{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EL24THPL6GYLNCT57A3MCTSGAD","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":"e44ca14b896bd1117d49f558fb3258a8722e4dfd9e0c3b8520e7c5b5480747d2","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-09T10:02:32Z","title_canon_sha256":"11100b4c936225519e525a2ad4934dc4e203ebed902bcf1304d62687e32b641c"},"schema_version":"1.0","source":{"id":"1604.04297","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04297","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04297v1","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04297","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"pith_short_12","alias_value":"EL24THPL6GYL","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EL24THPL6GYLNCT5","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EL24THPL","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:5a3158399ab296545e9668bf7961184ce99175945dd3c2e485950580d3811270","target":"graph","created_at":"2026-05-18T01:17:04Z","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 Herglotz problem is a generalization of the fundamental problem of the calculus of variations. In this paper, we consider a class of non-differentiable functions, where the dynamics is described by a scale derivative. Necessary conditions are derived to determine the optimal solution for the problem. Some other problems are considered, like transversality conditions, the multi-dimensional case, higher-order derivatives and for several independent variables.","authors_text":"Ricardo Almeida","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-09T10:02:32Z","title":"A Scale Variational Principle of Herglotz"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04297","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:a61d678d833db433521e0661d3a8cec932f70d353f1b819a95e923a666b181bb","target":"record","created_at":"2026-05-18T01:17:04Z","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":"e44ca14b896bd1117d49f558fb3258a8722e4dfd9e0c3b8520e7c5b5480747d2","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-09T10:02:32Z","title_canon_sha256":"11100b4c936225519e525a2ad4934dc4e203ebed902bcf1304d62687e32b641c"},"schema_version":"1.0","source":{"id":"1604.04297","kind":"arxiv","version":1}},"canonical_sha256":"22f5c99debf1b0b68a7df836c14e4600c7a7e7e451ca92305b7c58777de17260","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22f5c99debf1b0b68a7df836c14e4600c7a7e7e451ca92305b7c58777de17260","first_computed_at":"2026-05-18T01:17:04.611722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:04.611722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/qK7nyMzAQ3hxN07o93Izi1ap7nfUytGWXk/evnqCK7YmDVKl9i5lsDpZMwoWTpUfZADygOVVzs8/Xdbrc48BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:04.612593Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.04297","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a61d678d833db433521e0661d3a8cec932f70d353f1b819a95e923a666b181bb","sha256:5a3158399ab296545e9668bf7961184ce99175945dd3c2e485950580d3811270"],"state_sha256":"7aab27891eb2390be7b3dec6e21894af808d1b8ee83d6e188a6181c070b30ac3"}