{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:BTKQDC43YKU7S4BAY2KSU3Q5C7","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":"d83b3f8c4f48c1eb9c9c79ea39fffbc8929e35e24105645c90a28b291680ca09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-03-04T19:28:11Z","title_canon_sha256":"c0efcb07b7c11fadca1d0e7893463daf9d93b53aee7cde0967ec0ae29fb624ab"},"schema_version":"1.0","source":{"id":"0803.0524","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.0524","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"arxiv_version","alias_value":"0803.0524v1","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.0524","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"pith_short_12","alias_value":"BTKQDC43YKU7","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"BTKQDC43YKU7S4BA","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"BTKQDC43","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:ee25cf9d574840296444c3ff9ebfcdec8eddd4ca8a3f9c50e3f8f6832717e926","target":"graph","created_at":"2026-05-18T04:09:36Z","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":"We consider the minimization of the number of non-zero coefficients (the $\\ell_0$ \"norm\") of the representation of a data set in terms of a dictionary under a fidelity constraint. (Both the dictionary and the norm defining the constraint are arbitrary.) This (nonconvex) optimization problem naturally leads to the sparsest representations, compared with other functionals instead of the $\\ell_0$ \"norm\". Our goal is to measure the sets of data yielding a $K$-sparse solution--i.e. involving $K$ non-zero components. Data are assumed uniformly distributed on a domain defined by any norm--to be chose","authors_text":"Francois Malgouyres (LAGA), Mila Nikolova (CMLA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-03-04T19:28:11Z","title":"Average performance of the sparsest approximation using a general dictionary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.0524","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:ceb41525ed68e0eac88ce4bb9cc6616009eb8a3097acc7ef89db89344bb6e110","target":"record","created_at":"2026-05-18T04:09:36Z","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":"d83b3f8c4f48c1eb9c9c79ea39fffbc8929e35e24105645c90a28b291680ca09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-03-04T19:28:11Z","title_canon_sha256":"c0efcb07b7c11fadca1d0e7893463daf9d93b53aee7cde0967ec0ae29fb624ab"},"schema_version":"1.0","source":{"id":"0803.0524","kind":"arxiv","version":1}},"canonical_sha256":"0cd5018b9bc2a9f97020c6952a6e1d17f82f2f56d5b932058bd7a5645951300d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0cd5018b9bc2a9f97020c6952a6e1d17f82f2f56d5b932058bd7a5645951300d","first_computed_at":"2026-05-18T04:09:36.487908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:36.487908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CAMdDlSEAwmJp2aLWaBWUADCZNpzridpO8pNof25pLPIY6W/XlTFR/0r/8MZC934VefaYsnRvsdXtTWQyrhkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:36.488325Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.0524","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ceb41525ed68e0eac88ce4bb9cc6616009eb8a3097acc7ef89db89344bb6e110","sha256:ee25cf9d574840296444c3ff9ebfcdec8eddd4ca8a3f9c50e3f8f6832717e926"],"state_sha256":"8d77aa69116757c1d8feb657e42b87522513741d18e31b525467d18d7b05772f"}