{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PO7UBSEE7ZBHMHQQKBBFLR7OBK","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":"dd5912598aabb405ae1ec3f197635567f4aa8150779b42de8d21004df9e35499","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-03T18:57:00Z","title_canon_sha256":"10193f634ecdd3a560ef70df7e925f9bc89ae5ef0b83bcd601a4ef828c7b009d"},"schema_version":"1.0","source":{"id":"1404.1043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1043","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1043v1","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1043","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"pith_short_12","alias_value":"PO7UBSEE7ZBH","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PO7UBSEE7ZBHMHQQ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PO7UBSEE","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:0da4df09c102b987d29506188d23a5be4c0cdc5f6c2d050b17898a0e746bfcf4","target":"graph","created_at":"2026-05-18T02:54:54Z","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":"It is well-known that curvelets provide optimal approximations for so-called cartoon images which are defined as piecewise $C^2$-functions, separated by a $C^2$ singularity curve. In this paper, we consider the more general case of piecewise $C^\\beta$-functions, separated by a $C^\\beta$ singularity curve for $\\beta \\in (1,2]$. We first prove a benchmark result for the possibly achievable best $N$-term approximation rate for this more general signal model. Then we introduce what we call $\\alpha$-curvelets, which are systems that interpolate between wavelet systems on the one hand ($\\alpha = 1$)","authors_text":"Gitta Kutyniok, Martin Sch\\\"afer, Philipp Grohs, Sandra Keiper","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-03T18:57:00Z","title":"Cartoon Approximation with $\\alpha$-Curvelets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1043","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":"sha256:745c758635b7673875877e2904dfcc72bc9bede0b20ed44b071ee5883071af3f","target":"record","created_at":"2026-05-18T02:54:54Z","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":"dd5912598aabb405ae1ec3f197635567f4aa8150779b42de8d21004df9e35499","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-03T18:57:00Z","title_canon_sha256":"10193f634ecdd3a560ef70df7e925f9bc89ae5ef0b83bcd601a4ef828c7b009d"},"schema_version":"1.0","source":{"id":"1404.1043","kind":"arxiv","version":1}},"canonical_sha256":"7bbf40c884fe42761e10504255c7ee0ab7fd608516009c707be7b2c05fb75f40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bbf40c884fe42761e10504255c7ee0ab7fd608516009c707be7b2c05fb75f40","first_computed_at":"2026-05-18T02:54:54.719400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:54.719400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mDDCaqfD8XN6aQO1xJE9E250pNqOamFYFvJh9AykKbMmuxL9SPQsu0/te66ilwqk4g/6TNHCt+Ksx82erkvqBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:54.719954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:745c758635b7673875877e2904dfcc72bc9bede0b20ed44b071ee5883071af3f","sha256:0da4df09c102b987d29506188d23a5be4c0cdc5f6c2d050b17898a0e746bfcf4"],"state_sha256":"2d338a8f99420cc5043fda2d489c090d2308e4d53d625c5faebd5d2af849d40d"}