{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:ZHSHSN2QUCZCVXRLMFGETEVH6J","short_pith_number":"pith:ZHSHSN2Q","canonical_record":{"source":{"id":"0905.0044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-05-01T03:55:00Z","cross_cats_sorted":["cs.IT","cs.NA","math.IT"],"title_canon_sha256":"ad917649b0be83ceb2bd35180e71e11f82e58bf8937dd2ea93ac4f68b548536c","abstract_canon_sha256":"110d42c6b6f6e58b0f90f13b5abcccda8e03894b6e700d657bfeb5004aaf6782"},"schema_version":"1.0"},"canonical_sha256":"c9e4793750a0b22ade2b614c4992a7f25109e8070daf212bd308e5ea1450834f","source":{"kind":"arxiv","id":"0905.0044","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.0044","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"arxiv_version","alias_value":"0905.0044v2","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.0044","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_12","alias_value":"ZHSHSN2QUCZC","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_16","alias_value":"ZHSHSN2QUCZCVXRL","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_8","alias_value":"ZHSHSN2Q","created_at":"2026-06-03T23:06:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:ZHSHSN2QUCZCVXRLMFGETEVH6J","target":"record","payload":{"canonical_record":{"source":{"id":"0905.0044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-05-01T03:55:00Z","cross_cats_sorted":["cs.IT","cs.NA","math.IT"],"title_canon_sha256":"ad917649b0be83ceb2bd35180e71e11f82e58bf8937dd2ea93ac4f68b548536c","abstract_canon_sha256":"110d42c6b6f6e58b0f90f13b5abcccda8e03894b6e700d657bfeb5004aaf6782"},"schema_version":"1.0"},"canonical_sha256":"c9e4793750a0b22ade2b614c4992a7f25109e8070daf212bd308e5ea1450834f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:06:25.863603Z","signature_b64":"bC8C03XrFJrXvyjJZd41e6uTVfCMGuledKrZ+NhF1ujgYx/ouT6EQ0YW0+yClnRY+pL9C17SWX/INx07WkomAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9e4793750a0b22ade2b614c4992a7f25109e8070daf212bd308e5ea1450834f","last_reissued_at":"2026-06-03T23:06:25.863147Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:06:25.863147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.0044","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":"2026-06-03T23:06:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5kRxawULDzd5J9O8LqOnN/nYIZoKbZQLPufz1bBi0j65u6IVvF1oolmkUHTKSgZ+PDyqkOKvL8gNO0x5NRD4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:23:54.724253Z"},"content_sha256":"f9bce880d0c01a0d9168ae84b48fc6822429fe64c70136c52e557e9fe2570385","schema_version":"1.0","event_id":"sha256:f9bce880d0c01a0d9168ae84b48fc6822429fe64c70136c52e557e9fe2570385"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:ZHSHSN2QUCZCVXRLMFGETEVH6J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"ADMiRA: Atomic Decomposition for Minimum Rank Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.NA","math.IT"],"primary_cat":"math.NA","authors_text":"Kiryung Lee, Yoram Bresler","submitted_at":"2009-05-01T03:55:00Z","abstract_excerpt":"We address the inverse problem that arises in compressed sensing of a low-rank matrix. Our approach is to pose the inverse problem as an approximation problem with a specified target rank of the solution. A simple search over the target rank then provides the minimum rank solution satisfying a prescribed data approximation bound. We propose an atomic decomposition that provides an analogy between parsimonious representations of a sparse vector and a low-rank matrix. Efficient greedy algorithms to solve the inverse problem for the vector case are extended to the matrix case through this atomic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0044","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/0905.0044/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":"2026-06-03T23:06:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A794R5FBtlCJ1UwpI+0yYZADi2tMKM0Ff8HuK4noWLZWBA/urbf0RwICFg502wWKb+0p6gHKlP2aG8Z/SNhpCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:23:54.725067Z"},"content_sha256":"7c7dc3c328fffb669990cc08943ec5d3a98d46cc8ab8bef08bed6b821bce3970","schema_version":"1.0","event_id":"sha256:7c7dc3c328fffb669990cc08943ec5d3a98d46cc8ab8bef08bed6b821bce3970"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZHSHSN2QUCZCVXRLMFGETEVH6J/bundle.json","state_url":"https://pith.science/pith/ZHSHSN2QUCZCVXRLMFGETEVH6J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZHSHSN2QUCZCVXRLMFGETEVH6J/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":"2026-06-08T19:23:54Z","links":{"resolver":"https://pith.science/pith/ZHSHSN2QUCZCVXRLMFGETEVH6J","bundle":"https://pith.science/pith/ZHSHSN2QUCZCVXRLMFGETEVH6J/bundle.json","state":"https://pith.science/pith/ZHSHSN2QUCZCVXRLMFGETEVH6J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZHSHSN2QUCZCVXRLMFGETEVH6J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZHSHSN2QUCZCVXRLMFGETEVH6J","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":"110d42c6b6f6e58b0f90f13b5abcccda8e03894b6e700d657bfeb5004aaf6782","cross_cats_sorted":["cs.IT","cs.NA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-05-01T03:55:00Z","title_canon_sha256":"ad917649b0be83ceb2bd35180e71e11f82e58bf8937dd2ea93ac4f68b548536c"},"schema_version":"1.0","source":{"id":"0905.0044","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.0044","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"arxiv_version","alias_value":"0905.0044v2","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.0044","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_12","alias_value":"ZHSHSN2QUCZC","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_16","alias_value":"ZHSHSN2QUCZCVXRL","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_8","alias_value":"ZHSHSN2Q","created_at":"2026-06-03T23:06:25Z"}],"graph_snapshots":[{"event_id":"sha256:7c7dc3c328fffb669990cc08943ec5d3a98d46cc8ab8bef08bed6b821bce3970","target":"graph","created_at":"2026-06-03T23:06:25Z","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/0905.0044/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We address the inverse problem that arises in compressed sensing of a low-rank matrix. Our approach is to pose the inverse problem as an approximation problem with a specified target rank of the solution. A simple search over the target rank then provides the minimum rank solution satisfying a prescribed data approximation bound. We propose an atomic decomposition that provides an analogy between parsimonious representations of a sparse vector and a low-rank matrix. Efficient greedy algorithms to solve the inverse problem for the vector case are extended to the matrix case through this atomic ","authors_text":"Kiryung Lee, Yoram Bresler","cross_cats":["cs.IT","cs.NA","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-05-01T03:55:00Z","title":"ADMiRA: Atomic Decomposition for Minimum Rank Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0044","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:f9bce880d0c01a0d9168ae84b48fc6822429fe64c70136c52e557e9fe2570385","target":"record","created_at":"2026-06-03T23:06:25Z","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":"110d42c6b6f6e58b0f90f13b5abcccda8e03894b6e700d657bfeb5004aaf6782","cross_cats_sorted":["cs.IT","cs.NA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-05-01T03:55:00Z","title_canon_sha256":"ad917649b0be83ceb2bd35180e71e11f82e58bf8937dd2ea93ac4f68b548536c"},"schema_version":"1.0","source":{"id":"0905.0044","kind":"arxiv","version":2}},"canonical_sha256":"c9e4793750a0b22ade2b614c4992a7f25109e8070daf212bd308e5ea1450834f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9e4793750a0b22ade2b614c4992a7f25109e8070daf212bd308e5ea1450834f","first_computed_at":"2026-06-03T23:06:25.863147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:25.863147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bC8C03XrFJrXvyjJZd41e6uTVfCMGuledKrZ+NhF1ujgYx/ouT6EQ0YW0+yClnRY+pL9C17SWX/INx07WkomAg==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:25.863603Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.0044","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9bce880d0c01a0d9168ae84b48fc6822429fe64c70136c52e557e9fe2570385","sha256:7c7dc3c328fffb669990cc08943ec5d3a98d46cc8ab8bef08bed6b821bce3970"],"state_sha256":"96ddfc04b2fab741a7da5a0c0befc6e6f035550de15e23df00843efb3b8c2e68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e7VbRVARYn47cQZ1AA6PSXNtgUF1t9VA7xHigcW8NxBTICkFPRuc0DN+sT6NCqPQL5wz+ZO+R2bKxkwin7S3CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:23:54.729248Z","bundle_sha256":"7a0a60030cb32739ac3a90395f32a60c13e54d70b97de7e216680b923b3759c5"}}