{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZZJAAWEPCZBLEJUB5L5R6JF3GG","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":"e83eb9fa1b468eadc86b318c323f7eb8618cf2663a6048f99bbf2b6ad55847eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-28T02:05:01Z","title_canon_sha256":"e6a277510d151773df0fc5a011f8259a9db874d7a8e150d2b039282018210af0"},"schema_version":"1.0","source":{"id":"1801.09171","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09171","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09171v1","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09171","created_at":"2026-05-18T00:24:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZZJAAWEPCZBL","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZZJAAWEPCZBLEJUB","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZZJAAWEP","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:7ff60c54f2b2a36f5b14345466a0e406eb2d5d8902cb7795972f8062a5ca849f","target":"graph","created_at":"2026-05-18T00:24:58Z","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":"In this paper, a continuous and non-convex promoting sparsity fraction function is studied in two sparse portfolio selection models with and without short-selling constraints. Firstly, we study the properties of the optimal solution to the problem $(FP_{a,\\lambda,\\eta})$ including the first-order and the second optimality condition and the lower and upper bound of the absolute value for its nonzero entries. Secondly, we develop the thresholding representation theory of the problem $(FP_{a,\\lambda,\\eta})$. Based on it, we prove the existence of the resolvent operator of gradient of $P_{a}(x)$, ","authors_text":"Angang Cui, Chengyi Zhang, Haiyang Li, Jigen Peng, Meng Wen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-28T02:05:01Z","title":"Sparse Portfolio Selection via Non-convex Fraction Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09171","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":"sha256:2249838d08d63143389808fc2eb4faa8b2ede6ce81294252ced7b289b118379a","target":"record","created_at":"2026-05-18T00:24:58Z","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":"e83eb9fa1b468eadc86b318c323f7eb8618cf2663a6048f99bbf2b6ad55847eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-28T02:05:01Z","title_canon_sha256":"e6a277510d151773df0fc5a011f8259a9db874d7a8e150d2b039282018210af0"},"schema_version":"1.0","source":{"id":"1801.09171","kind":"arxiv","version":1}},"canonical_sha256":"ce5200588f1642b22681eafb1f24bb319627a4143172869ffe277bb3c118ea79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce5200588f1642b22681eafb1f24bb319627a4143172869ffe277bb3c118ea79","first_computed_at":"2026-05-18T00:24:58.328703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:58.328703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IQxP5yP91UuLs1m6WFqSxSJcQdTWjdfucTO+9hx8w7+s2vikhR1Zfb5UP0da/Qw7rbqRHSNEnmYpEbyb3f0MDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:58.329448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09171","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2249838d08d63143389808fc2eb4faa8b2ede6ce81294252ced7b289b118379a","sha256:7ff60c54f2b2a36f5b14345466a0e406eb2d5d8902cb7795972f8062a5ca849f"],"state_sha256":"3593546da30e273d572a4b5537eb82bc9e840d97ac8f7c3a732d7d72a21817ad"}