{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PHHRDYATM6DMZOHBV3DF5M3K7K","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":"720892b63fd429d3e55fb8611c296c2a48dfec77d670469dcf9a1220c13167ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-08T08:57:56Z","title_canon_sha256":"d57fd398ae52c20f0f119aacd47e5246ba91e2f920a2adacbf5d2b7a18027df7"},"schema_version":"1.0","source":{"id":"1203.1707","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1707","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1707v1","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1707","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"PHHRDYATM6DM","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PHHRDYATM6DMZOHB","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PHHRDYAT","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:f87dc7f0d6315795612877ef383faf2c3be167f160e887990ff1333abe9f74b0","target":"graph","created_at":"2026-05-18T04:00:37Z","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":"Fractional Pontryagin's systems emerge in the study of a class of fractional optimal control problems but they are not resolvable in most cases. In this paper, we suggest a numerical approach for these fractional systems. Precisely, we construct a variational integrator allowing to preserve at the discrete level their intrinsic variational structure. The variational integrator obtained is then called shifted discrete fractional Pontryagin's system. We provide a solved fractional example in a certain sense. It allows us to test in this paper the convergence of the variational integrator constru","authors_text":"Lo\\\"ic Bourdin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-08T08:57:56Z","title":"Variational integrator for fractional Pontryagin's systems. Existence of a discrete fractional Noether's theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1707","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:f80bc6a3e0c571617d6026b75c8de4066fb21c3274e322969e4d0e00c5d40a8f","target":"record","created_at":"2026-05-18T04:00:37Z","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":"720892b63fd429d3e55fb8611c296c2a48dfec77d670469dcf9a1220c13167ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-08T08:57:56Z","title_canon_sha256":"d57fd398ae52c20f0f119aacd47e5246ba91e2f920a2adacbf5d2b7a18027df7"},"schema_version":"1.0","source":{"id":"1203.1707","kind":"arxiv","version":1}},"canonical_sha256":"79cf11e0136786ccb8e1aec65eb36afab81a4a8e97cdf901a27267b83639b60c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79cf11e0136786ccb8e1aec65eb36afab81a4a8e97cdf901a27267b83639b60c","first_computed_at":"2026-05-18T04:00:37.219888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:37.219888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ys2BP5446TwHWKedNyNLN1GnIK3Dint4nyVxefhrSI9Y9HoyNjbx/+zE8wRxPwNf1iza1hfjg6tKDjYZSpd3CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:37.220672Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1707","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f80bc6a3e0c571617d6026b75c8de4066fb21c3274e322969e4d0e00c5d40a8f","sha256:f87dc7f0d6315795612877ef383faf2c3be167f160e887990ff1333abe9f74b0"],"state_sha256":"8d05906f45de3ca127e0d00b970498d01c4e97217b271e8308b8697d5528cb4d"}