{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LR4O6BFNW3EHUEDDEXQ3VE36MY","short_pith_number":"pith:LR4O6BFN","canonical_record":{"source":{"id":"1304.0537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-04-02T05:45:58Z","cross_cats_sorted":[],"title_canon_sha256":"95ce06040a4964df273d963c8c7eab8711f86ad21992ebce633297f3985e1b8b","abstract_canon_sha256":"edb61ded64f96d2e593d3b61d1cfde2c7d1cfccd92933fc03e6243899818f8cd"},"schema_version":"1.0"},"canonical_sha256":"5c78ef04adb6c87a106325e1ba937e66304ef31ee5f6bea8e3ef3f474aaef7c6","source":{"kind":"arxiv","id":"1304.0537","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0537","created_at":"2026-05-18T03:29:15Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0537v1","created_at":"2026-05-18T03:29:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0537","created_at":"2026-05-18T03:29:15Z"},{"alias_kind":"pith_short_12","alias_value":"LR4O6BFNW3EH","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LR4O6BFNW3EHUEDD","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LR4O6BFN","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LR4O6BFNW3EHUEDDEXQ3VE36MY","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-04-02T05:45:58Z","cross_cats_sorted":[],"title_canon_sha256":"95ce06040a4964df273d963c8c7eab8711f86ad21992ebce633297f3985e1b8b","abstract_canon_sha256":"edb61ded64f96d2e593d3b61d1cfde2c7d1cfccd92933fc03e6243899818f8cd"},"schema_version":"1.0"},"canonical_sha256":"5c78ef04adb6c87a106325e1ba937e66304ef31ee5f6bea8e3ef3f474aaef7c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:15.123482Z","signature_b64":"HpXL9IGwHHdPjbOeyqLOwAZsfaMoMhhTRoQ76Ar0socSesPqQP9jJmYo0GqnCAazveduWgLIfgFbuSVT3DaICQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c78ef04adb6c87a106325e1ba937e66304ef31ee5f6bea8e3ef3f474aaef7c6","last_reissued_at":"2026-05-18T03:29:15.122764Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:15.122764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0537","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":"2026-05-18T03:29:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9sfJYxsIy+oOJsLwbmEUYY0fBRRqSPetzzRkTm444pgXetK7T9Jej4TKPORANGlwnKWXhoa344BZrVLV9GP5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:30:28.764145Z"},"content_sha256":"573a4b7b3931ac2eb8211bb9b78d7dbb7dfcdbf5691e4254a509cb2bf7545b85","schema_version":"1.0","event_id":"sha256:573a4b7b3931ac2eb8211bb9b78d7dbb7dfcdbf5691e4254a509cb2bf7545b85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LR4O6BFNW3EHUEDDEXQ3VE36MY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dual To Ratio Cum Product Estimator In Stratified Random Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Cem Kadilar, Manoj K. Chaudhary, Mukesh Kumar, Rajesh Singh","submitted_at":"2013-04-02T05:45:58Z","abstract_excerpt":"Tracy et al.[8] have introduced a family of estimators using Srivenkataramana and Tracy ([6],[7]) transformation in simple random sampling. In this article, we have proposed a dual to ratio-cum-product estimator in stratified random sampling. The expressions of the mean square error of the proposed estimators are derived. Also, the theoretical findings are supported by a numerical example."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0537","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":"2026-05-18T03:29:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iZ/fplES2dbHFbmOs0+c6a9GZjkJ6dUL8ziulGXO9alYkIc4d4Eg3kVgmHPe9+mhaTJjepYCyfPHBO27Va7xAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:30:28.764818Z"},"content_sha256":"dc3c5232a40de8e0e3530a97ff8bc75bf73a20750e2ab41e3869afb93df22d7a","schema_version":"1.0","event_id":"sha256:dc3c5232a40de8e0e3530a97ff8bc75bf73a20750e2ab41e3869afb93df22d7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LR4O6BFNW3EHUEDDEXQ3VE36MY/bundle.json","state_url":"https://pith.science/pith/LR4O6BFNW3EHUEDDEXQ3VE36MY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LR4O6BFNW3EHUEDDEXQ3VE36MY/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":"2026-06-07T14:30:28Z","links":{"resolver":"https://pith.science/pith/LR4O6BFNW3EHUEDDEXQ3VE36MY","bundle":"https://pith.science/pith/LR4O6BFNW3EHUEDDEXQ3VE36MY/bundle.json","state":"https://pith.science/pith/LR4O6BFNW3EHUEDDEXQ3VE36MY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LR4O6BFNW3EHUEDDEXQ3VE36MY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LR4O6BFNW3EHUEDDEXQ3VE36MY","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":"edb61ded64f96d2e593d3b61d1cfde2c7d1cfccd92933fc03e6243899818f8cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-04-02T05:45:58Z","title_canon_sha256":"95ce06040a4964df273d963c8c7eab8711f86ad21992ebce633297f3985e1b8b"},"schema_version":"1.0","source":{"id":"1304.0537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0537","created_at":"2026-05-18T03:29:15Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0537v1","created_at":"2026-05-18T03:29:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0537","created_at":"2026-05-18T03:29:15Z"},{"alias_kind":"pith_short_12","alias_value":"LR4O6BFNW3EH","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LR4O6BFNW3EHUEDD","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LR4O6BFN","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:dc3c5232a40de8e0e3530a97ff8bc75bf73a20750e2ab41e3869afb93df22d7a","target":"graph","created_at":"2026-05-18T03:29:15Z","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":"Tracy et al.[8] have introduced a family of estimators using Srivenkataramana and Tracy ([6],[7]) transformation in simple random sampling. In this article, we have proposed a dual to ratio-cum-product estimator in stratified random sampling. The expressions of the mean square error of the proposed estimators are derived. Also, the theoretical findings are supported by a numerical example.","authors_text":"Cem Kadilar, Manoj K. Chaudhary, Mukesh Kumar, Rajesh Singh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-04-02T05:45:58Z","title":"Dual To Ratio Cum Product Estimator In Stratified Random Sampling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0537","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":"sha256:573a4b7b3931ac2eb8211bb9b78d7dbb7dfcdbf5691e4254a509cb2bf7545b85","target":"record","created_at":"2026-05-18T03:29:15Z","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":"edb61ded64f96d2e593d3b61d1cfde2c7d1cfccd92933fc03e6243899818f8cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-04-02T05:45:58Z","title_canon_sha256":"95ce06040a4964df273d963c8c7eab8711f86ad21992ebce633297f3985e1b8b"},"schema_version":"1.0","source":{"id":"1304.0537","kind":"arxiv","version":1}},"canonical_sha256":"5c78ef04adb6c87a106325e1ba937e66304ef31ee5f6bea8e3ef3f474aaef7c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c78ef04adb6c87a106325e1ba937e66304ef31ee5f6bea8e3ef3f474aaef7c6","first_computed_at":"2026-05-18T03:29:15.122764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:15.122764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HpXL9IGwHHdPjbOeyqLOwAZsfaMoMhhTRoQ76Ar0socSesPqQP9jJmYo0GqnCAazveduWgLIfgFbuSVT3DaICQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:15.123482Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:573a4b7b3931ac2eb8211bb9b78d7dbb7dfcdbf5691e4254a509cb2bf7545b85","sha256:dc3c5232a40de8e0e3530a97ff8bc75bf73a20750e2ab41e3869afb93df22d7a"],"state_sha256":"b65da78fa910fdd763739d6aa9ed173de1d3a9db45a1f246c3887023de0efced"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lJo/cp2hwiTKMWiqAeLPhzoHfrzoh+VQPRXS1XfGauyvzSP2GRT2xqOqSlRVJgVbnZm2yL/oPxfo7GvW0/sACQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:30:28.768067Z","bundle_sha256":"2fd7203d8b5b814323d9daa28023eb3644e7b4daea9bb7475e9ec23331bddc03"}}