{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:BG2M6BLV2LXXBOENCT24OTN33T","short_pith_number":"pith:BG2M6BLV","canonical_record":{"source":{"id":"2409.00679","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2024-09-01T09:44:37Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"e0149df1a517f0709c8a94a3ce531d0a78eb138bbaba767a1a17592e780d7914","abstract_canon_sha256":"a7b6d64b7f93ccdd3648515416aaa7e17744af8d4e19bf7245c471e2ce390b4c"},"schema_version":"1.0"},"canonical_sha256":"09b4cf0575d2ef70b88d14f5c74dbbdce2ca01c07f5c18df5d34e5f7fa847bdd","source":{"kind":"arxiv","id":"2409.00679","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.00679","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"2409.00679v2","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.00679","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"BG2M6BLV2LXX","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"pith_short_16","alias_value":"BG2M6BLV2LXXBOEN","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"pith_short_8","alias_value":"BG2M6BLV","created_at":"2026-07-05T11:06:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:BG2M6BLV2LXXBOENCT24OTN33T","target":"record","payload":{"canonical_record":{"source":{"id":"2409.00679","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2024-09-01T09:44:37Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"e0149df1a517f0709c8a94a3ce531d0a78eb138bbaba767a1a17592e780d7914","abstract_canon_sha256":"a7b6d64b7f93ccdd3648515416aaa7e17744af8d4e19bf7245c471e2ce390b4c"},"schema_version":"1.0"},"canonical_sha256":"09b4cf0575d2ef70b88d14f5c74dbbdce2ca01c07f5c18df5d34e5f7fa847bdd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:06:08.705556Z","signature_b64":"OUeC2ovv4bjmRtGc0V3c55SvHwxBBhQ2VKhZkzG72fEHcd+wntndZ2rN379lh4ASnoQRrap2zkp1Nx1iIMOXCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09b4cf0575d2ef70b88d14f5c74dbbdce2ca01c07f5c18df5d34e5f7fa847bdd","last_reissued_at":"2026-07-05T11:06:08.705021Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:06:08.705021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.00679","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":"2026-07-05T11:06:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AYYSb20gqj2kcPRQjTBd8KOKFQwP/nJlbR4NRAlXVfggrFfZ0KTyZq9/tkb+cEpEtIxoG+SmYq5907igzEdrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:33:23.405310Z"},"content_sha256":"e05114a1241a6327dea373af45c663253c333fa7306f06d67bfe6b59574c385f","schema_version":"1.0","event_id":"sha256:e05114a1241a6327dea373af45c663253c333fa7306f06d67bfe6b59574c385f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:BG2M6BLV2LXXBOENCT24OTN33T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact Exploratory Bi-factor Analysis: A Constraint-based Optimisation Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Jiawei Qiao, Yunxiao Chen, Zhiliang Ying","submitted_at":"2024-09-01T09:44:37Z","abstract_excerpt":"Bi-factor analysis is a form of confirmatory factor analysis widely used in psychological and educational measurement. The use of a bi-factor model requires the specification of an explicit bi-factor structure on the relationship between the observed variables and the group factors. In practice, the bi-factor structure is sometimes unknown, in which case an exploratory form of bi-factor analysis is needed to find the bi-factor structure. Unfortunately, there are few methods for exploratory bi-factor analysis, with the exception of a rotation-based method proposed in Jennrich and Bentler (2011,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.00679","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.00679/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:06:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nHecVaDoTXxqv+xPAwMpcR4j6KgyoTgrUQPJ/Zj3dbN0DHJSb5pPdymmT0d47GXtyL2tItlsHcatwmKlzhVQBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:33:23.406138Z"},"content_sha256":"3a08b96e01b4089ab07816d556b2f7d69f83f2b1275d76f83582074113f077a6","schema_version":"1.0","event_id":"sha256:3a08b96e01b4089ab07816d556b2f7d69f83f2b1275d76f83582074113f077a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BG2M6BLV2LXXBOENCT24OTN33T/bundle.json","state_url":"https://pith.science/pith/BG2M6BLV2LXXBOENCT24OTN33T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BG2M6BLV2LXXBOENCT24OTN33T/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":"2026-08-16T12:33:23Z","links":{"resolver":"https://pith.science/pith/BG2M6BLV2LXXBOENCT24OTN33T","bundle":"https://pith.science/pith/BG2M6BLV2LXXBOENCT24OTN33T/bundle.json","state":"https://pith.science/pith/BG2M6BLV2LXXBOENCT24OTN33T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BG2M6BLV2LXXBOENCT24OTN33T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:BG2M6BLV2LXXBOENCT24OTN33T","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":"a7b6d64b7f93ccdd3648515416aaa7e17744af8d4e19bf7245c471e2ce390b4c","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2024-09-01T09:44:37Z","title_canon_sha256":"e0149df1a517f0709c8a94a3ce531d0a78eb138bbaba767a1a17592e780d7914"},"schema_version":"1.0","source":{"id":"2409.00679","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.00679","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"2409.00679v2","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.00679","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"BG2M6BLV2LXX","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"pith_short_16","alias_value":"BG2M6BLV2LXXBOEN","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"pith_short_8","alias_value":"BG2M6BLV","created_at":"2026-07-05T11:06:08Z"}],"graph_snapshots":[{"event_id":"sha256:3a08b96e01b4089ab07816d556b2f7d69f83f2b1275d76f83582074113f077a6","target":"graph","created_at":"2026-07-05T11:06:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.00679/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Bi-factor analysis is a form of confirmatory factor analysis widely used in psychological and educational measurement. The use of a bi-factor model requires the specification of an explicit bi-factor structure on the relationship between the observed variables and the group factors. In practice, the bi-factor structure is sometimes unknown, in which case an exploratory form of bi-factor analysis is needed to find the bi-factor structure. Unfortunately, there are few methods for exploratory bi-factor analysis, with the exception of a rotation-based method proposed in Jennrich and Bentler (2011,","authors_text":"Jiawei Qiao, Yunxiao Chen, Zhiliang Ying","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2024-09-01T09:44:37Z","title":"Exact Exploratory Bi-factor Analysis: A Constraint-based Optimisation Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.00679","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:e05114a1241a6327dea373af45c663253c333fa7306f06d67bfe6b59574c385f","target":"record","created_at":"2026-07-05T11:06:08Z","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":"a7b6d64b7f93ccdd3648515416aaa7e17744af8d4e19bf7245c471e2ce390b4c","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2024-09-01T09:44:37Z","title_canon_sha256":"e0149df1a517f0709c8a94a3ce531d0a78eb138bbaba767a1a17592e780d7914"},"schema_version":"1.0","source":{"id":"2409.00679","kind":"arxiv","version":2}},"canonical_sha256":"09b4cf0575d2ef70b88d14f5c74dbbdce2ca01c07f5c18df5d34e5f7fa847bdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09b4cf0575d2ef70b88d14f5c74dbbdce2ca01c07f5c18df5d34e5f7fa847bdd","first_computed_at":"2026-07-05T11:06:08.705021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:06:08.705021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OUeC2ovv4bjmRtGc0V3c55SvHwxBBhQ2VKhZkzG72fEHcd+wntndZ2rN379lh4ASnoQRrap2zkp1Nx1iIMOXCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:06:08.705556Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.00679","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e05114a1241a6327dea373af45c663253c333fa7306f06d67bfe6b59574c385f","sha256:3a08b96e01b4089ab07816d556b2f7d69f83f2b1275d76f83582074113f077a6"],"state_sha256":"213ece824d3b8f9f3cb62f5abd6bff27d8be16325ff9e3b35ed994785eff51ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h2T2z/CpySVZd9hLN7X8ZbH8noX2J8X8QuxV7d5HEi5yf5le8ckE3ky8p0chRNznEVMGtLbdrV6O/7nO7SI4BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T12:33:23.411893Z","bundle_sha256":"336b46f96ad419dfe0a037da3cc67951f72b83db784d011c978bf8a56f249d09"}}