{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HZD7HSABLRMISTV2JDA7IPQNIB","short_pith_number":"pith:HZD7HSAB","canonical_record":{"source":{"id":"1805.07962","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-21T09:49:06Z","cross_cats_sorted":["cs.CV","cs.NA","math.NA"],"title_canon_sha256":"e6a1ab9aa52ceb6a5ced0630bcbd903261423c30ba63e344dba148df6d0ed2ef","abstract_canon_sha256":"47e8d8a35453faeba3b17a6ad677be9b3eca317131b58ff10b33a36a15277d7d"},"schema_version":"1.0"},"canonical_sha256":"3e47f3c8015c58894eba48c1f43e0d404b882fc072873643b4a7df9c1813198f","source":{"kind":"arxiv","id":"1805.07962","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07962","created_at":"2026-07-05T00:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07962v2","created_at":"2026-07-05T00:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07962","created_at":"2026-07-05T00:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"HZD7HSABLRMI","created_at":"2026-07-05T00:35:24Z"},{"alias_kind":"pith_short_16","alias_value":"HZD7HSABLRMISTV2","created_at":"2026-07-05T00:35:24Z"},{"alias_kind":"pith_short_8","alias_value":"HZD7HSAB","created_at":"2026-07-05T00:35:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HZD7HSABLRMISTV2JDA7IPQNIB","target":"record","payload":{"canonical_record":{"source":{"id":"1805.07962","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-21T09:49:06Z","cross_cats_sorted":["cs.CV","cs.NA","math.NA"],"title_canon_sha256":"e6a1ab9aa52ceb6a5ced0630bcbd903261423c30ba63e344dba148df6d0ed2ef","abstract_canon_sha256":"47e8d8a35453faeba3b17a6ad677be9b3eca317131b58ff10b33a36a15277d7d"},"schema_version":"1.0"},"canonical_sha256":"3e47f3c8015c58894eba48c1f43e0d404b882fc072873643b4a7df9c1813198f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:35:24.103270Z","signature_b64":"HCWXyzFet+gmCfaM8tIY7RPmN/9w8PZnZ3CTaZBjJ6ugXJKCdS4oQ0ryxTDFtq3hMTBAoRdkBywVZnCSzu/BCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e47f3c8015c58894eba48c1f43e0d404b882fc072873643b4a7df9c1813198f","last_reissued_at":"2026-07-05T00:35:24.102822Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:35:24.102822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.07962","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":"2026-07-05T00:35:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NzRwa0kPf9tAswUiP684v82n7vX1uzv+HXqGnuDaU/4+O+cPUTl4xCZRuCCzafa5u97kqr2UaX7BjBPMSfvhBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T18:27:05.795864Z"},"content_sha256":"51ed305a99fc665761ffe8f8a5473426cf446b989394e451e12376377db23ea2","schema_version":"1.0","event_id":"sha256:51ed305a99fc665761ffe8f8a5473426cf446b989394e451e12376377db23ea2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HZD7HSABLRMISTV2JDA7IPQNIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Nonconvex Projection Method for Robust PCA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Aritra Dutta, Filip Hanzely, Peter Richt\\'arik","submitted_at":"2018-05-21T09:49:06Z","abstract_excerpt":"Robust principal component analysis (RPCA) is a well-studied problem with the goal of decomposing a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and apply an alternating projection method to solve it. To the best of our knowledge, we are the first to propose a method that solves RPCA problem without considering any objective function, convex relaxation, or surrogate convex constraints. We demonstrate through extensive numerical experiments on a variety of applications, including shadow removal, background"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07962","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1805.07962/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:35:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"590JaaE6vsnke0g7p6AF8mayA2oAyLhtJbbW7YsPT9d55P0rtfhevUlZkAUJTLifMV4PKKvwCQKRhH7+OpB9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T18:27:05.796807Z"},"content_sha256":"50720d378d954d7b8323afeae6a1cc3147c0684853ad0377a16ed35c42e96f8b","schema_version":"1.0","event_id":"sha256:50720d378d954d7b8323afeae6a1cc3147c0684853ad0377a16ed35c42e96f8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HZD7HSABLRMISTV2JDA7IPQNIB/bundle.json","state_url":"https://pith.science/pith/HZD7HSABLRMISTV2JDA7IPQNIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HZD7HSABLRMISTV2JDA7IPQNIB/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":"2026-08-04T18:27:05Z","links":{"resolver":"https://pith.science/pith/HZD7HSABLRMISTV2JDA7IPQNIB","bundle":"https://pith.science/pith/HZD7HSABLRMISTV2JDA7IPQNIB/bundle.json","state":"https://pith.science/pith/HZD7HSABLRMISTV2JDA7IPQNIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HZD7HSABLRMISTV2JDA7IPQNIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HZD7HSABLRMISTV2JDA7IPQNIB","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":"47e8d8a35453faeba3b17a6ad677be9b3eca317131b58ff10b33a36a15277d7d","cross_cats_sorted":["cs.CV","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-21T09:49:06Z","title_canon_sha256":"e6a1ab9aa52ceb6a5ced0630bcbd903261423c30ba63e344dba148df6d0ed2ef"},"schema_version":"1.0","source":{"id":"1805.07962","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07962","created_at":"2026-07-05T00:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07962v2","created_at":"2026-07-05T00:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07962","created_at":"2026-07-05T00:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"HZD7HSABLRMI","created_at":"2026-07-05T00:35:24Z"},{"alias_kind":"pith_short_16","alias_value":"HZD7HSABLRMISTV2","created_at":"2026-07-05T00:35:24Z"},{"alias_kind":"pith_short_8","alias_value":"HZD7HSAB","created_at":"2026-07-05T00:35:24Z"}],"graph_snapshots":[{"event_id":"sha256:50720d378d954d7b8323afeae6a1cc3147c0684853ad0377a16ed35c42e96f8b","target":"graph","created_at":"2026-07-05T00:35:24Z","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/1805.07962/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Robust principal component analysis (RPCA) is a well-studied problem with the goal of decomposing a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and apply an alternating projection method to solve it. To the best of our knowledge, we are the first to propose a method that solves RPCA problem without considering any objective function, convex relaxation, or surrogate convex constraints. We demonstrate through extensive numerical experiments on a variety of applications, including shadow removal, background","authors_text":"Aritra Dutta, Filip Hanzely, Peter Richt\\'arik","cross_cats":["cs.CV","cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-21T09:49:06Z","title":"A Nonconvex Projection Method for Robust PCA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07962","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":"sha256:51ed305a99fc665761ffe8f8a5473426cf446b989394e451e12376377db23ea2","target":"record","created_at":"2026-07-05T00:35:24Z","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":"47e8d8a35453faeba3b17a6ad677be9b3eca317131b58ff10b33a36a15277d7d","cross_cats_sorted":["cs.CV","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-21T09:49:06Z","title_canon_sha256":"e6a1ab9aa52ceb6a5ced0630bcbd903261423c30ba63e344dba148df6d0ed2ef"},"schema_version":"1.0","source":{"id":"1805.07962","kind":"arxiv","version":2}},"canonical_sha256":"3e47f3c8015c58894eba48c1f43e0d404b882fc072873643b4a7df9c1813198f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e47f3c8015c58894eba48c1f43e0d404b882fc072873643b4a7df9c1813198f","first_computed_at":"2026-07-05T00:35:24.102822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:35:24.102822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HCWXyzFet+gmCfaM8tIY7RPmN/9w8PZnZ3CTaZBjJ6ugXJKCdS4oQ0ryxTDFtq3hMTBAoRdkBywVZnCSzu/BCg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:35:24.103270Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07962","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51ed305a99fc665761ffe8f8a5473426cf446b989394e451e12376377db23ea2","sha256:50720d378d954d7b8323afeae6a1cc3147c0684853ad0377a16ed35c42e96f8b"],"state_sha256":"a07d3fa9fc5dc61dc96b47240e61886ba45e078b09026dac155164a134fff6f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VPKlKftMT2YQHdVItrtX3ZPH6oZeBliFPw2ZoMlTYRmUZxqaZp04GNUyzLCix1AG5HfcXLYU1jA8LDgE0X5xCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T18:27:05.804491Z","bundle_sha256":"88bf618f70d87dc8f80797c966e54f259d36a9e8ca676a61051fa5866ec5bb4e"}}