{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZF5BLYARQXIQD5OXKFPH5MA6K2","short_pith_number":"pith:ZF5BLYAR","schema_version":"1.0","canonical_sha256":"c97a15e01185d101f5d7515e7eb01e568ec3203a97a6e2b4de820a68c39274e0","source":{"kind":"arxiv","id":"1508.01256","version":1},"attestation_state":"computed","paper":{"title":"Expander $\\ell_0$-Decoding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CO","math.IT"],"primary_cat":"math.NA","authors_text":"Jared Tanner, Rodrigo Mendoza-Smith","submitted_at":"2015-08-06T01:37:46Z","abstract_excerpt":"We introduce two new algorithms, Serial-$\\ell_0$ and Parallel-$\\ell_0$ for solving a large underdetermined linear system of equations $y = Ax \\in \\mathbb{R}^m$ when it is known that $x \\in \\mathbb{R}^n$ has at most $k < m$ nonzero entries and that $A$ is the adjacency matrix of an unbalanced left $d$-regular expander graph. The matrices in this class are sparse and allow a highly efficient implementation. A number of algorithms have been designed to work exclusively under this setting, composing the branch of combinatorial compressed-sensing (CCS).\n  Serial-$\\ell_0$ and Parallel-$\\ell_0$ itera"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1508.01256","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-06T01:37:46Z","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"title_canon_sha256":"1f144d3102907a174f69ada0207870f5205a9eba080a50422b56aa46f24fecde","abstract_canon_sha256":"6abb471e2eda8d82f723273613f8e9d8ab214226b3f40ef89e8247c702f90c12"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:43.055729Z","signature_b64":"BIjxgr1/OnwWo0UBSlTyya9RmqzXBBKepGvpb8cdRUKfdVm2ZsLlyTU3DDsPw1XQo9EXVjhiz+qgxXMKbzuEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c97a15e01185d101f5d7515e7eb01e568ec3203a97a6e2b4de820a68c39274e0","last_reissued_at":"2026-05-18T01:35:43.055258Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:43.055258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Expander $\\ell_0$-Decoding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CO","math.IT"],"primary_cat":"math.NA","authors_text":"Jared Tanner, Rodrigo Mendoza-Smith","submitted_at":"2015-08-06T01:37:46Z","abstract_excerpt":"We introduce two new algorithms, Serial-$\\ell_0$ and Parallel-$\\ell_0$ for solving a large underdetermined linear system of equations $y = Ax \\in \\mathbb{R}^m$ when it is known that $x \\in \\mathbb{R}^n$ has at most $k < m$ nonzero entries and that $A$ is the adjacency matrix of an unbalanced left $d$-regular expander graph. The matrices in this class are sparse and allow a highly efficient implementation. A number of algorithms have been designed to work exclusively under this setting, composing the branch of combinatorial compressed-sensing (CCS).\n  Serial-$\\ell_0$ and Parallel-$\\ell_0$ itera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01256","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1508.01256","created_at":"2026-05-18T01:35:43.055327+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.01256v1","created_at":"2026-05-18T01:35:43.055327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01256","created_at":"2026-05-18T01:35:43.055327+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZF5BLYARQXIQ","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZF5BLYARQXIQD5OX","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZF5BLYAR","created_at":"2026-05-18T12:29:52.810259+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZF5BLYARQXIQD5OXKFPH5MA6K2","json":"https://pith.science/pith/ZF5BLYARQXIQD5OXKFPH5MA6K2.json","graph_json":"https://pith.science/api/pith-number/ZF5BLYARQXIQD5OXKFPH5MA6K2/graph.json","events_json":"https://pith.science/api/pith-number/ZF5BLYARQXIQD5OXKFPH5MA6K2/events.json","paper":"https://pith.science/paper/ZF5BLYAR"},"agent_actions":{"view_html":"https://pith.science/pith/ZF5BLYARQXIQD5OXKFPH5MA6K2","download_json":"https://pith.science/pith/ZF5BLYARQXIQD5OXKFPH5MA6K2.json","view_paper":"https://pith.science/paper/ZF5BLYAR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.01256&json=true","fetch_graph":"https://pith.science/api/pith-number/ZF5BLYARQXIQD5OXKFPH5MA6K2/graph.json","fetch_events":"https://pith.science/api/pith-number/ZF5BLYARQXIQD5OXKFPH5MA6K2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZF5BLYARQXIQD5OXKFPH5MA6K2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZF5BLYARQXIQD5OXKFPH5MA6K2/action/storage_attestation","attest_author":"https://pith.science/pith/ZF5BLYARQXIQD5OXKFPH5MA6K2/action/author_attestation","sign_citation":"https://pith.science/pith/ZF5BLYARQXIQD5OXKFPH5MA6K2/action/citation_signature","submit_replication":"https://pith.science/pith/ZF5BLYARQXIQD5OXKFPH5MA6K2/action/replication_record"}},"created_at":"2026-05-18T01:35:43.055327+00:00","updated_at":"2026-05-18T01:35:43.055327+00:00"}