{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OZCB6H2CWEPEZN5BUNKC4DHGWN","short_pith_number":"pith:OZCB6H2C","canonical_record":{"source":{"id":"1507.08751","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-07-31T04:46:25Z","cross_cats_sorted":["cs.IT","cs.NA","math.IT","math.OC"],"title_canon_sha256":"370df9572228b54cef914a51c39b80329b89e56eec225d5e9b7113dcb17e73ca","abstract_canon_sha256":"b647ef91393e97de83bd5980b4b6af09dcfa107e9734f01fca027f34e374a9b1"},"schema_version":"1.0"},"canonical_sha256":"76441f1f42b11e4cb7a1a3542e0ce6b36087f99a45e1e6d5027a12ec236658ad","source":{"kind":"arxiv","id":"1507.08751","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08751","created_at":"2026-05-18T01:09:57Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08751v3","created_at":"2026-05-18T01:09:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08751","created_at":"2026-05-18T01:09:57Z"},{"alias_kind":"pith_short_12","alias_value":"OZCB6H2CWEPE","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OZCB6H2CWEPEZN5B","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OZCB6H2C","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OZCB6H2CWEPEZN5BUNKC4DHGWN","target":"record","payload":{"canonical_record":{"source":{"id":"1507.08751","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-07-31T04:46:25Z","cross_cats_sorted":["cs.IT","cs.NA","math.IT","math.OC"],"title_canon_sha256":"370df9572228b54cef914a51c39b80329b89e56eec225d5e9b7113dcb17e73ca","abstract_canon_sha256":"b647ef91393e97de83bd5980b4b6af09dcfa107e9734f01fca027f34e374a9b1"},"schema_version":"1.0"},"canonical_sha256":"76441f1f42b11e4cb7a1a3542e0ce6b36087f99a45e1e6d5027a12ec236658ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:57.929725Z","signature_b64":"wWEnHy47LSvtLo2RjpVDDWPD1SVdGlhL9ESzC5rmg2YiGILFRNYA8QAiddv2iJSfvzeVJKzSfIioa0zS3p5CDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76441f1f42b11e4cb7a1a3542e0ce6b36087f99a45e1e6d5027a12ec236658ad","last_reissued_at":"2026-05-18T01:09:57.929044Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:57.929044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.08751","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SqcV8+sByFR/eprUukHrmpgW2FIDzb83upSJ/8nuT93MMSehMfB4U8fmDlwDLjau4qCune1RxK7VDtaWwkoVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T06:21:59.215236Z"},"content_sha256":"d6c9117621484e7ca8ddfdd0652ac17cf4953e20919d494efd679b2d83bcf5c8","schema_version":"1.0","event_id":"sha256:d6c9117621484e7ca8ddfdd0652ac17cf4953e20919d494efd679b2d83bcf5c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OZCB6H2CWEPEZN5BUNKC4DHGWN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Beyond Low Rank + Sparse: Multi-scale Low Rank Matrix Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.NA","math.IT","math.OC"],"primary_cat":"cs.SY","authors_text":"Frank Ong, Michael Lustig","submitted_at":"2015-07-31T04:46:25Z","abstract_excerpt":"We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multi-scale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components and approach the problem via a convex f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08751","kind":"arxiv","version":3},"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":"2026-05-18T01:09:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VMD1DGX6dt5uOH45xVvi6eZo0wBHr1ohDUdSXkx7tIE+KyTtgpfHJ9Ys7wC4TeD8iApF7YiacukjqozzcO5LAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T06:21:59.216026Z"},"content_sha256":"671c62b9f15809226856551302ab6188740995af8b6c911ecc9cfadc6ef48410","schema_version":"1.0","event_id":"sha256:671c62b9f15809226856551302ab6188740995af8b6c911ecc9cfadc6ef48410"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OZCB6H2CWEPEZN5BUNKC4DHGWN/bundle.json","state_url":"https://pith.science/pith/OZCB6H2CWEPEZN5BUNKC4DHGWN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OZCB6H2CWEPEZN5BUNKC4DHGWN/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":"2026-05-25T06:21:59Z","links":{"resolver":"https://pith.science/pith/OZCB6H2CWEPEZN5BUNKC4DHGWN","bundle":"https://pith.science/pith/OZCB6H2CWEPEZN5BUNKC4DHGWN/bundle.json","state":"https://pith.science/pith/OZCB6H2CWEPEZN5BUNKC4DHGWN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OZCB6H2CWEPEZN5BUNKC4DHGWN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OZCB6H2CWEPEZN5BUNKC4DHGWN","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":"b647ef91393e97de83bd5980b4b6af09dcfa107e9734f01fca027f34e374a9b1","cross_cats_sorted":["cs.IT","cs.NA","math.IT","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-07-31T04:46:25Z","title_canon_sha256":"370df9572228b54cef914a51c39b80329b89e56eec225d5e9b7113dcb17e73ca"},"schema_version":"1.0","source":{"id":"1507.08751","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08751","created_at":"2026-05-18T01:09:57Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08751v3","created_at":"2026-05-18T01:09:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08751","created_at":"2026-05-18T01:09:57Z"},{"alias_kind":"pith_short_12","alias_value":"OZCB6H2CWEPE","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OZCB6H2CWEPEZN5B","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OZCB6H2C","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:671c62b9f15809226856551302ab6188740995af8b6c911ecc9cfadc6ef48410","target":"graph","created_at":"2026-05-18T01:09:57Z","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 present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multi-scale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components and approach the problem via a convex f","authors_text":"Frank Ong, Michael Lustig","cross_cats":["cs.IT","cs.NA","math.IT","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-07-31T04:46:25Z","title":"Beyond Low Rank + Sparse: Multi-scale Low Rank Matrix Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08751","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:d6c9117621484e7ca8ddfdd0652ac17cf4953e20919d494efd679b2d83bcf5c8","target":"record","created_at":"2026-05-18T01:09:57Z","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":"b647ef91393e97de83bd5980b4b6af09dcfa107e9734f01fca027f34e374a9b1","cross_cats_sorted":["cs.IT","cs.NA","math.IT","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-07-31T04:46:25Z","title_canon_sha256":"370df9572228b54cef914a51c39b80329b89e56eec225d5e9b7113dcb17e73ca"},"schema_version":"1.0","source":{"id":"1507.08751","kind":"arxiv","version":3}},"canonical_sha256":"76441f1f42b11e4cb7a1a3542e0ce6b36087f99a45e1e6d5027a12ec236658ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76441f1f42b11e4cb7a1a3542e0ce6b36087f99a45e1e6d5027a12ec236658ad","first_computed_at":"2026-05-18T01:09:57.929044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:57.929044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wWEnHy47LSvtLo2RjpVDDWPD1SVdGlhL9ESzC5rmg2YiGILFRNYA8QAiddv2iJSfvzeVJKzSfIioa0zS3p5CDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:57.929725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.08751","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6c9117621484e7ca8ddfdd0652ac17cf4953e20919d494efd679b2d83bcf5c8","sha256:671c62b9f15809226856551302ab6188740995af8b6c911ecc9cfadc6ef48410"],"state_sha256":"dccf08a2437ebd5a475c81c98cbd72f218a88c2b1ce6e6c94bd31e6564029957"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WrXWmQqJ4xBok8A+TJ6RM/8X5dGrGa8s3c2795EjjnAynAcLtWUPhTPaSC3XZ8j4TJr0cIlaYQZWd3gg9fZ4Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T06:21:59.219999Z","bundle_sha256":"acedf453218111c9d49d56d98cd71a10eb8109e592f287b8759aeab05434b1ef"}}