{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NIZDOB4ME256FXR4RJL53CIFJY","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":"48c561070416955d01456cb948ecb24bbcb3df4118f40847e41c5fddba62aab6","cross_cats_sorted":["cs.DS","cs.IT","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-11-05T21:39:22Z","title_canon_sha256":"6669b0179ae60b4f9df2dc30582365f97fcff249b04b4c827e09385a0a063b55"},"schema_version":"1.0","source":{"id":"1211.1041","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1041","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1041v3","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1041","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"NIZDOB4ME256","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NIZDOB4ME256FXR4","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NIZDOB4M","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:0b1b647b7d52f036420d89e8ca98bbeb1db610721f1cba0828484a77113baa0f","target":"graph","created_at":"2026-05-18T03:05:36Z","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 consider a fundamental problem in unsupervised learning called \\emph{subspace recovery}: given a collection of $m$ points in $\\mathbb{R}^n$, if many but not necessarily all of these points are contained in a $d$-dimensional subspace $T$ can we find it? The points contained in $T$ are called {\\em inliers} and the remaining points are {\\em outliers}. This problem has received considerable attention in computer science and in statistics. Yet efficient algorithms from computer science are not robust to {\\em adversarial} outliers, and the estimators from robust statistics are hard to compute in ","authors_text":"Ankur Moitra, Moritz Hardt","cross_cats":["cs.DS","cs.IT","cs.LG","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-11-05T21:39:22Z","title":"Algorithms and Hardness for Robust Subspace Recovery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1041","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":"sha256:5dd6b9b0c2789051d08f3eee7f594cd899586826097cc6b2bd0d16963ac79500","target":"record","created_at":"2026-05-18T03:05:36Z","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":"48c561070416955d01456cb948ecb24bbcb3df4118f40847e41c5fddba62aab6","cross_cats_sorted":["cs.DS","cs.IT","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-11-05T21:39:22Z","title_canon_sha256":"6669b0179ae60b4f9df2dc30582365f97fcff249b04b4c827e09385a0a063b55"},"schema_version":"1.0","source":{"id":"1211.1041","kind":"arxiv","version":3}},"canonical_sha256":"6a3237078c26bbe2de3c8a57dd89054e18215a92b75bec82e8cb9e5a2a767911","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a3237078c26bbe2de3c8a57dd89054e18215a92b75bec82e8cb9e5a2a767911","first_computed_at":"2026-05-18T03:05:36.288202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:36.288202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k+eGiW+Yh4xP4Is6bWtBWI4eaHDRyvBJN5schsjQdiJxoRAApAlszS6sAuFvV8Gm/pM+hbYv5FCNQAbcQ8SVBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:36.288670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1041","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dd6b9b0c2789051d08f3eee7f594cd899586826097cc6b2bd0d16963ac79500","sha256:0b1b647b7d52f036420d89e8ca98bbeb1db610721f1cba0828484a77113baa0f"],"state_sha256":"0239cfe1eb3556a6bb250f3e594b03aa2dc817f7c222d32517ad977dd834cf79"}