{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:D7MKMRNBO2K2DGTCFBQJ4ILN3A","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":"30ca43e8ae719c28b88ec57e5d6cc8723842608071365527ad23eed082cd349a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-06-01T17:57:32Z","title_canon_sha256":"c8071b7e407bbf60ccf0489148bdd9d6c1558417223ef383687e29911d024818"},"schema_version":"1.0","source":{"id":"1406.0187","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0187","created_at":"2026-05-18T01:18:19Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0187v1","created_at":"2026-05-18T01:18:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0187","created_at":"2026-05-18T01:18:19Z"},{"alias_kind":"pith_short_12","alias_value":"D7MKMRNBO2K2","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D7MKMRNBO2K2DGTC","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D7MKMRNB","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:b3ccb2968e23effe3a8deb80de34219612592023151b77e23fa5e5a824e686d9","target":"graph","created_at":"2026-05-18T01:18:19Z","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 proposes a set of piecewise Toeplitz matrices as the linear mapping/sensing operator $\\mathcal{A}: \\mathbf{R}^{n_1 \\times n_2} \\rightarrow \\mathbf{R}^M$ for recovering low rank matrices from few measurements. We prove that such operators efficiently encode the information so there exists a unique reconstruction matrix under mild assumptions. This work provides a significant extension of the compressed sensing and rank minimization theory, and it achieves a tradeoff between reducing the memory required for storing the sampling operator from $\\mathcal{O}(n_1n_2M)$ to $\\mathcal{O}(\\max","authors_text":"Cristian R. Rojas, H\\r{a}kan Hjalmarsson, Kezhi Li, Saikat Chatterjee","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-06-01T17:57:32Z","title":"Piecewise Toeplitz Matrices-based Sensing for Rank Minimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0187","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:c0f54f0a07285cd6c80827a14ea61d32b0e2757297baaa881527b8a9f01c7f47","target":"record","created_at":"2026-05-18T01:18:19Z","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":"30ca43e8ae719c28b88ec57e5d6cc8723842608071365527ad23eed082cd349a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-06-01T17:57:32Z","title_canon_sha256":"c8071b7e407bbf60ccf0489148bdd9d6c1558417223ef383687e29911d024818"},"schema_version":"1.0","source":{"id":"1406.0187","kind":"arxiv","version":1}},"canonical_sha256":"1fd8a645a17695a19a6228609e216dd8333c86194a2ccd75fd0c27d847b77155","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fd8a645a17695a19a6228609e216dd8333c86194a2ccd75fd0c27d847b77155","first_computed_at":"2026-05-18T01:18:19.164362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:19.164362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NcEvKKAnyyHEIMPqlTZD9GB8s5JfH38dAAWI1zQt/sUEmhnJQNLqDDWPk98tMybtVxj1X20XUju2DjkVnmGrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:19.164909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.0187","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0f54f0a07285cd6c80827a14ea61d32b0e2757297baaa881527b8a9f01c7f47","sha256:b3ccb2968e23effe3a8deb80de34219612592023151b77e23fa5e5a824e686d9"],"state_sha256":"c8d7488a83c24fdb92deb26f13615f6bd33cab26dda6bb8aa25c5733cd48f00f"}