{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UGFDMLJ63WUYNHVTAFVUJXLR7T","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":"d30dfb74fd474a92d190d295f084b2f133dcf93845b9aaaf9617b0e5bb057d3d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-05-07T15:03:10Z","title_canon_sha256":"7600e87fc206d03b03e7da335a3d6503c39ce06b7aeb25bd1f5697a8b6d1c94e"},"schema_version":"1.0","source":{"id":"1205.1423","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1423","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1423v3","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1423","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"pith_short_12","alias_value":"UGFDMLJ63WUY","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UGFDMLJ63WUYNHVT","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UGFDMLJ6","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:5c58698c43a298281d6f6e177afc238233c45bf7b3649c569c1bec24697ed03d","target":"graph","created_at":"2026-05-18T02:58:22Z","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":"Compressed sensing is the art of reconstructing a sparse vector from its inner products with respect to a small set of randomly chosen measurement vectors. It is usually assumed that the ensemble of measurement vectors is in isotropic position in the sense that the associated covariance matrix is proportional to the identity matrix. In this paper, we establish bounds on the number of required measurements in the anisotropic case, where the ensemble of measurement vectors possesses a non-trivial covariance matrix. Essentially, we find that the required sampling rate grows proportionally to the ","authors_text":"David Gross, Richard Kueng","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-05-07T15:03:10Z","title":"RIPless compressed sensing from anisotropic measurements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1423","kind":"arxiv","version":3},"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":"sha256:80715f72c12ea260924f8b180192cce603264274abd9071ab5c68a0698ba5596","target":"record","created_at":"2026-05-18T02:58:22Z","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":"d30dfb74fd474a92d190d295f084b2f133dcf93845b9aaaf9617b0e5bb057d3d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-05-07T15:03:10Z","title_canon_sha256":"7600e87fc206d03b03e7da335a3d6503c39ce06b7aeb25bd1f5697a8b6d1c94e"},"schema_version":"1.0","source":{"id":"1205.1423","kind":"arxiv","version":3}},"canonical_sha256":"a18a362d3edda9869eb3016b44dd71fcca74e2aaf9b560a6acf3488343469d4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a18a362d3edda9869eb3016b44dd71fcca74e2aaf9b560a6acf3488343469d4e","first_computed_at":"2026-05-18T02:58:22.228338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:22.228338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LjId/t84ibIzxEkaTBboaj0dF5epeWB+qxQ6OdxCH2R1ZZZQILM4Pwgjt3EJbLSgYx0YmWUFglCG02HIbr14CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:22.228792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1423","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80715f72c12ea260924f8b180192cce603264274abd9071ab5c68a0698ba5596","sha256:5c58698c43a298281d6f6e177afc238233c45bf7b3649c569c1bec24697ed03d"],"state_sha256":"ed10595b41642746d493033062571ef754aae0a8d87e2e3fbc45d459f0c3b102"}