{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:WAM5M4AY3LYUEVAQCQCKOJLYQV","short_pith_number":"pith:WAM5M4AY","canonical_record":{"source":{"id":"2110.15205","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-10-28T15:25:05Z","cross_cats_sorted":["math.FA","stat.TH"],"title_canon_sha256":"6bdb71d563b132a1d14a2c9d10b112d54af5768528e7f9356ee0a74c0b32668e","abstract_canon_sha256":"e712c02e7fcd936d103fa988dca27c815c967622193e24290e7824d829398b86"},"schema_version":"1.0"},"canonical_sha256":"b019d67018daf14254101404a7257885539088fa6316a904ac8a39a22065c1da","source":{"kind":"arxiv","id":"2110.15205","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.15205","created_at":"2026-07-05T05:47:44Z"},{"alias_kind":"arxiv_version","alias_value":"2110.15205v2","created_at":"2026-07-05T05:47:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.15205","created_at":"2026-07-05T05:47:44Z"},{"alias_kind":"pith_short_12","alias_value":"WAM5M4AY3LYU","created_at":"2026-07-05T05:47:44Z"},{"alias_kind":"pith_short_16","alias_value":"WAM5M4AY3LYUEVAQ","created_at":"2026-07-05T05:47:44Z"},{"alias_kind":"pith_short_8","alias_value":"WAM5M4AY","created_at":"2026-07-05T05:47:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:WAM5M4AY3LYUEVAQCQCKOJLYQV","target":"record","payload":{"canonical_record":{"source":{"id":"2110.15205","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-10-28T15:25:05Z","cross_cats_sorted":["math.FA","stat.TH"],"title_canon_sha256":"6bdb71d563b132a1d14a2c9d10b112d54af5768528e7f9356ee0a74c0b32668e","abstract_canon_sha256":"e712c02e7fcd936d103fa988dca27c815c967622193e24290e7824d829398b86"},"schema_version":"1.0"},"canonical_sha256":"b019d67018daf14254101404a7257885539088fa6316a904ac8a39a22065c1da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:47:44.021502Z","signature_b64":"hKkjpTwfo3NslyE+MoyFTAUYfLSQZtdfgD4qDF3yjMzrdhg6ZEZqM6rJc6r74XhsASEK879C+AiGxmzZI2XIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b019d67018daf14254101404a7257885539088fa6316a904ac8a39a22065c1da","last_reissued_at":"2026-07-05T05:47:44.021010Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:47:44.021010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.15205","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":"2026-07-05T05:47:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HGKun2hHOOKK6h8alIP5RnBA5kgkzXGV/TrFkqR4zDwqRv+GHZBS6rIXncPExjVSdTVNNU93k4itSPT9OK1UAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T15:01:41.925963Z"},"content_sha256":"cf8b24ad59788cb5b5c33d7c4e9c905f32cabd82a2b00bc699b5bbdd1167c3ba","schema_version":"1.0","event_id":"sha256:cf8b24ad59788cb5b5c33d7c4e9c905f32cabd82a2b00bc699b5bbdd1167c3ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:WAM5M4AY3LYUEVAQCQCKOJLYQV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximately low-rank recovery from noisy and local measurements by convex program","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","stat.TH"],"primary_cat":"math.ST","authors_text":"Justin Romberg, Kiryung Lee, Marius Junge, Rakshith Sharma Srinivasa","submitted_at":"2021-10-28T15:25:05Z","abstract_excerpt":"Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low rankness has an excellent analogy with the $\\ell_1$ norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.15205","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/2110.15205/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":"2026-07-05T05:47:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q27wNIIEfr9knKd1+nk6rdETHidq1eJBPEFn+zTXB4CaYXPkMGGgeZy5JEvIA6wijhaz20SqXauhHiwzo9tEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T15:01:41.927042Z"},"content_sha256":"048cad417be2a033c892363db9e3c4ab689b531511f83a09c0fde049f80bc164","schema_version":"1.0","event_id":"sha256:048cad417be2a033c892363db9e3c4ab689b531511f83a09c0fde049f80bc164"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WAM5M4AY3LYUEVAQCQCKOJLYQV/bundle.json","state_url":"https://pith.science/pith/WAM5M4AY3LYUEVAQCQCKOJLYQV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WAM5M4AY3LYUEVAQCQCKOJLYQV/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":"2026-08-21T15:01:41Z","links":{"resolver":"https://pith.science/pith/WAM5M4AY3LYUEVAQCQCKOJLYQV","bundle":"https://pith.science/pith/WAM5M4AY3LYUEVAQCQCKOJLYQV/bundle.json","state":"https://pith.science/pith/WAM5M4AY3LYUEVAQCQCKOJLYQV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WAM5M4AY3LYUEVAQCQCKOJLYQV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:WAM5M4AY3LYUEVAQCQCKOJLYQV","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":"e712c02e7fcd936d103fa988dca27c815c967622193e24290e7824d829398b86","cross_cats_sorted":["math.FA","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-10-28T15:25:05Z","title_canon_sha256":"6bdb71d563b132a1d14a2c9d10b112d54af5768528e7f9356ee0a74c0b32668e"},"schema_version":"1.0","source":{"id":"2110.15205","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.15205","created_at":"2026-07-05T05:47:44Z"},{"alias_kind":"arxiv_version","alias_value":"2110.15205v2","created_at":"2026-07-05T05:47:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.15205","created_at":"2026-07-05T05:47:44Z"},{"alias_kind":"pith_short_12","alias_value":"WAM5M4AY3LYU","created_at":"2026-07-05T05:47:44Z"},{"alias_kind":"pith_short_16","alias_value":"WAM5M4AY3LYUEVAQ","created_at":"2026-07-05T05:47:44Z"},{"alias_kind":"pith_short_8","alias_value":"WAM5M4AY","created_at":"2026-07-05T05:47:44Z"}],"graph_snapshots":[{"event_id":"sha256:048cad417be2a033c892363db9e3c4ab689b531511f83a09c0fde049f80bc164","target":"graph","created_at":"2026-07-05T05:47:44Z","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/2110.15205/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low rankness has an excellent analogy with the $\\ell_1$ norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various","authors_text":"Justin Romberg, Kiryung Lee, Marius Junge, Rakshith Sharma Srinivasa","cross_cats":["math.FA","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-10-28T15:25:05Z","title":"Approximately low-rank recovery from noisy and local measurements by convex program"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.15205","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:cf8b24ad59788cb5b5c33d7c4e9c905f32cabd82a2b00bc699b5bbdd1167c3ba","target":"record","created_at":"2026-07-05T05:47:44Z","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":"e712c02e7fcd936d103fa988dca27c815c967622193e24290e7824d829398b86","cross_cats_sorted":["math.FA","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-10-28T15:25:05Z","title_canon_sha256":"6bdb71d563b132a1d14a2c9d10b112d54af5768528e7f9356ee0a74c0b32668e"},"schema_version":"1.0","source":{"id":"2110.15205","kind":"arxiv","version":2}},"canonical_sha256":"b019d67018daf14254101404a7257885539088fa6316a904ac8a39a22065c1da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b019d67018daf14254101404a7257885539088fa6316a904ac8a39a22065c1da","first_computed_at":"2026-07-05T05:47:44.021010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:47:44.021010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hKkjpTwfo3NslyE+MoyFTAUYfLSQZtdfgD4qDF3yjMzrdhg6ZEZqM6rJc6r74XhsASEK879C+AiGxmzZI2XIAw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:47:44.021502Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.15205","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf8b24ad59788cb5b5c33d7c4e9c905f32cabd82a2b00bc699b5bbdd1167c3ba","sha256:048cad417be2a033c892363db9e3c4ab689b531511f83a09c0fde049f80bc164"],"state_sha256":"a830e9bfc14eebef5512ed4ef9f517234e40ca9b10e51650de9f5ced1e8127bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qW95dZa+HGQmGnD1X+O0XD3hxvP+Nk6ylZMBJsQ/SVnmmiewswgWzNOfmET/XT8dSfcl77w8DzoH9s5+oCEVCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T15:01:41.933300Z","bundle_sha256":"e59a696a9571fbef95fd1654d06c2e24b6804d744f7782d47357100632fe77d3"}}