{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TCVNLSKEAEOHTIPEFVKTH66LMY","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":"124b87314eea89e226be82644c4d918685d21c6e1b960b60c6dd717a11ae7ff9","cross_cats_sorted":["cs.IT","math.IT","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-07-22T11:00:16Z","title_canon_sha256":"20f4b350e7c08614c3fea2b2ee22426739cb044f42e4621249d50b4f5186898d"},"schema_version":"1.0","source":{"id":"2607.20020","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.20020","created_at":"2026-07-23T01:24:55Z"},{"alias_kind":"arxiv_version","alias_value":"2607.20020v1","created_at":"2026-07-23T01:24:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.20020","created_at":"2026-07-23T01:24:55Z"},{"alias_kind":"pith_short_12","alias_value":"TCVNLSKEAEOH","created_at":"2026-07-23T01:24:55Z"},{"alias_kind":"pith_short_16","alias_value":"TCVNLSKEAEOHTIPE","created_at":"2026-07-23T01:24:55Z"},{"alias_kind":"pith_short_8","alias_value":"TCVNLSKE","created_at":"2026-07-23T01:24:55Z"}],"graph_snapshots":[{"event_id":"sha256:c4c3291ba8aff3a7cca50566e60301d8b3e7ae0af3a8800a6606907cc821b076","target":"graph","created_at":"2026-07-23T01:24:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.20020/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper explores the measurement requirements for signal recovery in compressed sensing, comparing the performance of shearlet frames with traditional wavelet systems. Directional representation systems such as shearlets are known for their ability to sparsely represent images with anisotropic features, which allows for efficient nonlinear approximations. The central question we address is whether this difference in sparsity allows for a proportional reduction in the number of Fourier measurements needed for successful reconstruction.\n  On the theoretical front, we study the obstacles encou","authors_text":"Alessandro Felisi, Giovanni S. Alberti, I\\c{s}{\\i}l G\\\"uleken","cross_cats":["cs.IT","math.IT","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-07-22T11:00:16Z","title":"On the sample complexity of Fourier compressed sensing: wavelets versus shearlets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20020","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":"sha256:5a5b483c1ab566e6ff24653fc6279be0359ad132b3bf816fe77cc47b4948c094","target":"record","created_at":"2026-07-23T01:24:55Z","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":"124b87314eea89e226be82644c4d918685d21c6e1b960b60c6dd717a11ae7ff9","cross_cats_sorted":["cs.IT","math.IT","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-07-22T11:00:16Z","title_canon_sha256":"20f4b350e7c08614c3fea2b2ee22426739cb044f42e4621249d50b4f5186898d"},"schema_version":"1.0","source":{"id":"2607.20020","kind":"arxiv","version":1}},"canonical_sha256":"98aad5c944011c79a1e42d5533fbcb6633b21f0ea1b44320be6925de42fd1e05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98aad5c944011c79a1e42d5533fbcb6633b21f0ea1b44320be6925de42fd1e05","first_computed_at":"2026-07-23T01:24:55.894003Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-23T01:24:55.894003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pfd6e7enlTl7g7gof5jo84/R4BvXjv9uX+WLmX3wn/h9rp7VoCCMgbXYtzq17Ip2wEz229sDbt+kwzeOwMEYDg==","signature_status":"signed_v1","signed_at":"2026-07-23T01:24:55.894849Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.20020","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a5b483c1ab566e6ff24653fc6279be0359ad132b3bf816fe77cc47b4948c094","sha256:c4c3291ba8aff3a7cca50566e60301d8b3e7ae0af3a8800a6606907cc821b076"],"state_sha256":"8f9d13450b8f8b5b61a692fa3c302e1e58916ba092c72cb1313e48da34b7bb53"}