{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:27GMZLFA65W2HJDLVKP4DWV56U","short_pith_number":"pith:27GMZLFA","canonical_record":{"source":{"id":"1707.06576","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-20T15:38:13Z","cross_cats_sorted":[],"title_canon_sha256":"a6173a5f04b6395f1bcd565c82fac89da1f9837d216b62b7b73798fedad70c91","abstract_canon_sha256":"f28c27024256497d80a2c04cd3ddd6d1949ab3eea586e5dcf96bba86ab071bb2"},"schema_version":"1.0"},"canonical_sha256":"d7ccccaca0f76da3a46baa9fc1dabdf50d1a036d119b6ea6333560d411199a27","source":{"kind":"arxiv","id":"1707.06576","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06576","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06576v2","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06576","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"pith_short_12","alias_value":"27GMZLFA65W2","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"27GMZLFA65W2HJDL","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"27GMZLFA","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:27GMZLFA65W2HJDLVKP4DWV56U","target":"record","payload":{"canonical_record":{"source":{"id":"1707.06576","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-20T15:38:13Z","cross_cats_sorted":[],"title_canon_sha256":"a6173a5f04b6395f1bcd565c82fac89da1f9837d216b62b7b73798fedad70c91","abstract_canon_sha256":"f28c27024256497d80a2c04cd3ddd6d1949ab3eea586e5dcf96bba86ab071bb2"},"schema_version":"1.0"},"canonical_sha256":"d7ccccaca0f76da3a46baa9fc1dabdf50d1a036d119b6ea6333560d411199a27","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:38.217853Z","signature_b64":"qB8QygwO5+/1/I9JDrpdd6MX+ShY8j4JrhMrCtqvYrnEQIVYyqMuyzPcxznNCZglQfZ+qFSCVu8xJKdP0j3+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7ccccaca0f76da3a46baa9fc1dabdf50d1a036d119b6ea6333560d411199a27","last_reissued_at":"2026-05-18T00:36:38.217142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:38.217142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.06576","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RGx/JLPCKMhLBy74S00mqrdlcsNEO0hrF8iNh+EO77eUL8xw6WUX11JbGCOfKsLLYuhwgNbCkCSsJ88xSaGWDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:09:56.257376Z"},"content_sha256":"474dd6db75f5a7e433bb6ad6d87e9901f38e08965b1fff8df50770fbeae66125","schema_version":"1.0","event_id":"sha256:474dd6db75f5a7e433bb6ad6d87e9901f38e08965b1fff8df50770fbeae66125"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:27GMZLFA65W2HJDLVKP4DWV56U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recovering Sparse Nonnegative Signals via Non-convex Fraction Function Penalty","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Angang Cui, Haiyang Li, Jigen Peng, Meng Wen","submitted_at":"2017-07-20T15:38:13Z","abstract_excerpt":"Many real world practical problems can be formulated as $\\ell_{0}$-minimization problems with nonnegativity constraints, which seek the sparsest nonnegative signals to underdetermined linear systems. They have been widely applied in signal and image processing, machine learning, pattern recognition and computer vision. Unfortunately, this $\\ell_{0}$-minimization problem with nonnegativity constraint is computational and NP-hard because of the discrete and discontinuous nature of the $\\ell_{0}$-norm. In this paper, we replace the $\\ell_{0}$-norm with a non-convex fraction function, and study th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06576","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cZmQ+vxcuLC4N6APkAy5wOnCkPANePWz9JHftzV6m1VglBtIH94r3qnyaVhUZ3dr2zo8W4o9+8zZED8gEwS+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:09:56.258017Z"},"content_sha256":"6430ed36f77f7a2a1d6878d7a20c82daf0232509d446b84c35c3d74bc43645e2","schema_version":"1.0","event_id":"sha256:6430ed36f77f7a2a1d6878d7a20c82daf0232509d446b84c35c3d74bc43645e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/27GMZLFA65W2HJDLVKP4DWV56U/bundle.json","state_url":"https://pith.science/pith/27GMZLFA65W2HJDLVKP4DWV56U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/27GMZLFA65W2HJDLVKP4DWV56U/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T03:09:56Z","links":{"resolver":"https://pith.science/pith/27GMZLFA65W2HJDLVKP4DWV56U","bundle":"https://pith.science/pith/27GMZLFA65W2HJDLVKP4DWV56U/bundle.json","state":"https://pith.science/pith/27GMZLFA65W2HJDLVKP4DWV56U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/27GMZLFA65W2HJDLVKP4DWV56U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:27GMZLFA65W2HJDLVKP4DWV56U","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":"f28c27024256497d80a2c04cd3ddd6d1949ab3eea586e5dcf96bba86ab071bb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-20T15:38:13Z","title_canon_sha256":"a6173a5f04b6395f1bcd565c82fac89da1f9837d216b62b7b73798fedad70c91"},"schema_version":"1.0","source":{"id":"1707.06576","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06576","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06576v2","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06576","created_at":"2026-05-18T00:36:38Z"},{"alias_kind":"pith_short_12","alias_value":"27GMZLFA65W2","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"27GMZLFA65W2HJDL","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"27GMZLFA","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:6430ed36f77f7a2a1d6878d7a20c82daf0232509d446b84c35c3d74bc43645e2","target":"graph","created_at":"2026-05-18T00:36:38Z","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":"Many real world practical problems can be formulated as $\\ell_{0}$-minimization problems with nonnegativity constraints, which seek the sparsest nonnegative signals to underdetermined linear systems. They have been widely applied in signal and image processing, machine learning, pattern recognition and computer vision. Unfortunately, this $\\ell_{0}$-minimization problem with nonnegativity constraint is computational and NP-hard because of the discrete and discontinuous nature of the $\\ell_{0}$-norm. In this paper, we replace the $\\ell_{0}$-norm with a non-convex fraction function, and study th","authors_text":"Angang Cui, Haiyang Li, Jigen Peng, Meng Wen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-20T15:38:13Z","title":"Recovering Sparse Nonnegative Signals via Non-convex Fraction Function Penalty"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06576","kind":"arxiv","version":2},"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":"sha256:474dd6db75f5a7e433bb6ad6d87e9901f38e08965b1fff8df50770fbeae66125","target":"record","created_at":"2026-05-18T00:36:38Z","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":"f28c27024256497d80a2c04cd3ddd6d1949ab3eea586e5dcf96bba86ab071bb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-20T15:38:13Z","title_canon_sha256":"a6173a5f04b6395f1bcd565c82fac89da1f9837d216b62b7b73798fedad70c91"},"schema_version":"1.0","source":{"id":"1707.06576","kind":"arxiv","version":2}},"canonical_sha256":"d7ccccaca0f76da3a46baa9fc1dabdf50d1a036d119b6ea6333560d411199a27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7ccccaca0f76da3a46baa9fc1dabdf50d1a036d119b6ea6333560d411199a27","first_computed_at":"2026-05-18T00:36:38.217142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:38.217142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qB8QygwO5+/1/I9JDrpdd6MX+ShY8j4JrhMrCtqvYrnEQIVYyqMuyzPcxznNCZglQfZ+qFSCVu8xJKdP0j3+BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:38.217853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06576","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:474dd6db75f5a7e433bb6ad6d87e9901f38e08965b1fff8df50770fbeae66125","sha256:6430ed36f77f7a2a1d6878d7a20c82daf0232509d446b84c35c3d74bc43645e2"],"state_sha256":"cccadda2e402d0a263213fef4ab2fb48f49c24ae9f25013246b83daf0f85ca81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bZ+HVT5FFGM3Ss+MqtBJOxBBK7F7vO6aTC9XIAZ7h/WAkJQmMFmjJaTzYvW3JrISCYS5ep0kBtCt5ruOfjNSDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:09:56.261149Z","bundle_sha256":"26fb48606d18c03cdb40ebada6cb553d313b087ba6347b8785c8d07d421a7c58"}}