{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:YOABL4XHHPESLG24ALWQ6CWETW","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":"7a3e05ed7d763e165d87184176e9d3f738d30818559bd8001119a34a085d5a6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-10-09T17:07:52Z","title_canon_sha256":"abcb24533b961f1cac49af5726bb5d7f7b7b528b2cebd380927e449668565193"},"schema_version":"1.0","source":{"id":"2010.04684","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.04684","created_at":"2026-07-05T05:35:40Z"},{"alias_kind":"arxiv_version","alias_value":"2010.04684v3","created_at":"2026-07-05T05:35:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.04684","created_at":"2026-07-05T05:35:40Z"},{"alias_kind":"pith_short_12","alias_value":"YOABL4XHHPES","created_at":"2026-07-05T05:35:40Z"},{"alias_kind":"pith_short_16","alias_value":"YOABL4XHHPESLG24","created_at":"2026-07-05T05:35:40Z"},{"alias_kind":"pith_short_8","alias_value":"YOABL4XH","created_at":"2026-07-05T05:35:40Z"}],"graph_snapshots":[{"event_id":"sha256:9c12aaf788a4f807b80c2ec77ff356b0b26ac550a0d1893348fa3bc8cb188abb","target":"graph","created_at":"2026-07-05T05:35:40Z","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/2010.04684/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work develops a sparse and outlier-insensitive method to fit a one-dimensional subspace that can be used as a replacement for eigenvector methods such as principal component analysis (PCA). The method is insensitive to outlier observations by formulating procedures as optimization problems that seek the best-fit line according to the $\\ell^1$ norm. It is also capable of producing sparse principal components by leveraging an additional penalty term induce sparsity. The algorithm has a worst-case time complexity of $O{(m^2n \\log n)}$ and, under certain conditions, produces a globally optima","authors_text":"J. Paul Brooks, Xiao Ling","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-10-09T17:07:52Z","title":"$L_1$-norm regularized $L_1$-norm best-fit line problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.04684","kind":"arxiv","version":3},"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:b7e9d178df9d95c742fb6b894a2a150ab163f2ed64db357bbae5d424e68e1b76","target":"record","created_at":"2026-07-05T05:35:40Z","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":"7a3e05ed7d763e165d87184176e9d3f738d30818559bd8001119a34a085d5a6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-10-09T17:07:52Z","title_canon_sha256":"abcb24533b961f1cac49af5726bb5d7f7b7b528b2cebd380927e449668565193"},"schema_version":"1.0","source":{"id":"2010.04684","kind":"arxiv","version":3}},"canonical_sha256":"c38015f2e73bc9259b5c02ed0f0ac49dae6fb7d5302b6e3e46a55475c93cb6e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c38015f2e73bc9259b5c02ed0f0ac49dae6fb7d5302b6e3e46a55475c93cb6e7","first_computed_at":"2026-07-05T05:35:40.701128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:35:40.701128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E5tbklK2vAA6g6oAMQ3BFIoBRtg5MnI6QSU6Fw4PlWX5PgsE41vgszSbmRYrWPuVw6JPYgpbur3dZz8WP/aKBA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:35:40.701595Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.04684","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7e9d178df9d95c742fb6b894a2a150ab163f2ed64db357bbae5d424e68e1b76","sha256:9c12aaf788a4f807b80c2ec77ff356b0b26ac550a0d1893348fa3bc8cb188abb"],"state_sha256":"0b40ec4a906c794033e6450a1e7ffccad3335f294f718980fd87d783ed02a99e"}