{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WA7AG7HHD66HKWQ5KLIJJSZQDV","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":"d587c545e887035a774417f9b7478fb1a8f8e65d0ff8ecf6b71dbe64c16489c9","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-12T12:47:48Z","title_canon_sha256":"1401cfba40705d93438674ce1a28a4b5aa28c61a96f72c7f5d44d7480841e8e4"},"schema_version":"1.0","source":{"id":"1811.04693","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04693","created_at":"2026-05-18T00:01:04Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04693v1","created_at":"2026-05-18T00:01:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04693","created_at":"2026-05-18T00:01:04Z"},{"alias_kind":"pith_short_12","alias_value":"WA7AG7HHD66H","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WA7AG7HHD66HKWQ5","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WA7AG7HH","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:5e4701f52444db97425ce5b65cb0b6c9c3f62368679dc21d29dc2c57cf42156e","target":"graph","created_at":"2026-05-18T00:01:04Z","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":"The present paper extends the classical second-order variational problem of Herglotz type to the more general context of the Euclidean sphere S^n following variational and optimal control approaches. The relation between the Hamiltonian equations and the generalized Euler-Lagrange equations is established. This problem covers some classical variational problems posed on the Riemannian manifold S^n such as the problem of finding cubic polynomials on S^n. It also finds applicability on the dynamics of the simple pendulum in a resistive medium.","authors_text":"L. Abrunheiro, L. Machado, N. Martins","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-12T12:47:48Z","title":"Variational and Optimal Control Approaches for the Second-Order Herglotz Problem on Spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04693","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:f8915a78c979f29ec704fc1c362266a1557be3fb1a8929d9dec4ae7897bbb179","target":"record","created_at":"2026-05-18T00:01:04Z","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":"d587c545e887035a774417f9b7478fb1a8f8e65d0ff8ecf6b71dbe64c16489c9","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-12T12:47:48Z","title_canon_sha256":"1401cfba40705d93438674ce1a28a4b5aa28c61a96f72c7f5d44d7480841e8e4"},"schema_version":"1.0","source":{"id":"1811.04693","kind":"arxiv","version":1}},"canonical_sha256":"b03e037ce71fbc755a1d52d094cb301d5517ca686e17d17440a7f314c2bec364","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b03e037ce71fbc755a1d52d094cb301d5517ca686e17d17440a7f314c2bec364","first_computed_at":"2026-05-18T00:01:04.348946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:04.348946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JgouOfpk95YsSTHo0qEbm/TrIJD/Lmkz+tY8HKxQ9bQ1yLDnhI2gbjKuE1Ubmnd8lQ5Wa9ky3ALgKYC6btvqDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:04.349504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.04693","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8915a78c979f29ec704fc1c362266a1557be3fb1a8929d9dec4ae7897bbb179","sha256:5e4701f52444db97425ce5b65cb0b6c9c3f62368679dc21d29dc2c57cf42156e"],"state_sha256":"0847f82a0d0f5ac10be9c5ae5a0b836439298ae31af3042d715a009867d71243"}