{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:6OUEP2VYR5DFQ6SSPCVKGJPYSF","short_pith_number":"pith:6OUEP2VY","canonical_record":{"source":{"id":"2411.19272","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-11-28T17:07:07Z","cross_cats_sorted":[],"title_canon_sha256":"7a60c8764b1dc26a938e8206d15e9da7cb09056763eb58c93d112d24282ff792","abstract_canon_sha256":"4b922313ff4270a25f5a08ab4a7798e34325193de5b3623956dc853045a7627e"},"schema_version":"1.0"},"canonical_sha256":"f3a847eab88f46587a5278aaa325f8916a79272279f45272ffa9147198c69cfe","source":{"kind":"arxiv","id":"2411.19272","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.19272","created_at":"2026-07-05T09:42:00Z"},{"alias_kind":"arxiv_version","alias_value":"2411.19272v1","created_at":"2026-07-05T09:42:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.19272","created_at":"2026-07-05T09:42:00Z"},{"alias_kind":"pith_short_12","alias_value":"6OUEP2VYR5DF","created_at":"2026-07-05T09:42:00Z"},{"alias_kind":"pith_short_16","alias_value":"6OUEP2VYR5DFQ6SS","created_at":"2026-07-05T09:42:00Z"},{"alias_kind":"pith_short_8","alias_value":"6OUEP2VY","created_at":"2026-07-05T09:42:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:6OUEP2VYR5DFQ6SSPCVKGJPYSF","target":"record","payload":{"canonical_record":{"source":{"id":"2411.19272","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-11-28T17:07:07Z","cross_cats_sorted":[],"title_canon_sha256":"7a60c8764b1dc26a938e8206d15e9da7cb09056763eb58c93d112d24282ff792","abstract_canon_sha256":"4b922313ff4270a25f5a08ab4a7798e34325193de5b3623956dc853045a7627e"},"schema_version":"1.0"},"canonical_sha256":"f3a847eab88f46587a5278aaa325f8916a79272279f45272ffa9147198c69cfe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:42:00.118763Z","signature_b64":"88nZSlYtdj1buj8JG7crgJyi1KeG73mEKn8HwqNphlenCCF2vONhlmC5+fojob4DTm+JQRQXKnAKF/Ns4AXqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3a847eab88f46587a5278aaa325f8916a79272279f45272ffa9147198c69cfe","last_reissued_at":"2026-07-05T09:42:00.118376Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:42:00.118376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.19272","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:42:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YgLoUPemfC3PXtn4Yn2mDISuE4p5/OwVsCIIiWPywZsXrnvqKm8pq2YboQ2ybLzCMtwmTuW4I40RO75SIb8NAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T06:27:40.029238Z"},"content_sha256":"4de49d44171fb397937387efdda69fec80860d0491c1beab214c315e3a155ae5","schema_version":"1.0","event_id":"sha256:4de49d44171fb397937387efdda69fec80860d0491c1beab214c315e3a155ae5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:6OUEP2VYR5DFQ6SSPCVKGJPYSF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Polyhedral DC Optimization Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Duong Thi Kim Huyen, Nguyen Dong Yen, Vu Thi Huong","submitted_at":"2024-11-28T17:07:07Z","abstract_excerpt":"The problem of minimizing the difference of two lower semicontinuous, proper, convex functions (a DC function) on a nonempty closed convex set in a locally convex Hausdorff topological vector space is studied in this paper. The focus is made on the situations where either the second component of the objective function is a generalized polyhedral convex function or the first component of the objective function is a generalized polyhedral convex function and the constraint set is generalized polyhedral convex. Various results on optimality conditions, the local solution set, the global solution "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19272","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/2411.19272/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:42:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oXl35yDRZsweXH5fNP7OHl9tLlz0ACebW+yl1BKDfqlaRpElLZvHCAmW+UQutIDfQAeyw/5dRMVs33ZLM4D0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T06:27:40.029751Z"},"content_sha256":"919c6d70f2ccbd1271d929b11aab3b9164864730a2954341fe2f880f568f4bb0","schema_version":"1.0","event_id":"sha256:919c6d70f2ccbd1271d929b11aab3b9164864730a2954341fe2f880f568f4bb0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6OUEP2VYR5DFQ6SSPCVKGJPYSF/bundle.json","state_url":"https://pith.science/pith/6OUEP2VYR5DFQ6SSPCVKGJPYSF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6OUEP2VYR5DFQ6SSPCVKGJPYSF/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":"2026-08-11T06:27:40Z","links":{"resolver":"https://pith.science/pith/6OUEP2VYR5DFQ6SSPCVKGJPYSF","bundle":"https://pith.science/pith/6OUEP2VYR5DFQ6SSPCVKGJPYSF/bundle.json","state":"https://pith.science/pith/6OUEP2VYR5DFQ6SSPCVKGJPYSF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6OUEP2VYR5DFQ6SSPCVKGJPYSF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6OUEP2VYR5DFQ6SSPCVKGJPYSF","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":"4b922313ff4270a25f5a08ab4a7798e34325193de5b3623956dc853045a7627e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-11-28T17:07:07Z","title_canon_sha256":"7a60c8764b1dc26a938e8206d15e9da7cb09056763eb58c93d112d24282ff792"},"schema_version":"1.0","source":{"id":"2411.19272","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.19272","created_at":"2026-07-05T09:42:00Z"},{"alias_kind":"arxiv_version","alias_value":"2411.19272v1","created_at":"2026-07-05T09:42:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.19272","created_at":"2026-07-05T09:42:00Z"},{"alias_kind":"pith_short_12","alias_value":"6OUEP2VYR5DF","created_at":"2026-07-05T09:42:00Z"},{"alias_kind":"pith_short_16","alias_value":"6OUEP2VYR5DFQ6SS","created_at":"2026-07-05T09:42:00Z"},{"alias_kind":"pith_short_8","alias_value":"6OUEP2VY","created_at":"2026-07-05T09:42:00Z"}],"graph_snapshots":[{"event_id":"sha256:919c6d70f2ccbd1271d929b11aab3b9164864730a2954341fe2f880f568f4bb0","target":"graph","created_at":"2026-07-05T09:42:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.19272/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The problem of minimizing the difference of two lower semicontinuous, proper, convex functions (a DC function) on a nonempty closed convex set in a locally convex Hausdorff topological vector space is studied in this paper. The focus is made on the situations where either the second component of the objective function is a generalized polyhedral convex function or the first component of the objective function is a generalized polyhedral convex function and the constraint set is generalized polyhedral convex. Various results on optimality conditions, the local solution set, the global solution ","authors_text":"Duong Thi Kim Huyen, Nguyen Dong Yen, Vu Thi Huong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-11-28T17:07:07Z","title":"Generalized Polyhedral DC Optimization Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19272","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":"sha256:4de49d44171fb397937387efdda69fec80860d0491c1beab214c315e3a155ae5","target":"record","created_at":"2026-07-05T09:42:00Z","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":"4b922313ff4270a25f5a08ab4a7798e34325193de5b3623956dc853045a7627e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-11-28T17:07:07Z","title_canon_sha256":"7a60c8764b1dc26a938e8206d15e9da7cb09056763eb58c93d112d24282ff792"},"schema_version":"1.0","source":{"id":"2411.19272","kind":"arxiv","version":1}},"canonical_sha256":"f3a847eab88f46587a5278aaa325f8916a79272279f45272ffa9147198c69cfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3a847eab88f46587a5278aaa325f8916a79272279f45272ffa9147198c69cfe","first_computed_at":"2026-07-05T09:42:00.118376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:42:00.118376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"88nZSlYtdj1buj8JG7crgJyi1KeG73mEKn8HwqNphlenCCF2vONhlmC5+fojob4DTm+JQRQXKnAKF/Ns4AXqCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:42:00.118763Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.19272","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4de49d44171fb397937387efdda69fec80860d0491c1beab214c315e3a155ae5","sha256:919c6d70f2ccbd1271d929b11aab3b9164864730a2954341fe2f880f568f4bb0"],"state_sha256":"606624de30315f74ab8ab06e0bb066319ec746d25a3856f5d50fe74848ec936a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVqcf/8lBvxPrjBw8H5mRV0LX3FKU6r5f6+3XMVwNFmSCyyewMq7uyS9LQh+b5AGLOVVn50t4YL4eMfc4nWUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T06:27:40.034453Z","bundle_sha256":"1f66c163b3d7fac4993b1607cdf6c58cafd6edac872757ab6cd4f21b69190c42"}}