{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XJF7KX6FRHKEL6FVBXYT5WE63K","short_pith_number":"pith:XJF7KX6F","canonical_record":{"source":{"id":"1304.0580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-02T10:17:54Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"3cafffb741f9b5e885181b7fe76be1b82892df810ce1d83cdfd07a69e7eb548d","abstract_canon_sha256":"a3252e6d18e0ab1444edef15d72e3844fb91d6e3a95e5e2071ff52568aad8e95"},"schema_version":"1.0"},"canonical_sha256":"ba4bf55fc589d445f8b50df13ed89eda9e2715dc76c78fd4f03f1af59c6d1aa4","source":{"kind":"arxiv","id":"1304.0580","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0580","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0580v1","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0580","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"pith_short_12","alias_value":"XJF7KX6FRHKE","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XJF7KX6FRHKEL6FV","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XJF7KX6F","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XJF7KX6FRHKEL6FVBXYT5WE63K","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-02T10:17:54Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"3cafffb741f9b5e885181b7fe76be1b82892df810ce1d83cdfd07a69e7eb548d","abstract_canon_sha256":"a3252e6d18e0ab1444edef15d72e3844fb91d6e3a95e5e2071ff52568aad8e95"},"schema_version":"1.0"},"canonical_sha256":"ba4bf55fc589d445f8b50df13ed89eda9e2715dc76c78fd4f03f1af59c6d1aa4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:14.985264Z","signature_b64":"gJw4E9UBhSewip/PcjcMf+WeonHXrwYlqXJ/tpLE5bV0fqxYXl81veIDSjxz+kttxYfnZyr6pUZvqS7bg6Q8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba4bf55fc589d445f8b50df13ed89eda9e2715dc76c78fd4f03f1af59c6d1aa4","last_reissued_at":"2026-05-18T03:29:14.984658Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:14.984658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0580","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":"2026-05-18T03:29:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v7DBS0B518Tfp/9Jc5pQj+2FZYTvmrAZAHtATe45TsJzu6exu5Ko1Lm1r5A9vM5GIB2PdMPDjv86ZMvsFlRlDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:02:45.721493Z"},"content_sha256":"f6793bbc5a77d2da89c54bc8e12e6b8a60fa6e1b3638af4603fd3404f5992bab","schema_version":"1.0","event_id":"sha256:f6793bbc5a77d2da89c54bc8e12e6b8a60fa6e1b3638af4603fd3404f5992bab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XJF7KX6FRHKEL6FVBXYT5WE63K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A general theory for nonlinear sufficient dimension reduction: Formulation and estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Bing Li, Francesca Chiaromonte, Kuang-Yao Lee","submitted_at":"2013-04-02T10:17:54Z","abstract_excerpt":"In this paper we introduce a general theory for nonlinear sufficient dimension reduction, and explore its ramifications and scope. This theory subsumes recent work employing reproducing kernel Hilbert spaces, and reveals many parallels between linear and nonlinear sufficient dimension reduction. Using these parallels we analyze the properties of existing methods and develop new ones. We begin by characterizing dimension reduction at the general level of $\\sigma$-fields and proceed to that of classes of functions, leading to the notions of sufficient, complete and central dimension reduction cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0580","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":"2026-05-18T03:29:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4mzhpakdYVuNw7qwyVUfo0N0tVHgvKYGx2/bBz9HCvcaTVXmWKOBYMBPPu4wYOYrkcl0Y1joLMY3Qq1pFB1dAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:02:45.721850Z"},"content_sha256":"8d138007221dacbcbe0aba7ff7e58d45b28cf357f7070c0f240d9fc9127c2a6e","schema_version":"1.0","event_id":"sha256:8d138007221dacbcbe0aba7ff7e58d45b28cf357f7070c0f240d9fc9127c2a6e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XJF7KX6FRHKEL6FVBXYT5WE63K/bundle.json","state_url":"https://pith.science/pith/XJF7KX6FRHKEL6FVBXYT5WE63K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XJF7KX6FRHKEL6FVBXYT5WE63K/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":"2026-06-05T08:02:45Z","links":{"resolver":"https://pith.science/pith/XJF7KX6FRHKEL6FVBXYT5WE63K","bundle":"https://pith.science/pith/XJF7KX6FRHKEL6FVBXYT5WE63K/bundle.json","state":"https://pith.science/pith/XJF7KX6FRHKEL6FVBXYT5WE63K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XJF7KX6FRHKEL6FVBXYT5WE63K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XJF7KX6FRHKEL6FVBXYT5WE63K","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":"a3252e6d18e0ab1444edef15d72e3844fb91d6e3a95e5e2071ff52568aad8e95","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-02T10:17:54Z","title_canon_sha256":"3cafffb741f9b5e885181b7fe76be1b82892df810ce1d83cdfd07a69e7eb548d"},"schema_version":"1.0","source":{"id":"1304.0580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0580","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0580v1","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0580","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"pith_short_12","alias_value":"XJF7KX6FRHKE","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XJF7KX6FRHKEL6FV","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XJF7KX6F","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:8d138007221dacbcbe0aba7ff7e58d45b28cf357f7070c0f240d9fc9127c2a6e","target":"graph","created_at":"2026-05-18T03:29:14Z","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":"In this paper we introduce a general theory for nonlinear sufficient dimension reduction, and explore its ramifications and scope. This theory subsumes recent work employing reproducing kernel Hilbert spaces, and reveals many parallels between linear and nonlinear sufficient dimension reduction. Using these parallels we analyze the properties of existing methods and develop new ones. We begin by characterizing dimension reduction at the general level of $\\sigma$-fields and proceed to that of classes of functions, leading to the notions of sufficient, complete and central dimension reduction cl","authors_text":"Bing Li, Francesca Chiaromonte, Kuang-Yao Lee","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-02T10:17:54Z","title":"A general theory for nonlinear sufficient dimension reduction: Formulation and estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0580","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:f6793bbc5a77d2da89c54bc8e12e6b8a60fa6e1b3638af4603fd3404f5992bab","target":"record","created_at":"2026-05-18T03:29:14Z","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":"a3252e6d18e0ab1444edef15d72e3844fb91d6e3a95e5e2071ff52568aad8e95","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-04-02T10:17:54Z","title_canon_sha256":"3cafffb741f9b5e885181b7fe76be1b82892df810ce1d83cdfd07a69e7eb548d"},"schema_version":"1.0","source":{"id":"1304.0580","kind":"arxiv","version":1}},"canonical_sha256":"ba4bf55fc589d445f8b50df13ed89eda9e2715dc76c78fd4f03f1af59c6d1aa4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba4bf55fc589d445f8b50df13ed89eda9e2715dc76c78fd4f03f1af59c6d1aa4","first_computed_at":"2026-05-18T03:29:14.984658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:14.984658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gJw4E9UBhSewip/PcjcMf+WeonHXrwYlqXJ/tpLE5bV0fqxYXl81veIDSjxz+kttxYfnZyr6pUZvqS7bg6Q8Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:14.985264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6793bbc5a77d2da89c54bc8e12e6b8a60fa6e1b3638af4603fd3404f5992bab","sha256:8d138007221dacbcbe0aba7ff7e58d45b28cf357f7070c0f240d9fc9127c2a6e"],"state_sha256":"523372492c8830cb027117ea46af2341ac1c7d764aecd8afbc8bcfe0dac37823"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y4bDk78U8FjMaI+L3nemaByOIEW/SNGShbZSwNy5TwT0yhUsCusKhGlX6SvQ2sqz+JzO/EHyLdbT0fCUrpyKCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:02:45.725056Z","bundle_sha256":"6153e28c4b9f1fbab5f7f13b73cf8a9acd9b6666154181dff086ea89c41e1a99"}}