{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ZGJIWZ3EHPNEEJA7TRKWAJZILO","short_pith_number":"pith:ZGJIWZ3E","schema_version":"1.0","canonical_sha256":"c9928b67643bda42241f9c556027285b9ef4f510036b61cfe7517dba2d9de92a","source":{"kind":"arxiv","id":"1101.2962","version":1},"attestation_state":"computed","paper":{"title":"Variational problems with fractional derivatives: Invariance conditions and N\\\"{o}ther's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sanja Konjik, Srboljub Simic, Stevan Pilipovic, Teodor M. Atanackovic","submitted_at":"2011-01-15T10:18:02Z","abstract_excerpt":"A variational principle for Lagrangian densities containing derivatives of real order is formulated and the invariance of this principle is studied in two characteristic cases. Necessary and sufficient conditions for an infinitesimal transformation group (basic N\\\"{o}ther's identity) are obtained. These conditions extend the classical results, valid for integer order derivatives. A generalization of N\\\"{o}ther's theorem leading to conservation laws for fractional Euler-Lagrangian equation is obtained as well. Results are illustrated by several concrete examples. Finally, an approximation of a "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1101.2962","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-01-15T10:18:02Z","cross_cats_sorted":[],"title_canon_sha256":"be32673e80a59f7c8124ce225af3268b15a1660aa818d2cdbc924b08b50d1282","abstract_canon_sha256":"a47c3caa3de5152fcccc455628418e8a1518c0ae0df2c8b7eab3ffb4d864d664"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:30.670683Z","signature_b64":"/Z9e+NAYYFx4L1Ba3IdhYbqfx/h+KDrXh9mRQEE/gdE0dx6JoQo2KB4eDaEQOfYZv4szLrCVnoO8awYpHXxlDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9928b67643bda42241f9c556027285b9ef4f510036b61cfe7517dba2d9de92a","last_reissued_at":"2026-05-18T04:31:30.670216Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:30.670216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Variational problems with fractional derivatives: Invariance conditions and N\\\"{o}ther's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sanja Konjik, Srboljub Simic, Stevan Pilipovic, Teodor M. Atanackovic","submitted_at":"2011-01-15T10:18:02Z","abstract_excerpt":"A variational principle for Lagrangian densities containing derivatives of real order is formulated and the invariance of this principle is studied in two characteristic cases. Necessary and sufficient conditions for an infinitesimal transformation group (basic N\\\"{o}ther's identity) are obtained. These conditions extend the classical results, valid for integer order derivatives. A generalization of N\\\"{o}ther's theorem leading to conservation laws for fractional Euler-Lagrangian equation is obtained as well. Results are illustrated by several concrete examples. Finally, an approximation of a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2962","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1101.2962","created_at":"2026-05-18T04:31:30.670295+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.2962v1","created_at":"2026-05-18T04:31:30.670295+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2962","created_at":"2026-05-18T04:31:30.670295+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZGJIWZ3EHPNE","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZGJIWZ3EHPNEEJA7","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZGJIWZ3E","created_at":"2026-05-18T12:26:47.523578+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZGJIWZ3EHPNEEJA7TRKWAJZILO","json":"https://pith.science/pith/ZGJIWZ3EHPNEEJA7TRKWAJZILO.json","graph_json":"https://pith.science/api/pith-number/ZGJIWZ3EHPNEEJA7TRKWAJZILO/graph.json","events_json":"https://pith.science/api/pith-number/ZGJIWZ3EHPNEEJA7TRKWAJZILO/events.json","paper":"https://pith.science/paper/ZGJIWZ3E"},"agent_actions":{"view_html":"https://pith.science/pith/ZGJIWZ3EHPNEEJA7TRKWAJZILO","download_json":"https://pith.science/pith/ZGJIWZ3EHPNEEJA7TRKWAJZILO.json","view_paper":"https://pith.science/paper/ZGJIWZ3E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.2962&json=true","fetch_graph":"https://pith.science/api/pith-number/ZGJIWZ3EHPNEEJA7TRKWAJZILO/graph.json","fetch_events":"https://pith.science/api/pith-number/ZGJIWZ3EHPNEEJA7TRKWAJZILO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZGJIWZ3EHPNEEJA7TRKWAJZILO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZGJIWZ3EHPNEEJA7TRKWAJZILO/action/storage_attestation","attest_author":"https://pith.science/pith/ZGJIWZ3EHPNEEJA7TRKWAJZILO/action/author_attestation","sign_citation":"https://pith.science/pith/ZGJIWZ3EHPNEEJA7TRKWAJZILO/action/citation_signature","submit_replication":"https://pith.science/pith/ZGJIWZ3EHPNEEJA7TRKWAJZILO/action/replication_record"}},"created_at":"2026-05-18T04:31:30.670295+00:00","updated_at":"2026-05-18T04:31:30.670295+00:00"}