{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O3EUDGOW4RTPMLGHSBEJHJKZM7","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":"1db4780fa1506e4876d169e4e8ae2a53f04b5d3871f0283ad61569a5d51f8dd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-16T17:54:57Z","title_canon_sha256":"531aa69df80c228c4fe8b371ddc0ec94d26a6ecaa5d214693408043960b360a7"},"schema_version":"1.0","source":{"id":"1403.3937","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3937","created_at":"2026-05-18T02:52:25Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3937v1","created_at":"2026-05-18T02:52:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3937","created_at":"2026-05-18T02:52:25Z"},{"alias_kind":"pith_short_12","alias_value":"O3EUDGOW4RTP","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O3EUDGOW4RTPMLGH","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O3EUDGOW","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:5ef95ed220f2bc5968ae7c5759d8b04fad502c4f71e685991501bb95d4f8688a","target":"graph","created_at":"2026-05-18T02:52:25Z","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 dynamic minimization problems of the calculus of variations with generalized Lagrangian functionals that depend on a general linear operator $K$ and defined on bounded-time intervals. Under assumptions of regularity, convexity and coercivity, we derive sufficient conditions ensuring the existence of a minimizer. Finally, we obtain necessary optimality conditions of Euler-Lagrange type. Main results are illustrated with special cases, when $K$ is a general kernel operator and, in particular, with $K$ the fractional integral of Riemann-Liouville and Hadamard. The application of our resu","authors_text":"Delfim F.M. Torres, Lo\\\"ic Bourdin, Tatiana Odzijewicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-16T17:54:57Z","title":"Existence of minimizers for generalized Lagrangian functionals and a necessary optimality condition --- Application to fractional variational problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3937","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":"sha256:603b4197c554ba8d829be9bae4acbeff9790b4361044ec61e1c6599e6f95174f","target":"record","created_at":"2026-05-18T02:52:25Z","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":"1db4780fa1506e4876d169e4e8ae2a53f04b5d3871f0283ad61569a5d51f8dd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-16T17:54:57Z","title_canon_sha256":"531aa69df80c228c4fe8b371ddc0ec94d26a6ecaa5d214693408043960b360a7"},"schema_version":"1.0","source":{"id":"1403.3937","kind":"arxiv","version":1}},"canonical_sha256":"76c94199d6e466f62cc7904893a55967e09357a7602ea3c4bfcc172f8c0b7d4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76c94199d6e466f62cc7904893a55967e09357a7602ea3c4bfcc172f8c0b7d4c","first_computed_at":"2026-05-18T02:52:25.366273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:25.366273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+CgHPVqqZqXkY2wOJ4gELLSp3ULU22VzAvJHehNmVQEAVR36RiALQD3nSs8tlzZpPG7z/VJFZRNp+drl00ujCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:25.366958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3937","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:603b4197c554ba8d829be9bae4acbeff9790b4361044ec61e1c6599e6f95174f","sha256:5ef95ed220f2bc5968ae7c5759d8b04fad502c4f71e685991501bb95d4f8688a"],"state_sha256":"e29f330492cd0a3f0606b23800be45903b63a1fb9aebecd6a5ce7b96e394984d"}