{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7EF42K6RZ5QPCE26DCXS3QZ4MI","short_pith_number":"pith:7EF42K6R","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"},"canonical_sha256":"f90bcd2bd1cf60f1135e18af2dc33c623bd04bbca62873fa46e67c98fe7f9bef","source":{"kind":"arxiv","id":"1002.0182","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0182","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0182v1","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0182","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"7EF42K6RZ5QP","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7EF42K6RZ5QPCE26","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7EF42K6R","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7EF42K6RZ5QPCE26DCXS3QZ4MI","target":"record","payload":{"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"},"canonical_sha256":"f90bcd2bd1cf60f1135e18af2dc33c623bd04bbca62873fa46e67c98fe7f9bef","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"},"source_kind":"arxiv","source_id":"1002.0182","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:39:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cMjODCcxWBE9HY2u+Vlc5TqDSk2su4uD2AT36YvgWbY01pIn4maUad0Endu5OCuUELtQ4Sn2z4r4CslMBlmeAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T02:40:13.393117Z"},"content_sha256":"4fbdcbed6fdfc1b2220a7a45e1d88b5796c64c696cfd3a0eb3303e49a5cfec9b","schema_version":"1.0","event_id":"sha256:4fbdcbed6fdfc1b2220a7a45e1d88b5796c64c696cfd3a0eb3303e49a5cfec9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7EF42K6RZ5QPCE26DCXS3QZ4MI","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:39:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vOv72FxJhN9/y7u2ekFgfjJFGJhdF6I6yHMomziDQfB2Vom5ggO5xPmN5r+BwNcmxsAa0pZzKQ1T6Qv4VZaVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T02:40:13.393818Z"},"content_sha256":"15cd15509684a1da1e717efc76bc8dc9ba802a03d1be3b6ba6640161123b66c3","schema_version":"1.0","event_id":"sha256:15cd15509684a1da1e717efc76bc8dc9ba802a03d1be3b6ba6640161123b66c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI/bundle.json","state_url":"https://pith.science/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI/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":"2026-05-23T02:40:13Z","links":{"resolver":"https://pith.science/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI","bundle":"https://pith.science/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI/bundle.json","state":"https://pith.science/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7EF42K6RZ5QPCE26DCXS3QZ4MI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7EF42K6RZ5QPCE26DCXS3QZ4MI","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":"b6671d86a1fe7ad961aa64b0dc19d59e20098b1812516bc7f4632a462cda8297","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-01T08:12:24Z","title_canon_sha256":"8d22ec0158007f2a4afeff6672ac8668adab7ed23ebc84b201c783308cc22dd5"},"schema_version":"1.0","source":{"id":"1002.0182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0182","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0182v1","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0182","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"7EF42K6RZ5QP","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7EF42K6RZ5QPCE26","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7EF42K6R","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:15cd15509684a1da1e717efc76bc8dc9ba802a03d1be3b6ba6640161123b66c3","target":"graph","created_at":"2026-05-18T04:39:51Z","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":"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","authors_text":"A. Powell, \\\"O. Y{\\i}lmaz, R. Saab, S. G\\\"unt\\\"urk","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-01T08:12:24Z","title":"Sobolev Duals for Random Frames and Sigma-Delta Quantization of Compressed Sensing Measurements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0182","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":"sha256:4fbdcbed6fdfc1b2220a7a45e1d88b5796c64c696cfd3a0eb3303e49a5cfec9b","target":"record","created_at":"2026-05-18T04:39:51Z","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":"b6671d86a1fe7ad961aa64b0dc19d59e20098b1812516bc7f4632a462cda8297","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-01T08:12:24Z","title_canon_sha256":"8d22ec0158007f2a4afeff6672ac8668adab7ed23ebc84b201c783308cc22dd5"},"schema_version":"1.0","source":{"id":"1002.0182","kind":"arxiv","version":1}},"canonical_sha256":"f90bcd2bd1cf60f1135e18af2dc33c623bd04bbca62873fa46e67c98fe7f9bef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f90bcd2bd1cf60f1135e18af2dc33c623bd04bbca62873fa46e67c98fe7f9bef","first_computed_at":"2026-05-18T04:39:51.302814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:51.302814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YjCrT9rb3e+5JKfIXzI1cwoLfn3nTMWLhXZZX1ozrTY/Vo600yMZSfAlyOFujddsadBiET+ixKmP0hLTYF2KDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:51.303458Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.0182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fbdcbed6fdfc1b2220a7a45e1d88b5796c64c696cfd3a0eb3303e49a5cfec9b","sha256:15cd15509684a1da1e717efc76bc8dc9ba802a03d1be3b6ba6640161123b66c3"],"state_sha256":"f6ab68c12e35a1ff390117cfff57807da8da93b093e01cb3856b54a045ba3d53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbYPRCTBpKGwRRJmdD4WsBQeWDFGU46I8ZfK+/nDXbKYMKCxhwJ5Tpw8SPuD7xIgT9WyTrWEOGgrggL9iM0yCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T02:40:13.397855Z","bundle_sha256":"6a96fe72094555b94ecc821f622fe3df5865f519d4a99b2932e7d94eb0acd2c7"}}