{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EL24THPL6GYLNCT57A3MCTSGAD","short_pith_number":"pith:EL24THPL","canonical_record":{"source":{"id":"1604.04297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-09T10:02:32Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"11100b4c936225519e525a2ad4934dc4e203ebed902bcf1304d62687e32b641c","abstract_canon_sha256":"e44ca14b896bd1117d49f558fb3258a8722e4dfd9e0c3b8520e7c5b5480747d2"},"schema_version":"1.0"},"canonical_sha256":"22f5c99debf1b0b68a7df836c14e4600c7a7e7e451ca92305b7c58777de17260","source":{"kind":"arxiv","id":"1604.04297","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EL24THPL6GYLNCT57A3MCTSGAD","target":"record","payload":{"canonical_record":{"source":{"id":"1604.04297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-09T10:02:32Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"11100b4c936225519e525a2ad4934dc4e203ebed902bcf1304d62687e32b641c","abstract_canon_sha256":"e44ca14b896bd1117d49f558fb3258a8722e4dfd9e0c3b8520e7c5b5480747d2"},"schema_version":"1.0"},"canonical_sha256":"22f5c99debf1b0b68a7df836c14e4600c7a7e7e451ca92305b7c58777de17260","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:04.612593Z","signature_b64":"/qK7nyMzAQ3hxN07o93Izi1ap7nfUytGWXk/evnqCK7YmDVKl9i5lsDpZMwoWTpUfZADygOVVzs8/Xdbrc48BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22f5c99debf1b0b68a7df836c14e4600c7a7e7e451ca92305b7c58777de17260","last_reissued_at":"2026-05-18T01:17:04.611722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:04.611722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.04297","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":"2026-05-18T01:17:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z1Do+YUM58N/K1Tk01iKwb37N/1zz7ZXK6dJESWEYKDeLCz6NUsDIEQGZ0eLfNF61Qv0bu5r6GaCe3JHl0lQBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:41:10.350543Z"},"content_sha256":"a61d678d833db433521e0661d3a8cec932f70d353f1b819a95e923a666b181bb","schema_version":"1.0","event_id":"sha256:a61d678d833db433521e0661d3a8cec932f70d353f1b819a95e923a666b181bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EL24THPL6GYLNCT57A3MCTSGAD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Scale Variational Principle of Herglotz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.OC","authors_text":"Ricardo Almeida","submitted_at":"2016-04-09T10:02:32Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04297","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":"2026-05-18T01:17:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BFQmWqA8dKwefNbTJbyweB4vIPGWa+pedMQ1bFUoSwOCnZ4S11nbLtIuRALohBZJyw9tsnCXFX88efp7VvmtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:41:10.350891Z"},"content_sha256":"5a3158399ab296545e9668bf7961184ce99175945dd3c2e485950580d3811270","schema_version":"1.0","event_id":"sha256:5a3158399ab296545e9668bf7961184ce99175945dd3c2e485950580d3811270"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EL24THPL6GYLNCT57A3MCTSGAD/bundle.json","state_url":"https://pith.science/pith/EL24THPL6GYLNCT57A3MCTSGAD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EL24THPL6GYLNCT57A3MCTSGAD/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":"2026-06-02T21:41:10Z","links":{"resolver":"https://pith.science/pith/EL24THPL6GYLNCT57A3MCTSGAD","bundle":"https://pith.science/pith/EL24THPL6GYLNCT57A3MCTSGAD/bundle.json","state":"https://pith.science/pith/EL24THPL6GYLNCT57A3MCTSGAD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EL24THPL6GYLNCT57A3MCTSGAD/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5x8Upe6UnpC96mbdvY8tHk2XBOy4fRayrCLCGJMdqNUpJIETxEEEvdm6ePeD+ZmZtFTSK22n3DfskiELYeauCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:41:10.352881Z","bundle_sha256":"075a807ec6ed2c2dfa081851a210940eda805ab1b82058498460b97b80c29d72"}}