{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OSJYM4WDCPMDG2M63JRCCT4C4Z","short_pith_number":"pith:OSJYM4WD","canonical_record":{"source":{"id":"1803.08308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-22T11:12:11Z","cross_cats_sorted":["math.MP","physics.class-ph"],"title_canon_sha256":"5b0817c1931beded121c2d4c39e83675157878963998464fe0c82a1714d3f759","abstract_canon_sha256":"717b533b64f130bfc15a1be8c76d4cc6626fc984a7cd973eb354e283fb7a6e89"},"schema_version":"1.0"},"canonical_sha256":"74938672c313d833699eda62214f82e67465d71abb5c1ad4dade5112d1fea31d","source":{"kind":"arxiv","id":"1803.08308","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08308","created_at":"2026-05-18T00:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08308v1","created_at":"2026-05-18T00:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08308","created_at":"2026-05-18T00:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"OSJYM4WDCPMD","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OSJYM4WDCPMDG2M6","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OSJYM4WD","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OSJYM4WDCPMDG2M63JRCCT4C4Z","target":"record","payload":{"canonical_record":{"source":{"id":"1803.08308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-22T11:12:11Z","cross_cats_sorted":["math.MP","physics.class-ph"],"title_canon_sha256":"5b0817c1931beded121c2d4c39e83675157878963998464fe0c82a1714d3f759","abstract_canon_sha256":"717b533b64f130bfc15a1be8c76d4cc6626fc984a7cd973eb354e283fb7a6e89"},"schema_version":"1.0"},"canonical_sha256":"74938672c313d833699eda62214f82e67465d71abb5c1ad4dade5112d1fea31d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:23.166509Z","signature_b64":"XqWokWNYIRX/cAN8Z7uUcYp/ltc9erTLaPflhhf6LwnsHXoHIfpjKsRGTOzzaBt4CWx9MkW65HSMLMjlUa0aAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74938672c313d833699eda62214f82e67465d71abb5c1ad4dade5112d1fea31d","last_reissued_at":"2026-05-18T00:20:23.166002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:23.166002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.08308","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":"2026-05-18T00:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6eGv7s52WvD3ubND91XldpGwMBi61SOSODGaJPbNxtkXt4t3eYBKPzt7dD2fTFQ9g+xN5WOsh+spscsIfHV0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:57:20.941544Z"},"content_sha256":"e02ec8b06a5396eab2fb60396603ace3b3f79ba92fc91be74c773a08b7b1a7b4","schema_version":"1.0","event_id":"sha256:e02ec8b06a5396eab2fb60396603ace3b3f79ba92fc91be74c773a08b7b1a7b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OSJYM4WDCPMDG2M63JRCCT4C4Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Action Principle for Action-dependent Lagrangians: toward an Action Principle to non-conservative systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.class-ph"],"primary_cat":"math-ph","authors_text":"Gast\\~ao S. F. Frederico, Jo\\~ao T. S. Amaral, Juilson Paiva, Matheus J. Lazo","submitted_at":"2018-03-22T11:12:11Z","abstract_excerpt":"In this work, we propose an Action Principle for Action-dependent Lagrangian functions by generalizing the Herglotz variational problem to the case with several independent variables. We obtain a necessary condition for the extremum equivalent to the Euler-Lagrange equation and, through some examples, we show that this generalized Action Principle enables us to construct simple and physically meaningful Action-dependent Lagrangian functions for a wide range of non-conservative classical and quantum systems. Furthermore, when the dependence on the Action is removed, the traditional Action Princ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08308","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":"2026-05-18T00:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YdSn3vDmyfLMkg6L6noWLTm5fox/9MazEFJNRlCpV6qdVclMZpRImi07RxcGe3jvaambbvLdYvSgZK+dD/KLAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:57:20.942241Z"},"content_sha256":"0c2f957c952cda5e841d09eab951635cd047142630cf34ca49075fd91a9738c3","schema_version":"1.0","event_id":"sha256:0c2f957c952cda5e841d09eab951635cd047142630cf34ca49075fd91a9738c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OSJYM4WDCPMDG2M63JRCCT4C4Z/bundle.json","state_url":"https://pith.science/pith/OSJYM4WDCPMDG2M63JRCCT4C4Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OSJYM4WDCPMDG2M63JRCCT4C4Z/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":"2026-05-25T17:57:20Z","links":{"resolver":"https://pith.science/pith/OSJYM4WDCPMDG2M63JRCCT4C4Z","bundle":"https://pith.science/pith/OSJYM4WDCPMDG2M63JRCCT4C4Z/bundle.json","state":"https://pith.science/pith/OSJYM4WDCPMDG2M63JRCCT4C4Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OSJYM4WDCPMDG2M63JRCCT4C4Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OSJYM4WDCPMDG2M63JRCCT4C4Z","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":"717b533b64f130bfc15a1be8c76d4cc6626fc984a7cd973eb354e283fb7a6e89","cross_cats_sorted":["math.MP","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-22T11:12:11Z","title_canon_sha256":"5b0817c1931beded121c2d4c39e83675157878963998464fe0c82a1714d3f759"},"schema_version":"1.0","source":{"id":"1803.08308","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08308","created_at":"2026-05-18T00:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08308v1","created_at":"2026-05-18T00:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08308","created_at":"2026-05-18T00:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"OSJYM4WDCPMD","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OSJYM4WDCPMDG2M6","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OSJYM4WD","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:0c2f957c952cda5e841d09eab951635cd047142630cf34ca49075fd91a9738c3","target":"graph","created_at":"2026-05-18T00:20:23Z","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 work, we propose an Action Principle for Action-dependent Lagrangian functions by generalizing the Herglotz variational problem to the case with several independent variables. We obtain a necessary condition for the extremum equivalent to the Euler-Lagrange equation and, through some examples, we show that this generalized Action Principle enables us to construct simple and physically meaningful Action-dependent Lagrangian functions for a wide range of non-conservative classical and quantum systems. Furthermore, when the dependence on the Action is removed, the traditional Action Princ","authors_text":"Gast\\~ao S. F. Frederico, Jo\\~ao T. S. Amaral, Juilson Paiva, Matheus J. Lazo","cross_cats":["math.MP","physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-22T11:12:11Z","title":"An Action Principle for Action-dependent Lagrangians: toward an Action Principle to non-conservative systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08308","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:e02ec8b06a5396eab2fb60396603ace3b3f79ba92fc91be74c773a08b7b1a7b4","target":"record","created_at":"2026-05-18T00:20:23Z","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":"717b533b64f130bfc15a1be8c76d4cc6626fc984a7cd973eb354e283fb7a6e89","cross_cats_sorted":["math.MP","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-22T11:12:11Z","title_canon_sha256":"5b0817c1931beded121c2d4c39e83675157878963998464fe0c82a1714d3f759"},"schema_version":"1.0","source":{"id":"1803.08308","kind":"arxiv","version":1}},"canonical_sha256":"74938672c313d833699eda62214f82e67465d71abb5c1ad4dade5112d1fea31d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74938672c313d833699eda62214f82e67465d71abb5c1ad4dade5112d1fea31d","first_computed_at":"2026-05-18T00:20:23.166002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:23.166002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XqWokWNYIRX/cAN8Z7uUcYp/ltc9erTLaPflhhf6LwnsHXoHIfpjKsRGTOzzaBt4CWx9MkW65HSMLMjlUa0aAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:23.166509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.08308","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e02ec8b06a5396eab2fb60396603ace3b3f79ba92fc91be74c773a08b7b1a7b4","sha256:0c2f957c952cda5e841d09eab951635cd047142630cf34ca49075fd91a9738c3"],"state_sha256":"8ab1dfb6259c9cae92e60788873a951a167a01e3de29c34ae712404d2f2589c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L3awBlG40bF17fePD8PfwKo+4m6mvxN6VY+N4if9Y040WaXtOokW35urTzF+qpXqILRrg8KMVUvwdJtJU8zDAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:57:20.946511Z","bundle_sha256":"06da476b74c5d90b8a5b392fd9f914fb16789e556fe77455f0b1d76707d27aad"}}