{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SINKFKHMLEN7YOLHUR2DWEAD6Q","short_pith_number":"pith:SINKFKHM","canonical_record":{"source":{"id":"1506.04009","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-06-12T13:01:32Z","cross_cats_sorted":[],"title_canon_sha256":"6e4d3d909f7e7e67c75c4412640cca4af70387c5b82570b164e2bc4f54ba2137","abstract_canon_sha256":"abba24ff7f497cee69aae98a5a8e4300192d01b63b39ca740998408c18434600"},"schema_version":"1.0"},"canonical_sha256":"921aa2a8ec591bfc3967a4743b1003f408e78cdce1284b6ef55a5e628bfde16d","source":{"kind":"arxiv","id":"1506.04009","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04009","created_at":"2026-05-18T01:51:18Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04009v1","created_at":"2026-05-18T01:51:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04009","created_at":"2026-05-18T01:51:18Z"},{"alias_kind":"pith_short_12","alias_value":"SINKFKHMLEN7","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SINKFKHMLEN7YOLH","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SINKFKHM","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SINKFKHMLEN7YOLHUR2DWEAD6Q","target":"record","payload":{"canonical_record":{"source":{"id":"1506.04009","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-06-12T13:01:32Z","cross_cats_sorted":[],"title_canon_sha256":"6e4d3d909f7e7e67c75c4412640cca4af70387c5b82570b164e2bc4f54ba2137","abstract_canon_sha256":"abba24ff7f497cee69aae98a5a8e4300192d01b63b39ca740998408c18434600"},"schema_version":"1.0"},"canonical_sha256":"921aa2a8ec591bfc3967a4743b1003f408e78cdce1284b6ef55a5e628bfde16d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:51:18.544602Z","signature_b64":"w6MG5LZIbshJQGdz40DY3/ZKpnKAgwxIhkruKN2xZXkM+J+6rGNC63k+16pDv7V8ZKJP+JEKljB6hgt6UmDhCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"921aa2a8ec591bfc3967a4743b1003f408e78cdce1284b6ef55a5e628bfde16d","last_reissued_at":"2026-05-18T01:51:18.544148Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:51:18.544148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.04009","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":"2026-05-18T01:51:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sskxctysu8vRE+KBZd7QqZXWQQqpO6SinW+k3BBGn0YHGaDobUZIgd/xOAk5g4tCN4tmFVxf2U0dgg+jg69sCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:19:08.110915Z"},"content_sha256":"22cca1943ce6a134423f5fcea709e47d89f6bfe24b435b71f93160714bf317eb","schema_version":"1.0","event_id":"sha256:22cca1943ce6a134423f5fcea709e47d89f6bfe24b435b71f93160714bf317eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SINKFKHMLEN7YOLHUR2DWEAD6Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficiency for multitime vector variational problems on Riemannian manifolds involving geodesic quasiinvex functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Constantin Udriste, Madalina Constantinescu, Stefan Mititelu","submitted_at":"2015-06-12T13:01:32Z","abstract_excerpt":"We study the connection between a multitime scalar variational problem (SVP), a multitime vector variational problem (VVP) and a multitime vector fractional variational problem (VFP). For (SVP), we establish necessary optimality conditions. For both vector variational problems, we define the notions of Pareto efficient solution and of normal efficient solution and we establish necessary efficiency conditions for (VVP) and (VFP) using both notions. The main purpose of the paper is to establish sufficient efficiency conditions for the vector problems (VVP) and (VFP). Moreover, we obtain sufficie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04009","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":"2026-05-18T01:51:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MS9iaXeIuL+MLV5XZ3vENsOysaqk7lVHCjWyyUPppKGEAJMqTqwIvVOh9HST+D8hwp2Gh+kBdnBnZrPUpM6OAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:19:08.111537Z"},"content_sha256":"7b4667cda6947cd164ac62d68623b44bd2dae96e932b0774a6cb84dfa71cf7be","schema_version":"1.0","event_id":"sha256:7b4667cda6947cd164ac62d68623b44bd2dae96e932b0774a6cb84dfa71cf7be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SINKFKHMLEN7YOLHUR2DWEAD6Q/bundle.json","state_url":"https://pith.science/pith/SINKFKHMLEN7YOLHUR2DWEAD6Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SINKFKHMLEN7YOLHUR2DWEAD6Q/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":"2026-06-03T17:19:08Z","links":{"resolver":"https://pith.science/pith/SINKFKHMLEN7YOLHUR2DWEAD6Q","bundle":"https://pith.science/pith/SINKFKHMLEN7YOLHUR2DWEAD6Q/bundle.json","state":"https://pith.science/pith/SINKFKHMLEN7YOLHUR2DWEAD6Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SINKFKHMLEN7YOLHUR2DWEAD6Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SINKFKHMLEN7YOLHUR2DWEAD6Q","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":"abba24ff7f497cee69aae98a5a8e4300192d01b63b39ca740998408c18434600","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-06-12T13:01:32Z","title_canon_sha256":"6e4d3d909f7e7e67c75c4412640cca4af70387c5b82570b164e2bc4f54ba2137"},"schema_version":"1.0","source":{"id":"1506.04009","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04009","created_at":"2026-05-18T01:51:18Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04009v1","created_at":"2026-05-18T01:51:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04009","created_at":"2026-05-18T01:51:18Z"},{"alias_kind":"pith_short_12","alias_value":"SINKFKHMLEN7","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SINKFKHMLEN7YOLH","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SINKFKHM","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:7b4667cda6947cd164ac62d68623b44bd2dae96e932b0774a6cb84dfa71cf7be","target":"graph","created_at":"2026-05-18T01:51:18Z","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":"We study the connection between a multitime scalar variational problem (SVP), a multitime vector variational problem (VVP) and a multitime vector fractional variational problem (VFP). For (SVP), we establish necessary optimality conditions. For both vector variational problems, we define the notions of Pareto efficient solution and of normal efficient solution and we establish necessary efficiency conditions for (VVP) and (VFP) using both notions. The main purpose of the paper is to establish sufficient efficiency conditions for the vector problems (VVP) and (VFP). Moreover, we obtain sufficie","authors_text":"Constantin Udriste, Madalina Constantinescu, Stefan Mititelu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-06-12T13:01:32Z","title":"Efficiency for multitime vector variational problems on Riemannian manifolds involving geodesic quasiinvex functionals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04009","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":"sha256:22cca1943ce6a134423f5fcea709e47d89f6bfe24b435b71f93160714bf317eb","target":"record","created_at":"2026-05-18T01:51:18Z","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":"abba24ff7f497cee69aae98a5a8e4300192d01b63b39ca740998408c18434600","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-06-12T13:01:32Z","title_canon_sha256":"6e4d3d909f7e7e67c75c4412640cca4af70387c5b82570b164e2bc4f54ba2137"},"schema_version":"1.0","source":{"id":"1506.04009","kind":"arxiv","version":1}},"canonical_sha256":"921aa2a8ec591bfc3967a4743b1003f408e78cdce1284b6ef55a5e628bfde16d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"921aa2a8ec591bfc3967a4743b1003f408e78cdce1284b6ef55a5e628bfde16d","first_computed_at":"2026-05-18T01:51:18.544148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:51:18.544148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w6MG5LZIbshJQGdz40DY3/ZKpnKAgwxIhkruKN2xZXkM+J+6rGNC63k+16pDv7V8ZKJP+JEKljB6hgt6UmDhCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:51:18.544602Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.04009","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22cca1943ce6a134423f5fcea709e47d89f6bfe24b435b71f93160714bf317eb","sha256:7b4667cda6947cd164ac62d68623b44bd2dae96e932b0774a6cb84dfa71cf7be"],"state_sha256":"71529957b22e10bdb06552c61e0756be8838ce1a6ef75aba562959c9fb8dd147"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GEaz6LBQazAUlWWz9XR1683QZFI3HMluJp5DzKaXFG/2NjkfBwdj342YmETBD0xpzCTtP9Js9Ryg+R4ZfGxJAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:19:08.114531Z","bundle_sha256":"72969feeb9f4b33d0e15d616fcc26d6a576812bd8729729034df3e35abc885c1"}}