{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RYNA643UTI5JOIAEGLOGSP7DS4","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":"268fc5321c7c1552c29ef6f8e4384fa3030568b78cf3100320100b031e22901b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-05T11:25:53Z","title_canon_sha256":"58b78cb8e0b5dfd7de1312c62c19394a2f5a8571500730813f8c79ed24614f13"},"schema_version":"1.0","source":{"id":"1609.01104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01104","created_at":"2026-07-05T05:49:51Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01104v1","created_at":"2026-07-05T05:49:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01104","created_at":"2026-07-05T05:49:51Z"},{"alias_kind":"pith_short_12","alias_value":"RYNA643UTI5J","created_at":"2026-07-05T05:49:51Z"},{"alias_kind":"pith_short_16","alias_value":"RYNA643UTI5JOIAE","created_at":"2026-07-05T05:49:51Z"},{"alias_kind":"pith_short_8","alias_value":"RYNA643U","created_at":"2026-07-05T05:49:51Z"}],"graph_snapshots":[{"event_id":"sha256:30c3f0af91d7dc39fed44e01b128f05d0df099f102be2a6a8390de9e4d8e1393","target":"graph","created_at":"2026-07-05T05:49:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1609.01104/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We are concerned with the recovery of $s-$sparse Wigner-D expansions in terms of $N$ Wigner-D functions. Considered as a generalization of spherical harmonics, Wigner-D functions are eigenfunctions of Laplace-Beltrami operator and form an orthonormal system. However, since they are not uniformly bounded, the existing results on BOS do not apply. Using previously introduced preconditioning technique, a new orthonormal and bounded system is obtained for which RIP property can be established. We show that the number of sufficient samples for sparse recovery scales with ${N}^{1/6} \\,s\\, \\log^3(s) ","authors_text":"Arash Behboodi, Arya Bangun, Rudolf Mathar","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-05T11:25:53Z","title":"Sparse recovery in Wigner-D basis expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01104","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":"sha256:67abcd676cd4a1d2a6e6423da9e6a23e411ba7e040c4e5d6db536b1a3a4b999e","target":"record","created_at":"2026-07-05T05:49:51Z","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":"268fc5321c7c1552c29ef6f8e4384fa3030568b78cf3100320100b031e22901b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-05T11:25:53Z","title_canon_sha256":"58b78cb8e0b5dfd7de1312c62c19394a2f5a8571500730813f8c79ed24614f13"},"schema_version":"1.0","source":{"id":"1609.01104","kind":"arxiv","version":1}},"canonical_sha256":"8e1a0f73749a3a97200432dc693fe39732bb0193dc599901c139919bb7e01fc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e1a0f73749a3a97200432dc693fe39732bb0193dc599901c139919bb7e01fc9","first_computed_at":"2026-07-05T05:49:51.707034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:49:51.707034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5IdLaNvClsynYN28uwR/L+s69+bA04UN+QbKpBthu10eoT87ir+XmXzIVSYsc9p0BiMQIyBtXTrZZIYDMrcPCg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:49:51.707411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67abcd676cd4a1d2a6e6423da9e6a23e411ba7e040c4e5d6db536b1a3a4b999e","sha256:30c3f0af91d7dc39fed44e01b128f05d0df099f102be2a6a8390de9e4d8e1393"],"state_sha256":"e88bf25889ab2cfaa29ee6afad173669c38be2c563e986f475d1c8a5aae9c376"}