{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LJKVH3EHY3WKBWYMCVPTXXCS37","short_pith_number":"pith:LJKVH3EH","canonical_record":{"source":{"id":"1507.03895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-07-14T15:42:07Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"228c370c3f17bd56ddabc24d908b22239f7eba9da228f6387e733235a54f2edb","abstract_canon_sha256":"3fdb7800d099989cf3f703d9c20c6399dc9cfcffa26e3a213a03ca6c45eaf7f2"},"schema_version":"1.0"},"canonical_sha256":"5a5553ec87c6eca0db0c155f3bdc52dffff1a670dc88ceea863d47be4a792555","source":{"kind":"arxiv","id":"1507.03895","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03895","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03895v2","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03895","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"LJKVH3EHY3WK","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LJKVH3EHY3WKBWYM","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LJKVH3EH","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LJKVH3EHY3WKBWYMCVPTXXCS37","target":"record","payload":{"canonical_record":{"source":{"id":"1507.03895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-07-14T15:42:07Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"228c370c3f17bd56ddabc24d908b22239f7eba9da228f6387e733235a54f2edb","abstract_canon_sha256":"3fdb7800d099989cf3f703d9c20c6399dc9cfcffa26e3a213a03ca6c45eaf7f2"},"schema_version":"1.0"},"canonical_sha256":"5a5553ec87c6eca0db0c155f3bdc52dffff1a670dc88ceea863d47be4a792555","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:38.281873Z","signature_b64":"TYBHOZashOe2YI3yz3xsmrcrPnuWcJ7RyM/3NI1BEyj7ifzBKOq7xMMvYy9RGu/eOWRVjDerlfqMZXxPdEIYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a5553ec87c6eca0db0c155f3bdc52dffff1a670dc88ceea863d47be4a792555","last_reissued_at":"2026-05-18T00:57:38.281453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:38.281453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.03895","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":"2026-05-18T00:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8bS7tPY/v8LPW745jrtNECM9zpKn4VRt5dnEazOjGa2uFyK0s4QG9qEP/gliMZOHpNVDM27/ETO59fj3HnHAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:39:36.081671Z"},"content_sha256":"adbfd972b632b5122fa1740fb006cd9057708c18c13a6f214408c62b81daafb9","schema_version":"1.0","event_id":"sha256:adbfd972b632b5122fa1740fb006cd9057708c18c13a6f214408c62b81daafb9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LJKVH3EHY3WKBWYMCVPTXXCS37","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On consistency and sparsity for sliced inverse regression in high dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jun S. Liu, Qian Lin, Zhigen Zhao","submitted_at":"2015-07-14T15:42:07Z","abstract_excerpt":"We provide here a framework to analyze the phase transition phenomenon of slice inverse regression (SIR), a supervised dimension reduction technique introduced by \\cite{Li:1991}. Under mild conditions, the asymptotic ratio $\\rho= \\lim p/n$ is the phase transition parameter and the SIR estimator is consistent if and only if $\\rho= 0$. When dimension $p$ is greater than $n$, we propose a diagonal thresholding screening SIR (DT-SIR) algorithm. This method provides us with an estimate of the eigen-space of the covariance matrix of the conditional expectation $var(\\mathbf{E}[\\boldsymbol{x}|y])$. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03895","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":"2026-05-18T00:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FabRc8EQPXvdQeyac90IjEkjdICMlUIu7EEDMdzdmkXdeCVCEFugCtKNe5rf5OBV114cYZVBdZHcn5XEN/DEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:39:36.082327Z"},"content_sha256":"54f2e0bf99e4ebaeb943f7457af9291f1eaef4458fa534b6ad172948cd03fed7","schema_version":"1.0","event_id":"sha256:54f2e0bf99e4ebaeb943f7457af9291f1eaef4458fa534b6ad172948cd03fed7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LJKVH3EHY3WKBWYMCVPTXXCS37/bundle.json","state_url":"https://pith.science/pith/LJKVH3EHY3WKBWYMCVPTXXCS37/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LJKVH3EHY3WKBWYMCVPTXXCS37/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":"2026-06-05T21:39:36Z","links":{"resolver":"https://pith.science/pith/LJKVH3EHY3WKBWYMCVPTXXCS37","bundle":"https://pith.science/pith/LJKVH3EHY3WKBWYMCVPTXXCS37/bundle.json","state":"https://pith.science/pith/LJKVH3EHY3WKBWYMCVPTXXCS37/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LJKVH3EHY3WKBWYMCVPTXXCS37/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LJKVH3EHY3WKBWYMCVPTXXCS37","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":"3fdb7800d099989cf3f703d9c20c6399dc9cfcffa26e3a213a03ca6c45eaf7f2","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-07-14T15:42:07Z","title_canon_sha256":"228c370c3f17bd56ddabc24d908b22239f7eba9da228f6387e733235a54f2edb"},"schema_version":"1.0","source":{"id":"1507.03895","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03895","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03895v2","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03895","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"LJKVH3EHY3WK","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LJKVH3EHY3WKBWYM","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LJKVH3EH","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:54f2e0bf99e4ebaeb943f7457af9291f1eaef4458fa534b6ad172948cd03fed7","target":"graph","created_at":"2026-05-18T00:57:38Z","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":"We provide here a framework to analyze the phase transition phenomenon of slice inverse regression (SIR), a supervised dimension reduction technique introduced by \\cite{Li:1991}. Under mild conditions, the asymptotic ratio $\\rho= \\lim p/n$ is the phase transition parameter and the SIR estimator is consistent if and only if $\\rho= 0$. When dimension $p$ is greater than $n$, we propose a diagonal thresholding screening SIR (DT-SIR) algorithm. This method provides us with an estimate of the eigen-space of the covariance matrix of the conditional expectation $var(\\mathbf{E}[\\boldsymbol{x}|y])$. Th","authors_text":"Jun S. Liu, Qian Lin, Zhigen Zhao","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-07-14T15:42:07Z","title":"On consistency and sparsity for sliced inverse regression in high dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03895","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:adbfd972b632b5122fa1740fb006cd9057708c18c13a6f214408c62b81daafb9","target":"record","created_at":"2026-05-18T00:57:38Z","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":"3fdb7800d099989cf3f703d9c20c6399dc9cfcffa26e3a213a03ca6c45eaf7f2","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-07-14T15:42:07Z","title_canon_sha256":"228c370c3f17bd56ddabc24d908b22239f7eba9da228f6387e733235a54f2edb"},"schema_version":"1.0","source":{"id":"1507.03895","kind":"arxiv","version":2}},"canonical_sha256":"5a5553ec87c6eca0db0c155f3bdc52dffff1a670dc88ceea863d47be4a792555","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a5553ec87c6eca0db0c155f3bdc52dffff1a670dc88ceea863d47be4a792555","first_computed_at":"2026-05-18T00:57:38.281453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:38.281453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TYBHOZashOe2YI3yz3xsmrcrPnuWcJ7RyM/3NI1BEyj7ifzBKOq7xMMvYy9RGu/eOWRVjDerlfqMZXxPdEIYBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:38.281873Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.03895","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adbfd972b632b5122fa1740fb006cd9057708c18c13a6f214408c62b81daafb9","sha256:54f2e0bf99e4ebaeb943f7457af9291f1eaef4458fa534b6ad172948cd03fed7"],"state_sha256":"f367946b455b8e879bf5ce4ed71f6cd89c5a4ff4d786c86c933378dc1dd06b9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VF1lAuLlb9e9Xncvdq6+PReRtqoJ5Mbi8HWyYlHzZF2N4rdQisrOD45pQUeSfvO4T6b+P9Wc6ziJjcVjp9agBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:39:36.087632Z","bundle_sha256":"07288160ae8cdfe2d5b2fbb07c1368d06c49e0d5c1cc496fab53d8669063cb9a"}}