{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:U6GBU6Y2BECBJMCFHEXZ4JZUIM","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":"26e22d15bc16fe079d7a0f98cde2fd147d34eeeb58f338c6397ae4b02e00adfb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-09T14:51:37Z","title_canon_sha256":"0d2acad5f73b8680b6713944f492c9a6d6c6891dd3e717a47de38ceb99987435"},"schema_version":"1.0","source":{"id":"1203.2102","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2102","created_at":"2026-05-18T04:00:27Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2102v1","created_at":"2026-05-18T04:00:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2102","created_at":"2026-05-18T04:00:27Z"},{"alias_kind":"pith_short_12","alias_value":"U6GBU6Y2BECB","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U6GBU6Y2BECBJMCF","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U6GBU6Y2","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:c54aca22047501d81003e26d8fcc59c992b1a393a81f5b847b90b41f7994e442","target":"graph","created_at":"2026-05-18T04:00:27Z","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":"We extend the second Noether theorem to fractional variational problems which are invariant under infinitesimal transformations that depend upon $r$ arbitrary functions and their fractional derivatives in the sense of Caputo. Our main result is illustrated using the fractional Lagrangian density of the electromagnetic field.","authors_text":"Agnieszka B. Malinowska","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-09T14:51:37Z","title":"On Fractional Variational Problems which Admit Local Transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2102","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:c5b4639b695af0efb89b33c5ad4e9a8fe0dbb760e0f183f03345046a85f238b6","target":"record","created_at":"2026-05-18T04:00:27Z","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":"26e22d15bc16fe079d7a0f98cde2fd147d34eeeb58f338c6397ae4b02e00adfb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-09T14:51:37Z","title_canon_sha256":"0d2acad5f73b8680b6713944f492c9a6d6c6891dd3e717a47de38ceb99987435"},"schema_version":"1.0","source":{"id":"1203.2102","kind":"arxiv","version":1}},"canonical_sha256":"a78c1a7b1a090414b045392f9e273443126619cf44fee3f661c20aa85558dc77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a78c1a7b1a090414b045392f9e273443126619cf44fee3f661c20aa85558dc77","first_computed_at":"2026-05-18T04:00:27.498522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:27.498522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e87Y+yocXsriweWZBBemWQvvjnw3850VDyLzVfXsUrHSuQ9u1VjZPXPhjCYANcC2hk+om+XqzwpD6PwKnoF/Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:27.499052Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2102","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5b4639b695af0efb89b33c5ad4e9a8fe0dbb760e0f183f03345046a85f238b6","sha256:c54aca22047501d81003e26d8fcc59c992b1a393a81f5b847b90b41f7994e442"],"state_sha256":"34bbd08bf2e67eb9eb7c7153aaf8ad9a2957392c9c35139f43eb8185dc9f8c6d"}