{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:44PBABCMZPDLAQLNCV2J3GSM6Q","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":"17e19d0cdfb85f8a0f28bb27aab94a48fb2500d1c68730b5c86b4c1d3798ec8c","cross_cats_sorted":["cs.IT","cs.NA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-14T17:27:24Z","title_canon_sha256":"b1fd67a535aa2bf0278a61dbaab2ebdaa7cfc758f528e5c3279bd4a993bd77b4"},"schema_version":"1.0","source":{"id":"1811.05919","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05919","created_at":"2026-05-17T23:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05919v2","created_at":"2026-05-17T23:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05919","created_at":"2026-05-17T23:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"44PBABCMZPDL","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"44PBABCMZPDLAQLN","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"44PBABCM","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:5a1c25b02a9a450753770ec36e251d8ad4bed0bc666a1ccf9e2d65d8ea7899bd","target":"graph","created_at":"2026-05-17T23:40:55Z","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":"Robust Principal Component Analysis (PCA) (Candes et al., 2011) and low-rank matrix completion (Recht et al., 2010) are extensions of PCA to allow for outliers and missing entries respectively. It is well-known that solving these problems requires a low coherence between the low-rank matrix and the canonical basis, since in the extreme cases -- when the low-rank matrix we wish to recover is also sparse -- there is an inherent ambiguity. However, the well-posedness issue in both problems is an even more fundamental one: in some cases, both Robust PCA and matrix completion can fail to have any s","authors_text":"Andrew Thompson, Jared Tanner, Simon Vary","cross_cats":["cs.IT","cs.NA","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-14T17:27:24Z","title":"Matrix rigidity and the ill-posedness of Robust PCA and matrix completion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05919","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":"sha256:1de891d818b35dbac2561962f185f70b50bea95d833d768baa819e00a40f8319","target":"record","created_at":"2026-05-17T23:40:55Z","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":"17e19d0cdfb85f8a0f28bb27aab94a48fb2500d1c68730b5c86b4c1d3798ec8c","cross_cats_sorted":["cs.IT","cs.NA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-14T17:27:24Z","title_canon_sha256":"b1fd67a535aa2bf0278a61dbaab2ebdaa7cfc758f528e5c3279bd4a993bd77b4"},"schema_version":"1.0","source":{"id":"1811.05919","kind":"arxiv","version":2}},"canonical_sha256":"e71e10044ccbc6b0416d15749d9a4cf40418b5a0412b4aaf1a0fb4bbaf061b21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e71e10044ccbc6b0416d15749d9a4cf40418b5a0412b4aaf1a0fb4bbaf061b21","first_computed_at":"2026-05-17T23:40:55.694437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:55.694437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+OfOrj2gb6Y9XZlBHRhonxZn4J8FlI+3g8KrloGYmvDQZTLw8gLq3whP2SA6ogmrR74U2ZVyK7fkHsuEcEZeCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:55.695291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05919","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1de891d818b35dbac2561962f185f70b50bea95d833d768baa819e00a40f8319","sha256:5a1c25b02a9a450753770ec36e251d8ad4bed0bc666a1ccf9e2d65d8ea7899bd"],"state_sha256":"74ad13e691fb98b3466c7a21f289f8f520dd3742bc3f01bee41a70d167c96365"}