{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:H57DCNZFC7FFCXCT6AG7746VXM","short_pith_number":"pith:H57DCNZF","schema_version":"1.0","canonical_sha256":"3f7e31372517ca515c53f00dfff3d5bb2682f6c44a763c35761758cb54501390","source":{"kind":"arxiv","id":"1401.4269","version":3},"attestation_state":"computed","paper":{"title":"SUPER: Sparse signals with Unknown Phases Efficiently Recovered","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mayank Bakshi, Minghua Chen, Sheng Cai, Sidharth Jaggi","submitted_at":"2014-01-17T08:34:17Z","abstract_excerpt":"Suppose ${\\bf x}$ is any exactly $k$-sparse vector in $\\mathbb{C}^{n}$. We present a class of phase measurement matrix $A$ in $\\mathbb{C}^{m\\times n}$, and a corresponding algorithm, called SUPER, that can resolve ${\\bf x}$ up to a global phase from intensity measurements $|A{\\bf x}|$ with high probability over $A$. Here $|A{\\bf x}|$ is a vector of component-wise magnitudes of $A{\\bf x}$. The SUPER algorithm is the first to simultaneously have the following properties: (a) it requires only ${\\cal O}(k)$ (order-optimal) measurements, (b) the computational complexity of decoding is ${\\cal O}(k\\l"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.4269","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-01-17T08:34:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"cf8ac356c13a8972e17e622572d6008e7d58421be067f59432f479bb214286b4","abstract_canon_sha256":"7ec50671b43c73c262f01febd3e5114eb622ccda3cb86e8fd3794f94c41649e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:01.871722Z","signature_b64":"8BJWhgZxc+bo0RJJsUN29x9sRk4SfyVeExEsuu4xxwy25/JmFTGwqPQRKl0U3tj8blSAAekFQd1soYGzHc28Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f7e31372517ca515c53f00dfff3d5bb2682f6c44a763c35761758cb54501390","last_reissued_at":"2026-05-18T03:01:01.871086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:01.871086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"SUPER: Sparse signals with Unknown Phases Efficiently Recovered","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mayank Bakshi, Minghua Chen, Sheng Cai, Sidharth Jaggi","submitted_at":"2014-01-17T08:34:17Z","abstract_excerpt":"Suppose ${\\bf x}$ is any exactly $k$-sparse vector in $\\mathbb{C}^{n}$. We present a class of phase measurement matrix $A$ in $\\mathbb{C}^{m\\times n}$, and a corresponding algorithm, called SUPER, that can resolve ${\\bf x}$ up to a global phase from intensity measurements $|A{\\bf x}|$ with high probability over $A$. Here $|A{\\bf x}|$ is a vector of component-wise magnitudes of $A{\\bf x}$. The SUPER algorithm is the first to simultaneously have the following properties: (a) it requires only ${\\cal O}(k)$ (order-optimal) measurements, (b) the computational complexity of decoding is ${\\cal O}(k\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4269","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1401.4269","created_at":"2026-05-18T03:01:01.871218+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.4269v3","created_at":"2026-05-18T03:01:01.871218+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4269","created_at":"2026-05-18T03:01:01.871218+00:00"},{"alias_kind":"pith_short_12","alias_value":"H57DCNZFC7FF","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"H57DCNZFC7FFCXCT","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"H57DCNZF","created_at":"2026-05-18T12:28:30.664211+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/H57DCNZFC7FFCXCT6AG7746VXM","json":"https://pith.science/pith/H57DCNZFC7FFCXCT6AG7746VXM.json","graph_json":"https://pith.science/api/pith-number/H57DCNZFC7FFCXCT6AG7746VXM/graph.json","events_json":"https://pith.science/api/pith-number/H57DCNZFC7FFCXCT6AG7746VXM/events.json","paper":"https://pith.science/paper/H57DCNZF"},"agent_actions":{"view_html":"https://pith.science/pith/H57DCNZFC7FFCXCT6AG7746VXM","download_json":"https://pith.science/pith/H57DCNZFC7FFCXCT6AG7746VXM.json","view_paper":"https://pith.science/paper/H57DCNZF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.4269&json=true","fetch_graph":"https://pith.science/api/pith-number/H57DCNZFC7FFCXCT6AG7746VXM/graph.json","fetch_events":"https://pith.science/api/pith-number/H57DCNZFC7FFCXCT6AG7746VXM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H57DCNZFC7FFCXCT6AG7746VXM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H57DCNZFC7FFCXCT6AG7746VXM/action/storage_attestation","attest_author":"https://pith.science/pith/H57DCNZFC7FFCXCT6AG7746VXM/action/author_attestation","sign_citation":"https://pith.science/pith/H57DCNZFC7FFCXCT6AG7746VXM/action/citation_signature","submit_replication":"https://pith.science/pith/H57DCNZFC7FFCXCT6AG7746VXM/action/replication_record"}},"created_at":"2026-05-18T03:01:01.871218+00:00","updated_at":"2026-05-18T03:01:01.871218+00:00"}