{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GLPIOIFWHF5ZAD3LWAPIS5MFZF","short_pith_number":"pith:GLPIOIFW","canonical_record":{"source":{"id":"1110.1740","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-08T14:17:31Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"574bab724dd6a3b08961281ae6c4a79755eaede851e3bc03aebc8f99df422467","abstract_canon_sha256":"698d8085949e65bdd57433d384a2c90a0dc5a6f5b0a43970ce3a72e5b64cc157"},"schema_version":"1.0"},"canonical_sha256":"32de8720b6397b900f6bb01e897585c966fc81788cc08f03461760936dab0735","source":{"kind":"arxiv","id":"1110.1740","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1740","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1740v2","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1740","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"GLPIOIFWHF5Z","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GLPIOIFWHF5ZAD3L","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GLPIOIFW","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GLPIOIFWHF5ZAD3LWAPIS5MFZF","target":"record","payload":{"canonical_record":{"source":{"id":"1110.1740","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-08T14:17:31Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"574bab724dd6a3b08961281ae6c4a79755eaede851e3bc03aebc8f99df422467","abstract_canon_sha256":"698d8085949e65bdd57433d384a2c90a0dc5a6f5b0a43970ce3a72e5b64cc157"},"schema_version":"1.0"},"canonical_sha256":"32de8720b6397b900f6bb01e897585c966fc81788cc08f03461760936dab0735","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:38.247589Z","signature_b64":"C5PmJmVE7pi05YWlzIUqrtRSfQpb7I2z2hT2O/vlMpofCe6AF7mLpf7SYeG5ieo0D3Cv+Omoo2QKoSjL5DA8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32de8720b6397b900f6bb01e897585c966fc81788cc08f03461760936dab0735","last_reissued_at":"2026-05-18T04:05:38.247146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:38.247146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.1740","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:05:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wCl0HvJiT+DchAaHOHJ2ROP2uo7JhfPJatH5K2O7YtoKIl2BOHm7wnxPXlzbgRhd4vHfJ7V8qOSSLc5Zm5ljDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:25:28.656008Z"},"content_sha256":"82b300b98ee8292cd21be53b0ef9079af93b3f86e102cb9091d93d76218e9422","schema_version":"1.0","event_id":"sha256:82b300b98ee8292cd21be53b0ef9079af93b3f86e102cb9091d93d76218e9422"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GLPIOIFWHF5ZAD3LWAPIS5MFZF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Average Collapsibility of Some Association Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"P. Vellaisamy","submitted_at":"2011-10-08T14:17:31Z","abstract_excerpt":"Collapsibility deals with the conditions under which a conditional (on a covariate W) measure of association between two random variables X and Y equals the marginal measure of association, under the assumption of homogeneity over the covariate. In this paper, we discuss the average collapsibility of certain well-known measures of association, and also with respect to a new measure of association. The concept of average collapsibility is more general than collapsibility, and requires that the conditional average of an association measure equals the corresponding marginal measure. Sufficient co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1740","kind":"arxiv","version":2},"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":"2026-05-18T04:05:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+PSkk2e0EAA+9yUEJWZL6A1Af7uyADcELv9oun4v5XFFD/OC+JnXKhTA+FMEnD0DQhVzBoO5Cprj7u4xsn3bDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:25:28.656362Z"},"content_sha256":"44a918ac639f0906dbc490c891a52171d02a970584f983faaa5c06ec093a1008","schema_version":"1.0","event_id":"sha256:44a918ac639f0906dbc490c891a52171d02a970584f983faaa5c06ec093a1008"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GLPIOIFWHF5ZAD3LWAPIS5MFZF/bundle.json","state_url":"https://pith.science/pith/GLPIOIFWHF5ZAD3LWAPIS5MFZF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GLPIOIFWHF5ZAD3LWAPIS5MFZF/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":"2026-06-01T12:25:28Z","links":{"resolver":"https://pith.science/pith/GLPIOIFWHF5ZAD3LWAPIS5MFZF","bundle":"https://pith.science/pith/GLPIOIFWHF5ZAD3LWAPIS5MFZF/bundle.json","state":"https://pith.science/pith/GLPIOIFWHF5ZAD3LWAPIS5MFZF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GLPIOIFWHF5ZAD3LWAPIS5MFZF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GLPIOIFWHF5ZAD3LWAPIS5MFZF","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":"698d8085949e65bdd57433d384a2c90a0dc5a6f5b0a43970ce3a72e5b64cc157","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-08T14:17:31Z","title_canon_sha256":"574bab724dd6a3b08961281ae6c4a79755eaede851e3bc03aebc8f99df422467"},"schema_version":"1.0","source":{"id":"1110.1740","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1740","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1740v2","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1740","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"GLPIOIFWHF5Z","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GLPIOIFWHF5ZAD3L","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GLPIOIFW","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:44a918ac639f0906dbc490c891a52171d02a970584f983faaa5c06ec093a1008","target":"graph","created_at":"2026-05-18T04:05:38Z","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":"Collapsibility deals with the conditions under which a conditional (on a covariate W) measure of association between two random variables X and Y equals the marginal measure of association, under the assumption of homogeneity over the covariate. In this paper, we discuss the average collapsibility of certain well-known measures of association, and also with respect to a new measure of association. The concept of average collapsibility is more general than collapsibility, and requires that the conditional average of an association measure equals the corresponding marginal measure. Sufficient co","authors_text":"P. Vellaisamy","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-08T14:17:31Z","title":"Average Collapsibility of Some Association Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1740","kind":"arxiv","version":2},"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":"sha256:82b300b98ee8292cd21be53b0ef9079af93b3f86e102cb9091d93d76218e9422","target":"record","created_at":"2026-05-18T04:05:38Z","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":"698d8085949e65bdd57433d384a2c90a0dc5a6f5b0a43970ce3a72e5b64cc157","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-08T14:17:31Z","title_canon_sha256":"574bab724dd6a3b08961281ae6c4a79755eaede851e3bc03aebc8f99df422467"},"schema_version":"1.0","source":{"id":"1110.1740","kind":"arxiv","version":2}},"canonical_sha256":"32de8720b6397b900f6bb01e897585c966fc81788cc08f03461760936dab0735","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32de8720b6397b900f6bb01e897585c966fc81788cc08f03461760936dab0735","first_computed_at":"2026-05-18T04:05:38.247146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:38.247146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C5PmJmVE7pi05YWlzIUqrtRSfQpb7I2z2hT2O/vlMpofCe6AF7mLpf7SYeG5ieo0D3Cv+Omoo2QKoSjL5DA8Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:38.247589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1740","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82b300b98ee8292cd21be53b0ef9079af93b3f86e102cb9091d93d76218e9422","sha256:44a918ac639f0906dbc490c891a52171d02a970584f983faaa5c06ec093a1008"],"state_sha256":"6c8cfa8b38c9c6036de0cbd66eb77b8027420f29a9e961599d895bb12c2d4703"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3JKZQKZSLXIxp28udx1sEZQzpjq5j7RMWjt+QExvZOHGfjuL140n9JPof53Q/Z6Mi7fsptuaxYZycdGj+EhqBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:25:28.658272Z","bundle_sha256":"0993d8613188347415e7f2857920a140daa6c4df964a3f023dba3084dc482955"}}