{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VISWYHT63OEB2QBRAF5CA75PUL","short_pith_number":"pith:VISWYHT6","canonical_record":{"source":{"id":"1602.03367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-02-10T13:33:57Z","cross_cats_sorted":[],"title_canon_sha256":"a6087f585a9771b591fff6ae7038fe66a5dcb7cc533dc0ad791063bce6e7ec4a","abstract_canon_sha256":"25ead1ca85bd5b3da31ad4b594258fcc4c26c6846d2ccd13db8c42b754869b17"},"schema_version":"1.0"},"canonical_sha256":"aa256c1e7edb881d4031017a207fafa2d6525828c9e4d95000aaaea501790d40","source":{"kind":"arxiv","id":"1602.03367","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03367","created_at":"2026-05-18T01:21:00Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03367v1","created_at":"2026-05-18T01:21:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03367","created_at":"2026-05-18T01:21:00Z"},{"alias_kind":"pith_short_12","alias_value":"VISWYHT63OEB","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VISWYHT63OEB2QBR","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VISWYHT6","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VISWYHT63OEB2QBRAF5CA75PUL","target":"record","payload":{"canonical_record":{"source":{"id":"1602.03367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-02-10T13:33:57Z","cross_cats_sorted":[],"title_canon_sha256":"a6087f585a9771b591fff6ae7038fe66a5dcb7cc533dc0ad791063bce6e7ec4a","abstract_canon_sha256":"25ead1ca85bd5b3da31ad4b594258fcc4c26c6846d2ccd13db8c42b754869b17"},"schema_version":"1.0"},"canonical_sha256":"aa256c1e7edb881d4031017a207fafa2d6525828c9e4d95000aaaea501790d40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:00.158244Z","signature_b64":"wNuvkQrUa24437cZsfC/7QWpAtYyTDJXUiaSGHPQ0GI1YcZurCq38bf9ouotTD3orZaEs6RK+7uhm4YG29DnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa256c1e7edb881d4031017a207fafa2d6525828c9e4d95000aaaea501790d40","last_reissued_at":"2026-05-18T01:21:00.157468Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:00.157468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.03367","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":"2026-05-18T01:21:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J0Q0aLpv09TTnL0+T1cyhx3ryZtRzEb6rRXzJ9l1KpLkqdfLOiSal6WE2XY5gy4pmsXTo3p1ZbGO1xLhmZLoAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:52:26.900964Z"},"content_sha256":"22e788085fa15eee1b0244970e19d3b810ef87eca0e0544bbc720ba86ceb7865","schema_version":"1.0","event_id":"sha256:22e788085fa15eee1b0244970e19d3b810ef87eca0e0544bbc720ba86ceb7865"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VISWYHT63OEB2QBRAF5CA75PUL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizing weak solutions for vector optimization problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Dang H. Long, Marco A. L\\'opez, Miguel A. Goberna, Nguyen Dinh","submitted_at":"2016-02-10T13:33:57Z","abstract_excerpt":"This paper provides characterizations of the weak solutions of optimization problems where a given vector function $F,$ from a decision space $X$ to an objective space $Y$, is \"minimized\" on the set of elements $x\\in C$ (where $C\\subset X$ is a given nonempty constraint set), satisfying $G\\left( x\\right) \\leqq_{S}0_{Z},$ where $G$ is another given vector function from $X $ to a constraint space $Z$ with positive cone $S$. The three spaces $X,Y,$ and $Z$ are locally convex Hausdorff topological vector spaces, with $Y$ and $Z$ partially ordered by two convex cones $K$ and $S,$ respectively, and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03367","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":""},"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":"2026-05-18T01:21:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+HIP59gVxmz0jVbCv4NRNcujSEPY9HELOyxTLYxOqPBP7Y/eXNwX4S7og2NHf2POxalb1PILjHhueWMwNv1OAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:52:26.901719Z"},"content_sha256":"68a56c6a026a545db3a3731493f4aea00f2cca8ff2686b1540c3b6f070c5b448","schema_version":"1.0","event_id":"sha256:68a56c6a026a545db3a3731493f4aea00f2cca8ff2686b1540c3b6f070c5b448"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VISWYHT63OEB2QBRAF5CA75PUL/bundle.json","state_url":"https://pith.science/pith/VISWYHT63OEB2QBRAF5CA75PUL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VISWYHT63OEB2QBRAF5CA75PUL/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":"2026-06-10T12:52:26Z","links":{"resolver":"https://pith.science/pith/VISWYHT63OEB2QBRAF5CA75PUL","bundle":"https://pith.science/pith/VISWYHT63OEB2QBRAF5CA75PUL/bundle.json","state":"https://pith.science/pith/VISWYHT63OEB2QBRAF5CA75PUL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VISWYHT63OEB2QBRAF5CA75PUL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VISWYHT63OEB2QBRAF5CA75PUL","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":"25ead1ca85bd5b3da31ad4b594258fcc4c26c6846d2ccd13db8c42b754869b17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-02-10T13:33:57Z","title_canon_sha256":"a6087f585a9771b591fff6ae7038fe66a5dcb7cc533dc0ad791063bce6e7ec4a"},"schema_version":"1.0","source":{"id":"1602.03367","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03367","created_at":"2026-05-18T01:21:00Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03367v1","created_at":"2026-05-18T01:21:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03367","created_at":"2026-05-18T01:21:00Z"},{"alias_kind":"pith_short_12","alias_value":"VISWYHT63OEB","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VISWYHT63OEB2QBR","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VISWYHT6","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:68a56c6a026a545db3a3731493f4aea00f2cca8ff2686b1540c3b6f070c5b448","target":"graph","created_at":"2026-05-18T01:21:00Z","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"},"paper":{"abstract_excerpt":"This paper provides characterizations of the weak solutions of optimization problems where a given vector function $F,$ from a decision space $X$ to an objective space $Y$, is \"minimized\" on the set of elements $x\\in C$ (where $C\\subset X$ is a given nonempty constraint set), satisfying $G\\left( x\\right) \\leqq_{S}0_{Z},$ where $G$ is another given vector function from $X $ to a constraint space $Z$ with positive cone $S$. The three spaces $X,Y,$ and $Z$ are locally convex Hausdorff topological vector spaces, with $Y$ and $Z$ partially ordered by two convex cones $K$ and $S,$ respectively, and ","authors_text":"Dang H. Long, Marco A. L\\'opez, Miguel A. Goberna, Nguyen Dinh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-02-10T13:33:57Z","title":"Characterizing weak solutions for vector optimization problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03367","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":"sha256:22e788085fa15eee1b0244970e19d3b810ef87eca0e0544bbc720ba86ceb7865","target":"record","created_at":"2026-05-18T01:21:00Z","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":"25ead1ca85bd5b3da31ad4b594258fcc4c26c6846d2ccd13db8c42b754869b17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-02-10T13:33:57Z","title_canon_sha256":"a6087f585a9771b591fff6ae7038fe66a5dcb7cc533dc0ad791063bce6e7ec4a"},"schema_version":"1.0","source":{"id":"1602.03367","kind":"arxiv","version":1}},"canonical_sha256":"aa256c1e7edb881d4031017a207fafa2d6525828c9e4d95000aaaea501790d40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa256c1e7edb881d4031017a207fafa2d6525828c9e4d95000aaaea501790d40","first_computed_at":"2026-05-18T01:21:00.157468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:00.157468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wNuvkQrUa24437cZsfC/7QWpAtYyTDJXUiaSGHPQ0GI1YcZurCq38bf9ouotTD3orZaEs6RK+7uhm4YG29DnAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:00.158244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.03367","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22e788085fa15eee1b0244970e19d3b810ef87eca0e0544bbc720ba86ceb7865","sha256:68a56c6a026a545db3a3731493f4aea00f2cca8ff2686b1540c3b6f070c5b448"],"state_sha256":"d00132a2ccb38151dd0acaac3dcfc6868e50b758763e3c6ec10b53a381eabd91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dY3SAnRZ2GRVOKkCOiE6+5h+CBFIe/l4cwHa7oIeWszJc7AwVK+AL85AEZtktfp+6efzVswkQbUii9dzIdD0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T12:52:26.907739Z","bundle_sha256":"2ec7a766c9d094a22a8e242d06df149c8ed59854b728f252ea48b04c95d4b81d"}}