{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6ORYWHVAU7M7TYIOC4I6SJYV7X","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":"ae982cd9539af15e72bc30c3279ecbd8e438701b353e632aa4c41ab6d51c1949","cross_cats_sorted":["cs.CV","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-23T08:59:58Z","title_canon_sha256":"6730e7a25eab66b2f7087eec58fa845af0807b276b46eade3891880ee0142cdd"},"schema_version":"1.0","source":{"id":"1207.5326","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5326","created_at":"2026-05-18T03:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5326v1","created_at":"2026-05-18T03:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5326","created_at":"2026-05-18T03:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"6ORYWHVAU7M7","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6ORYWHVAU7M7TYIO","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6ORYWHVA","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:69a595ec7eedbb1fe9f35344a66cc9a285274b1093b53ddac69512ba4203e41b","target":"graph","created_at":"2026-05-18T03:50:23Z","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":"This paper studies the recovery guarantees of the models of minimizing $\\|\\mathcal{X}\\|_*+\\frac{1}{2\\alpha}\\|\\mathcal{X}\\|_F^2$ where $\\mathcal{X}$ is a tensor and $\\|\\mathcal{X}\\|_*$ and $\\|\\mathcal{X}\\|_F$ are the trace and Frobenius norm of respectively. We show that they can efficiently recover low-rank tensors. In particular, they enjoy exact guarantees similar to those known for minimizing $\\|\\mathcal{X}\\|_*$ under the conditions on the sensing operator such as its null-space property, restricted isometry property, or spherical section property. To recover a low-rank tensor $\\mathcal{X}^","authors_text":"Ji Li, Jiqing Han, Shiwen Deng, Tieran Zheng, Ziqiang Shi","cross_cats":["cs.CV","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-23T08:59:58Z","title":"Guarantees of Augmented Trace Norm Models in Tensor Recovery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5326","kind":"arxiv","version":1},"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":"sha256:4dfe68742c3e66606eb147ba9ae5b40c0b019eab4fa6880c6532a8d59add7f5a","target":"record","created_at":"2026-05-18T03:50:23Z","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":"ae982cd9539af15e72bc30c3279ecbd8e438701b353e632aa4c41ab6d51c1949","cross_cats_sorted":["cs.CV","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-23T08:59:58Z","title_canon_sha256":"6730e7a25eab66b2f7087eec58fa845af0807b276b46eade3891880ee0142cdd"},"schema_version":"1.0","source":{"id":"1207.5326","kind":"arxiv","version":1}},"canonical_sha256":"f3a38b1ea0a7d9f9e10e1711e92715fdc8c094a827a9b07f75b2b09dad2d4862","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3a38b1ea0a7d9f9e10e1711e92715fdc8c094a827a9b07f75b2b09dad2d4862","first_computed_at":"2026-05-18T03:50:23.868452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:23.868452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"80YNAvUjtuiYWnE2IzDYLIJE6JkjpAsHNBY0pjdWBZa4cY3nTj7UhSVqZplmUEI5ZA5wmrYv6u+D/iU9XfzmCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:23.869077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5326","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4dfe68742c3e66606eb147ba9ae5b40c0b019eab4fa6880c6532a8d59add7f5a","sha256:69a595ec7eedbb1fe9f35344a66cc9a285274b1093b53ddac69512ba4203e41b"],"state_sha256":"bb2f3eabdf44a2fc057ea2faa07f57e89344dc7dba866b1c0c042c186a194ad1"}