{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:7EF42K6RZ5QPCE26DCXS3QZ4MI","short_pith_number":"pith:7EF42K6R","schema_version":"1.0","canonical_sha256":"f90bcd2bd1cf60f1135e18af2dc33c623bd04bbca62873fa46e67c98fe7f9bef","source":{"kind":"arxiv","id":"1002.0182","version":1},"attestation_state":"computed","paper":{"title":"Sobolev Duals for Random Frames and Sigma-Delta Quantization of Compressed Sensing Measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"A. Powell, \\\"O. Y{\\i}lmaz, R. Saab, S. G\\\"unt\\\"urk","submitted_at":"2010-02-01T08:12:24Z","abstract_excerpt":"Quantization of compressed sensing measurements is typically justified by the robust recovery results of Cand\\`es, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size $\\delta$ is used to quantize $m$ measurements $y = \\Phi x$ of a $k$-sparse signal $x \\in \\R^N$, where $\\Phi$ satisfies the restricted isometry property, then the approximate recovery $x^#$ via $\\ell_1$-minimization is within $O(\\delta)$ of $x$. The simplest and commonly assumed approach is to quantize each measurement independently. In this paper, we show that if instead an $r$th order"},"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":"1002.0182","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-01T08:12:24Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"8d22ec0158007f2a4afeff6672ac8668adab7ed23ebc84b201c783308cc22dd5","abstract_canon_sha256":"b6671d86a1fe7ad961aa64b0dc19d59e20098b1812516bc7f4632a462cda8297"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:51.303458Z","signature_b64":"YjCrT9rb3e+5JKfIXzI1cwoLfn3nTMWLhXZZX1ozrTY/Vo600yMZSfAlyOFujddsadBiET+ixKmP0hLTYF2KDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f90bcd2bd1cf60f1135e18af2dc33c623bd04bbca62873fa46e67c98fe7f9bef","last_reissued_at":"2026-05-18T04:39:51.302814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:51.302814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sobolev Duals for Random Frames and Sigma-Delta Quantization of Compressed Sensing Measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"A. Powell, \\\"O. Y{\\i}lmaz, R. Saab, S. G\\\"unt\\\"urk","submitted_at":"2010-02-01T08:12:24Z","abstract_excerpt":"Quantization of compressed sensing measurements is typically justified by the robust recovery results of Cand\\`es, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size $\\delta$ is used to quantize $m$ measurements $y = \\Phi x$ of a $k$-sparse signal $x \\in \\R^N$, where $\\Phi$ satisfies the restricted isometry property, then the approximate recovery $x^#$ via $\\ell_1$-minimization is within $O(\\delta)$ of $x$. The simplest and commonly assumed approach is to quantize each measurement independently. In this paper, we show that if instead an $r$th order"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0182","kind":"arxiv","version":1},"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":"1002.0182","created_at":"2026-05-18T04:39:51.302940+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.0182v1","created_at":"2026-05-18T04:39:51.302940+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0182","created_at":"2026-05-18T04:39:51.302940+00:00"},{"alias_kind":"pith_short_12","alias_value":"7EF42K6RZ5QP","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"7EF42K6RZ5QPCE26","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"7EF42K6R","created_at":"2026-05-18T12:26:04.259169+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/7EF42K6RZ5QPCE26DCXS3QZ4MI","json":"https://pith.science/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI.json","graph_json":"https://pith.science/api/pith-number/7EF42K6RZ5QPCE26DCXS3QZ4MI/graph.json","events_json":"https://pith.science/api/pith-number/7EF42K6RZ5QPCE26DCXS3QZ4MI/events.json","paper":"https://pith.science/paper/7EF42K6R"},"agent_actions":{"view_html":"https://pith.science/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI","download_json":"https://pith.science/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI.json","view_paper":"https://pith.science/paper/7EF42K6R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.0182&json=true","fetch_graph":"https://pith.science/api/pith-number/7EF42K6RZ5QPCE26DCXS3QZ4MI/graph.json","fetch_events":"https://pith.science/api/pith-number/7EF42K6RZ5QPCE26DCXS3QZ4MI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI/action/storage_attestation","attest_author":"https://pith.science/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI/action/author_attestation","sign_citation":"https://pith.science/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI/action/citation_signature","submit_replication":"https://pith.science/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI/action/replication_record"}},"created_at":"2026-05-18T04:39:51.302940+00:00","updated_at":"2026-05-18T04:39:51.302940+00:00"}