{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QSHB62ASP7Q62VDBJOLGF6TUFW","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":"ca34f55ae28a30649e857c962dd459491f7e113e27434f1141d69d77b47870f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-07-04T20:54:11Z","title_canon_sha256":"408adb9e87b99e30248add89a8a1818dd75cd3d5d779a6221c6337d340b77066"},"schema_version":"1.0","source":{"id":"1007.0584","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0584","created_at":"2026-05-18T04:38:16Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0584v1","created_at":"2026-05-18T04:38:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0584","created_at":"2026-05-18T04:38:16Z"},{"alias_kind":"pith_short_12","alias_value":"QSHB62ASP7Q6","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QSHB62ASP7Q62VDB","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QSHB62AS","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:cb7a690ac65a8510af1cf2638d958749d23992a54cc657998c8573041320cee2","target":"graph","created_at":"2026-05-18T04:38:16Z","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":"In this paper we consider the problem of the calculus of variations for a functional which is the composition of a certain scalar function $H$ with the delta integral of a vector valued field $f$, i.e., of the form $H(\\int_{a}^{b}f(t,x^{\\sigma}(t),x^{\\Delta}(t))\\Delta t)$. Euler-Lagrange equations, natural boundary conditions for such problems as well as a necessary optimality condition for isoperimetric problems, on a general time scale, are given. A number of corollaries are obtained, and several examples illustrating the new results are discussed in detail.","authors_text":"Agnieszka B. Malinowska, Delfim F. M. Torres","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-07-04T20:54:11Z","title":"Euler-Lagrange equations for composition functionals in calculus of variations on time scales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0584","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":"sha256:6bd6bac90b20acae1fd8c05078bdd58586cbaa48f2e5d50bb0ec39bd77ec1ec4","target":"record","created_at":"2026-05-18T04:38:16Z","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":"ca34f55ae28a30649e857c962dd459491f7e113e27434f1141d69d77b47870f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-07-04T20:54:11Z","title_canon_sha256":"408adb9e87b99e30248add89a8a1818dd75cd3d5d779a6221c6337d340b77066"},"schema_version":"1.0","source":{"id":"1007.0584","kind":"arxiv","version":1}},"canonical_sha256":"848e1f68127fe1ed54614b9662fa742db9cf6619e2fb1ac4534644ef1fb250cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"848e1f68127fe1ed54614b9662fa742db9cf6619e2fb1ac4534644ef1fb250cf","first_computed_at":"2026-05-18T04:38:16.842212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:16.842212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BUXPUcnGLsiL1BPZVYmqAQop0D8GWPhb0v72taQ3EJLtTTJvGlo2s/TN9SUb0LTdnz7CB0AntfhXE9tkZQzcBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:16.842770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0584","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bd6bac90b20acae1fd8c05078bdd58586cbaa48f2e5d50bb0ec39bd77ec1ec4","sha256:cb7a690ac65a8510af1cf2638d958749d23992a54cc657998c8573041320cee2"],"state_sha256":"24bc6769f0580371876cff7f2783be26fa325cd39fb671a43a975456ae0cb98b"}