+wIcFxqr9vB61dQVjQkMTXE0Dw0S0ZYxlmcs9xRHkm9o3B2juzBhRa5+VPmU/Q5WxIlTsNuHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:21.267798Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.02332","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2639fb10c24e5eeeea847d337c6099865c9fb1ac9434ef3c7d40cb99cf170d09","sha256:ffd9a02a037302d614815e8ac5f97f3c8d8f967b3e20a120893140d598350c51"],"state_sha256":"7bc2669cb1e9891cf04d5462c94f7ef217f1052b62e4cd0f6fbc08d04c93fab8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ClTXCkzfNZO5garxeM9RggthLr/biVmqM1drFwWls4QUwV0Bxfd3M8/TK9kvjv+ApVxTH587AHPJNxh43bdICw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T08:00:29.233108Z","bundle_sha256":"dc4b4fcc47c689b248e734db54a60e1e350e86cf80636f71eab03664e22d7307"}}