{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FVW4GMZDXFGCDXZPKEWX5Z64JH","short_pith_number":"pith:FVW4GMZD","canonical_record":{"source":{"id":"1310.4132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-15T18:04:29Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"7c866af0c44b93aa006a4131910f9b2ced8d79d9da850f8d3cd137689044251e","abstract_canon_sha256":"312a1fe861d878e86fe5f9beec0b692fecbb21afdf6ce00f3f04c19dc2a7a8cb"},"schema_version":"1.0"},"canonical_sha256":"2d6dc33323b94c21df2f512d7ee7dc49eed8bed204c49a8d9c6c76cc276ba50c","source":{"kind":"arxiv","id":"1310.4132","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4132","created_at":"2026-05-18T03:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4132v1","created_at":"2026-05-18T03:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4132","created_at":"2026-05-18T03:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"FVW4GMZDXFGC","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FVW4GMZDXFGCDXZP","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FVW4GMZD","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FVW4GMZDXFGCDXZPKEWX5Z64JH","target":"record","payload":{"canonical_record":{"source":{"id":"1310.4132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-15T18:04:29Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"7c866af0c44b93aa006a4131910f9b2ced8d79d9da850f8d3cd137689044251e","abstract_canon_sha256":"312a1fe861d878e86fe5f9beec0b692fecbb21afdf6ce00f3f04c19dc2a7a8cb"},"schema_version":"1.0"},"canonical_sha256":"2d6dc33323b94c21df2f512d7ee7dc49eed8bed204c49a8d9c6c76cc276ba50c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:24.966148Z","signature_b64":"Wn/RIllbH7YGwkoEjt15bvaZ8PNe5m5vEdXshv2dEsRheEGRtBEezhrQWW9q5+GU86q0xTudAHDo28Rl/LRACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d6dc33323b94c21df2f512d7ee7dc49eed8bed204c49a8d9c6c76cc276ba50c","last_reissued_at":"2026-05-18T03:10:24.965414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:24.965414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.4132","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":"2026-05-18T03:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dXAe/zJWa7Q2qVufynUEaNJMXrgFROe1N168AaOkNRyA5hc8cadtVByImdelkj03TaNJu0ekGlKRL/WQk1gJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:10:35.596199Z"},"content_sha256":"428068180b560a05b93425fdbd9b5e6663680daac26aa91c758038d0903971e1","schema_version":"1.0","event_id":"sha256:428068180b560a05b93425fdbd9b5e6663680daac26aa91c758038d0903971e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FVW4GMZDXFGCDXZPKEWX5Z64JH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomization-based models for experiments: I. A chain of randomizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"C. J. Brien, R. A. Bailey","submitted_at":"2013-10-15T18:04:29Z","abstract_excerpt":"We derive randomization-based models for experiments with a chain of randomizations. The estimation theory for these models leads to formulae for the estimators of treatment effects, their standard errors, and expected mean squares in the analysis of variance. We discuss the practicalities in fitting these models and outline the difficulties that can occur, many of which do not arise in two-tiered experiments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4132","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":"2026-05-18T03:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gKdaA8R/ZfvNczo7bJc8PTv+DLBZfKs7YTQAoVxwS2e0EbvmqZ4zUEAl16J9Wp5ObyeYXAWKHooofjaKF0ENCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:10:35.596976Z"},"content_sha256":"5a8ec7acc71f9ccee1457b1dc326c6672fa1ad4d8bf33179b7e8de837bf31dc7","schema_version":"1.0","event_id":"sha256:5a8ec7acc71f9ccee1457b1dc326c6672fa1ad4d8bf33179b7e8de837bf31dc7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FVW4GMZDXFGCDXZPKEWX5Z64JH/bundle.json","state_url":"https://pith.science/pith/FVW4GMZDXFGCDXZPKEWX5Z64JH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FVW4GMZDXFGCDXZPKEWX5Z64JH/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":"2026-05-31T16:10:35Z","links":{"resolver":"https://pith.science/pith/FVW4GMZDXFGCDXZPKEWX5Z64JH","bundle":"https://pith.science/pith/FVW4GMZDXFGCDXZPKEWX5Z64JH/bundle.json","state":"https://pith.science/pith/FVW4GMZDXFGCDXZPKEWX5Z64JH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FVW4GMZDXFGCDXZPKEWX5Z64JH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FVW4GMZDXFGCDXZPKEWX5Z64JH","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":"312a1fe861d878e86fe5f9beec0b692fecbb21afdf6ce00f3f04c19dc2a7a8cb","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-15T18:04:29Z","title_canon_sha256":"7c866af0c44b93aa006a4131910f9b2ced8d79d9da850f8d3cd137689044251e"},"schema_version":"1.0","source":{"id":"1310.4132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4132","created_at":"2026-05-18T03:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4132v1","created_at":"2026-05-18T03:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4132","created_at":"2026-05-18T03:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"FVW4GMZDXFGC","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FVW4GMZDXFGCDXZP","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FVW4GMZD","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:5a8ec7acc71f9ccee1457b1dc326c6672fa1ad4d8bf33179b7e8de837bf31dc7","target":"graph","created_at":"2026-05-18T03:10:24Z","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":"We derive randomization-based models for experiments with a chain of randomizations. The estimation theory for these models leads to formulae for the estimators of treatment effects, their standard errors, and expected mean squares in the analysis of variance. We discuss the practicalities in fitting these models and outline the difficulties that can occur, many of which do not arise in two-tiered experiments.","authors_text":"C. J. Brien, R. A. Bailey","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-15T18:04:29Z","title":"Randomization-based models for experiments: I. A chain of randomizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4132","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":"sha256:428068180b560a05b93425fdbd9b5e6663680daac26aa91c758038d0903971e1","target":"record","created_at":"2026-05-18T03:10:24Z","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":"312a1fe861d878e86fe5f9beec0b692fecbb21afdf6ce00f3f04c19dc2a7a8cb","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-10-15T18:04:29Z","title_canon_sha256":"7c866af0c44b93aa006a4131910f9b2ced8d79d9da850f8d3cd137689044251e"},"schema_version":"1.0","source":{"id":"1310.4132","kind":"arxiv","version":1}},"canonical_sha256":"2d6dc33323b94c21df2f512d7ee7dc49eed8bed204c49a8d9c6c76cc276ba50c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d6dc33323b94c21df2f512d7ee7dc49eed8bed204c49a8d9c6c76cc276ba50c","first_computed_at":"2026-05-18T03:10:24.965414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:24.965414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wn/RIllbH7YGwkoEjt15bvaZ8PNe5m5vEdXshv2dEsRheEGRtBEezhrQWW9q5+GU86q0xTudAHDo28Rl/LRACg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:24.966148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:428068180b560a05b93425fdbd9b5e6663680daac26aa91c758038d0903971e1","sha256:5a8ec7acc71f9ccee1457b1dc326c6672fa1ad4d8bf33179b7e8de837bf31dc7"],"state_sha256":"74fb39b118b0e13e9d8b7c9929da893ed1660ff349cfb56761840650612f0a4e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3+/4YjxaHccrp7kEoNSC3FLzDBcFF4pSKWMtqylQqTATaU460EsLoYxqpK1V7b+QgykrfBwX2/o6HVx/cVqOAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:10:35.601443Z","bundle_sha256":"cae0e4a361fe8bc8cc33382ae255593bc63ffb4a02f2f5754d9820d521e8b9a0"}}