{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UGP7R3DEELJMSJK42PSJQA4GTB","short_pith_number":"pith:UGP7R3DE","canonical_record":{"source":{"id":"1609.02191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-07T20:55:38Z","cross_cats_sorted":["cond-mat.dis-nn","math.IT"],"title_canon_sha256":"46059ce1832b297ed3c649cb86fdf05c8d9ee30fb5dec88b482b3eff793586b5","abstract_canon_sha256":"2ca9bfa51102f8ca2b0d06fea82ee24953f19a11f9e23e7c6147b8c75c511a46"},"schema_version":"1.0"},"canonical_sha256":"a19ff8ec6422d2c9255cd3e498038698615069309314864fee226fccee452e77","source":{"kind":"arxiv","id":"1609.02191","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02191","created_at":"2026-05-18T01:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02191v1","created_at":"2026-05-18T01:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02191","created_at":"2026-05-18T01:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"UGP7R3DEELJM","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UGP7R3DEELJMSJK4","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UGP7R3DE","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UGP7R3DEELJMSJK42PSJQA4GTB","target":"record","payload":{"canonical_record":{"source":{"id":"1609.02191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-07T20:55:38Z","cross_cats_sorted":["cond-mat.dis-nn","math.IT"],"title_canon_sha256":"46059ce1832b297ed3c649cb86fdf05c8d9ee30fb5dec88b482b3eff793586b5","abstract_canon_sha256":"2ca9bfa51102f8ca2b0d06fea82ee24953f19a11f9e23e7c6147b8c75c511a46"},"schema_version":"1.0"},"canonical_sha256":"a19ff8ec6422d2c9255cd3e498038698615069309314864fee226fccee452e77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:55.225280Z","signature_b64":"N+I6XVTiTo7G7CX86mi7M4tkEw+9NcXxCkzO3xZU6LHnBd6FQK0w9IaRiLKMRlO4o1bFQ1ek7NNXmkYcFhgiBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a19ff8ec6422d2c9255cd3e498038698615069309314864fee226fccee452e77","last_reissued_at":"2026-05-18T01:04:55.224799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:55.224799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.02191","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":"2026-05-18T01:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KUZzgmp50XZXpDw6hWwI6LF0GBnow0xDxFyrIo/wGXMuXWeN1zt+TDh9cI2Qrhj8tITnxINOyQQSefVABvi8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T11:54:47.246252Z"},"content_sha256":"b03f84404c75cf1b73d0de8ebe9b6c608e436725810e65461f98a20a1021cf19","schema_version":"1.0","event_id":"sha256:b03f84404c75cf1b73d0de8ebe9b6c608e436725810e65461f98a20a1021cf19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UGP7R3DEELJMSJK42PSJQA4GTB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Online Learning for Sparse PCA in High Dimensions: Exact Dynamics and Phase Transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.IT"],"primary_cat":"cs.IT","authors_text":"Chuang Wang, Yue M. Lu","submitted_at":"2016-09-07T20:55:38Z","abstract_excerpt":"We study the dynamics of an online algorithm for learning a sparse leading eigenvector from samples generated from a spiked covariance model. This algorithm combines the classical Oja's method for online PCA with an element-wise nonlinearity at each iteration to promote sparsity. In the high-dimensional limit, the joint empirical measure of the underlying sparse eigenvector and its estimate provided by the algorithm is shown to converge weakly to a deterministic, measure-valued process. This scaling limit is characterized as the unique solution of a nonlinear PDE, and it provides exact informa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02191","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":"2026-05-18T01:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zpNo7+FKZcqSQ8Jt393gybo2wtr1fsmxZq1e3QacQQ5QFjPwaCod4TEk+U3nrimy0nhO3bRJ8x/S9zfFEbdsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T11:54:47.246612Z"},"content_sha256":"b47fe8c1fe338d8b16ea3ce50338579e2bf0415011835d5a25ae9ac7f69a8c2c","schema_version":"1.0","event_id":"sha256:b47fe8c1fe338d8b16ea3ce50338579e2bf0415011835d5a25ae9ac7f69a8c2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UGP7R3DEELJMSJK42PSJQA4GTB/bundle.json","state_url":"https://pith.science/pith/UGP7R3DEELJMSJK42PSJQA4GTB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UGP7R3DEELJMSJK42PSJQA4GTB/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":"2026-07-05T11:54:47Z","links":{"resolver":"https://pith.science/pith/UGP7R3DEELJMSJK42PSJQA4GTB","bundle":"https://pith.science/pith/UGP7R3DEELJMSJK42PSJQA4GTB/bundle.json","state":"https://pith.science/pith/UGP7R3DEELJMSJK42PSJQA4GTB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UGP7R3DEELJMSJK42PSJQA4GTB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UGP7R3DEELJMSJK42PSJQA4GTB","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":"2ca9bfa51102f8ca2b0d06fea82ee24953f19a11f9e23e7c6147b8c75c511a46","cross_cats_sorted":["cond-mat.dis-nn","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-07T20:55:38Z","title_canon_sha256":"46059ce1832b297ed3c649cb86fdf05c8d9ee30fb5dec88b482b3eff793586b5"},"schema_version":"1.0","source":{"id":"1609.02191","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02191","created_at":"2026-05-18T01:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02191v1","created_at":"2026-05-18T01:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02191","created_at":"2026-05-18T01:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"UGP7R3DEELJM","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UGP7R3DEELJMSJK4","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UGP7R3DE","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:b47fe8c1fe338d8b16ea3ce50338579e2bf0415011835d5a25ae9ac7f69a8c2c","target":"graph","created_at":"2026-05-18T01:04:55Z","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 study the dynamics of an online algorithm for learning a sparse leading eigenvector from samples generated from a spiked covariance model. This algorithm combines the classical Oja's method for online PCA with an element-wise nonlinearity at each iteration to promote sparsity. In the high-dimensional limit, the joint empirical measure of the underlying sparse eigenvector and its estimate provided by the algorithm is shown to converge weakly to a deterministic, measure-valued process. This scaling limit is characterized as the unique solution of a nonlinear PDE, and it provides exact informa","authors_text":"Chuang Wang, Yue M. Lu","cross_cats":["cond-mat.dis-nn","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-07T20:55:38Z","title":"Online Learning for Sparse PCA in High Dimensions: Exact Dynamics and Phase Transitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02191","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:b03f84404c75cf1b73d0de8ebe9b6c608e436725810e65461f98a20a1021cf19","target":"record","created_at":"2026-05-18T01:04:55Z","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":"2ca9bfa51102f8ca2b0d06fea82ee24953f19a11f9e23e7c6147b8c75c511a46","cross_cats_sorted":["cond-mat.dis-nn","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-07T20:55:38Z","title_canon_sha256":"46059ce1832b297ed3c649cb86fdf05c8d9ee30fb5dec88b482b3eff793586b5"},"schema_version":"1.0","source":{"id":"1609.02191","kind":"arxiv","version":1}},"canonical_sha256":"a19ff8ec6422d2c9255cd3e498038698615069309314864fee226fccee452e77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a19ff8ec6422d2c9255cd3e498038698615069309314864fee226fccee452e77","first_computed_at":"2026-05-18T01:04:55.224799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:55.224799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N+I6XVTiTo7G7CX86mi7M4tkEw+9NcXxCkzO3xZU6LHnBd6FQK0w9IaRiLKMRlO4o1bFQ1ek7NNXmkYcFhgiBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:55.225280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02191","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b03f84404c75cf1b73d0de8ebe9b6c608e436725810e65461f98a20a1021cf19","sha256:b47fe8c1fe338d8b16ea3ce50338579e2bf0415011835d5a25ae9ac7f69a8c2c"],"state_sha256":"42c284b007516d1e3bae1aec6af48e293763b38e6ac11403ecf000e42091f4d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zCbdiFMHjI3GwnnwlMVhZgKKHQitzmMA2JW0pukOc2keBT/Qor8KKWCwmMjuSOTFuxY4xriRdnqduVdwjl2VAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T11:54:47.248474Z","bundle_sha256":"f935053d177e289408b5c561412d75ca06da849f74712871983c3e4772a3093f"}}