{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PPDUNOJFZSUTGHJDQKUS6WNON5","short_pith_number":"pith:PPDUNOJF","canonical_record":{"source":{"id":"1403.2860","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-12T09:24:33Z","cross_cats_sorted":[],"title_canon_sha256":"a41bf4f1378dc5ad989047267284b3f616bfd0c5dd7b1d4a43d65f22b2ba9d61","abstract_canon_sha256":"d041e153f1a78b92f687ec601cabb0701c5c4b88264422e9a437b205d3753b51"},"schema_version":"1.0"},"canonical_sha256":"7bc746b925cca9331d2382a92f59ae6f45c9628f7baec4b2e4407a3ed5446035","source":{"kind":"arxiv","id":"1403.2860","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2860","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2860v5","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2860","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"pith_short_12","alias_value":"PPDUNOJFZSUT","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PPDUNOJFZSUTGHJD","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PPDUNOJF","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PPDUNOJFZSUTGHJDQKUS6WNON5","target":"record","payload":{"canonical_record":{"source":{"id":"1403.2860","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-12T09:24:33Z","cross_cats_sorted":[],"title_canon_sha256":"a41bf4f1378dc5ad989047267284b3f616bfd0c5dd7b1d4a43d65f22b2ba9d61","abstract_canon_sha256":"d041e153f1a78b92f687ec601cabb0701c5c4b88264422e9a437b205d3753b51"},"schema_version":"1.0"},"canonical_sha256":"7bc746b925cca9331d2382a92f59ae6f45c9628f7baec4b2e4407a3ed5446035","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:06.714757Z","signature_b64":"yNv/87wsLXwBw7rGjn5/eo6IpMmEcTVcw74ijrHR4fy4Ryk338SRgAzuqZVe3fYf4tN+ArNAkTSVbLryw5vUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bc746b925cca9331d2382a92f59ae6f45c9628f7baec4b2e4407a3ed5446035","last_reissued_at":"2026-05-18T00:56:06.714091Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:06.714091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.2860","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mjVJuZ4a2hILHctpTzceW31TzYBoELxEsqwqKw2ZJt1Yx76HsVzH5JfBSAk/7i115jf1rQejHm3rCxj/bk7vDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:45:59.862571Z"},"content_sha256":"cc0eefd9fbc23036225d89ffbf952424d16957054ae27e9f6bbc4ac3171d3d3f","schema_version":"1.0","event_id":"sha256:cc0eefd9fbc23036225d89ffbf952424d16957054ae27e9f6bbc4ac3171d3d3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PPDUNOJFZSUTGHJDQKUS6WNON5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Applying Set Optimization to Weak Efficiency","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Carola Schrage, Giovanni P. Crespi","submitted_at":"2014-03-12T09:24:33Z","abstract_excerpt":"Since the seminal papers by Giannessi, an interesting topic in vector optimization has been the characterization of (weak) efficiency thorough Minty and Stampacchia type variational inequalities. Several results have been proved to extend those known for the scalar case. However, in order to introduce a proper definition of variational inequality, some assumptions are usually made that may eventually be questioned. We find two major drawbacks in the papers we considered, that arise when defining generalized derivatives for vector-valued functions. First, some authors introduce set-valued deriv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2860","kind":"arxiv","version":5},"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":"2026-05-18T00:56:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mi6V/7rNoPjnqwXdV2vqQoGlM+T3F4irWoFl5aNqbHS+3+CaVKYWlXS2BiGdxhRDaAHJzRLNTBbDhQi+wMzJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:45:59.862914Z"},"content_sha256":"d2fc0fde9d128272c1eab248bf79876b452b818b29c6cbe1af2de43bd0478ebc","schema_version":"1.0","event_id":"sha256:d2fc0fde9d128272c1eab248bf79876b452b818b29c6cbe1af2de43bd0478ebc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PPDUNOJFZSUTGHJDQKUS6WNON5/bundle.json","state_url":"https://pith.science/pith/PPDUNOJFZSUTGHJDQKUS6WNON5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PPDUNOJFZSUTGHJDQKUS6WNON5/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":"2026-06-27T14:45:59Z","links":{"resolver":"https://pith.science/pith/PPDUNOJFZSUTGHJDQKUS6WNON5","bundle":"https://pith.science/pith/PPDUNOJFZSUTGHJDQKUS6WNON5/bundle.json","state":"https://pith.science/pith/PPDUNOJFZSUTGHJDQKUS6WNON5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PPDUNOJFZSUTGHJDQKUS6WNON5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PPDUNOJFZSUTGHJDQKUS6WNON5","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":"d041e153f1a78b92f687ec601cabb0701c5c4b88264422e9a437b205d3753b51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-12T09:24:33Z","title_canon_sha256":"a41bf4f1378dc5ad989047267284b3f616bfd0c5dd7b1d4a43d65f22b2ba9d61"},"schema_version":"1.0","source":{"id":"1403.2860","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2860","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2860v5","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2860","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"pith_short_12","alias_value":"PPDUNOJFZSUT","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PPDUNOJFZSUTGHJD","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PPDUNOJF","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:d2fc0fde9d128272c1eab248bf79876b452b818b29c6cbe1af2de43bd0478ebc","target":"graph","created_at":"2026-05-18T00:56:06Z","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":"Since the seminal papers by Giannessi, an interesting topic in vector optimization has been the characterization of (weak) efficiency thorough Minty and Stampacchia type variational inequalities. Several results have been proved to extend those known for the scalar case. However, in order to introduce a proper definition of variational inequality, some assumptions are usually made that may eventually be questioned. We find two major drawbacks in the papers we considered, that arise when defining generalized derivatives for vector-valued functions. First, some authors introduce set-valued deriv","authors_text":"Carola Schrage, Giovanni P. Crespi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-12T09:24:33Z","title":"Applying Set Optimization to Weak Efficiency"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2860","kind":"arxiv","version":5},"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:cc0eefd9fbc23036225d89ffbf952424d16957054ae27e9f6bbc4ac3171d3d3f","target":"record","created_at":"2026-05-18T00:56:06Z","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":"d041e153f1a78b92f687ec601cabb0701c5c4b88264422e9a437b205d3753b51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-12T09:24:33Z","title_canon_sha256":"a41bf4f1378dc5ad989047267284b3f616bfd0c5dd7b1d4a43d65f22b2ba9d61"},"schema_version":"1.0","source":{"id":"1403.2860","kind":"arxiv","version":5}},"canonical_sha256":"7bc746b925cca9331d2382a92f59ae6f45c9628f7baec4b2e4407a3ed5446035","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bc746b925cca9331d2382a92f59ae6f45c9628f7baec4b2e4407a3ed5446035","first_computed_at":"2026-05-18T00:56:06.714091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:06.714091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yNv/87wsLXwBw7rGjn5/eo6IpMmEcTVcw74ijrHR4fy4Ryk338SRgAzuqZVe3fYf4tN+ArNAkTSVbLryw5vUAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:06.714757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2860","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc0eefd9fbc23036225d89ffbf952424d16957054ae27e9f6bbc4ac3171d3d3f","sha256:d2fc0fde9d128272c1eab248bf79876b452b818b29c6cbe1af2de43bd0478ebc"],"state_sha256":"3e960463afd232ed7fb26655907e9bd917df02f261cf426dce05e29ad03fcb60"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wssh7IxyS8vaW3aZY5ElKlS+mFdLR4hSXZenQiftBCSmDi2ykhPTnH25sDF9LXd3o2Q3gtjC5ezmVRuT2z/5CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T14:45:59.864758Z","bundle_sha256":"736591f3a3c6a79658c5dd8bf47473e0198c6ce7882bb67eebe4ee21fc7e9e1c"}}