{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:GEC63PDAX6UOJZG6ZPMM4EAXPG","short_pith_number":"pith:GEC63PDA","schema_version":"1.0","canonical_sha256":"3105edbc60bfa8e4e4decbd8ce101779b07c5e04c8b13966f7e24ea41ede757e","source":{"kind":"arxiv","id":"2605.15838","version":1},"attestation_state":"computed","paper":{"title":"Finding directional stationary points of DC programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hoai An Le Thi, Tao Pham Dinh, Van Ngai Huynh","submitted_at":"2026-05-15T10:53:21Z","abstract_excerpt":"We address the problem of computing stationary points for non-smooth, non-convex optimization problems. While this topic is well studied in the smooth setting, fewer algorithmic and theoretical results exist for the non-smooth case. Within Difference-of-Convex functions (DC) programming, the well-known DC Algorithm (DCA) is a standard method for computing critical points, whose definition depends on the chosen DC decomposition. More recently, some works have focused on computing directional stationary points - a stronger notion that does not depend on any particular DC decomposition - for spec"},"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":"2605.15838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-05-15T10:53:21Z","cross_cats_sorted":[],"title_canon_sha256":"4d4cebb135a18177918e26d269b2ed8725743b0239b77a76f99e47411a67f33d","abstract_canon_sha256":"2676f2aee1fdc8536fc58f2dab4006d167d1863dfbaae3e724e5ed5c505b4c32"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:21.031306Z","signature_b64":"R/b6MkJNXM2h4DKi8RUOFJvjun1EL027Gj1p+sIw7jBaCIKigWnog1ZOLO6kS+qSKwlR1AVlJG47qD/fH9HRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3105edbc60bfa8e4e4decbd8ce101779b07c5e04c8b13966f7e24ea41ede757e","last_reissued_at":"2026-05-20T00:01:21.030479Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:21.030479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finding directional stationary points of DC programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hoai An Le Thi, Tao Pham Dinh, Van Ngai Huynh","submitted_at":"2026-05-15T10:53:21Z","abstract_excerpt":"We address the problem of computing stationary points for non-smooth, non-convex optimization problems. While this topic is well studied in the smooth setting, fewer algorithmic and theoretical results exist for the non-smooth case. Within Difference-of-Convex functions (DC) programming, the well-known DC Algorithm (DCA) is a standard method for computing critical points, whose definition depends on the chosen DC decomposition. More recently, some works have focused on computing directional stationary points - a stronger notion that does not depend on any particular DC decomposition - for spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.15838","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15838/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.715483Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.848091Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ebdaafcff48718306b80dcf830f27e43c4f777e8ab0b8032c3ebeadca698024c"},"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":"2605.15838","created_at":"2026-05-20T00:01:21.030607+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.15838v1","created_at":"2026-05-20T00:01:21.030607+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.15838","created_at":"2026-05-20T00:01:21.030607+00:00"},{"alias_kind":"pith_short_12","alias_value":"GEC63PDAX6UO","created_at":"2026-05-20T00:01:21.030607+00:00"},{"alias_kind":"pith_short_16","alias_value":"GEC63PDAX6UOJZG6","created_at":"2026-05-20T00:01:21.030607+00:00"},{"alias_kind":"pith_short_8","alias_value":"GEC63PDA","created_at":"2026-05-20T00:01:21.030607+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.23550","citing_title":"RA-DCA: A Randomized Active-Set DCA for Directional Stationarity in Max-Structured DC Programs","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GEC63PDAX6UOJZG6ZPMM4EAXPG","json":"https://pith.science/pith/GEC63PDAX6UOJZG6ZPMM4EAXPG.json","graph_json":"https://pith.science/api/pith-number/GEC63PDAX6UOJZG6ZPMM4EAXPG/graph.json","events_json":"https://pith.science/api/pith-number/GEC63PDAX6UOJZG6ZPMM4EAXPG/events.json","paper":"https://pith.science/paper/GEC63PDA"},"agent_actions":{"view_html":"https://pith.science/pith/GEC63PDAX6UOJZG6ZPMM4EAXPG","download_json":"https://pith.science/pith/GEC63PDAX6UOJZG6ZPMM4EAXPG.json","view_paper":"https://pith.science/paper/GEC63PDA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.15838&json=true","fetch_graph":"https://pith.science/api/pith-number/GEC63PDAX6UOJZG6ZPMM4EAXPG/graph.json","fetch_events":"https://pith.science/api/pith-number/GEC63PDAX6UOJZG6ZPMM4EAXPG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GEC63PDAX6UOJZG6ZPMM4EAXPG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GEC63PDAX6UOJZG6ZPMM4EAXPG/action/storage_attestation","attest_author":"https://pith.science/pith/GEC63PDAX6UOJZG6ZPMM4EAXPG/action/author_attestation","sign_citation":"https://pith.science/pith/GEC63PDAX6UOJZG6ZPMM4EAXPG/action/citation_signature","submit_replication":"https://pith.science/pith/GEC63PDAX6UOJZG6ZPMM4EAXPG/action/replication_record"}},"created_at":"2026-05-20T00:01:21.030607+00:00","updated_at":"2026-05-20T00:01:21.030607+00:00"}