{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2MOWHN4UMFWF44WHCL542YCBVZ","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":"41744e1817f3210eee8355380c34d92ad21044a8179b089deb07772cbb37a128","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-01T16:18:49Z","title_canon_sha256":"d5181666d0c5e91117372d86f6b097808de7b507def506d56fb7dd5b99589a2a"},"schema_version":"1.0","source":{"id":"1511.00265","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00265","created_at":"2026-05-18T01:20:18Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00265v1","created_at":"2026-05-18T01:20:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00265","created_at":"2026-05-18T01:20:18Z"},{"alias_kind":"pith_short_12","alias_value":"2MOWHN4UMFWF","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2MOWHN4UMFWF44WH","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2MOWHN4U","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:d4feb5dbc15530dc44f3a3ce6def9348e34f25004b473369809e3a415d693e92","target":"graph","created_at":"2026-05-18T01:20:18Z","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 paper infinite horizon optimal control problems for nonlinear high-dimensional dynamical systems are studied. Nonlinear feedback laws can be computed via the value function characterized as the unique viscosity solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation which stems from the dynamic programming approach. However, the bottleneck is mainly due to the curse of dimensionality and HJB equations are only solvable in a relatively small dimension. Therefore, a reduced-order model is derived for the dynamical system and for this purpose the method of proper orthogonal d","authors_text":"Alessandro Alla, Maurizio Falcone, Stefan Volkwein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-01T16:18:49Z","title":"Error analysis for POD Approximations of infinite horizon problems via the Dynamic Programming approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00265","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":"sha256:875bd886830dc3103944a896734bcfc46f78d7dee059fd87c7c5cb536c932102","target":"record","created_at":"2026-05-18T01:20:18Z","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":"41744e1817f3210eee8355380c34d92ad21044a8179b089deb07772cbb37a128","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-01T16:18:49Z","title_canon_sha256":"d5181666d0c5e91117372d86f6b097808de7b507def506d56fb7dd5b99589a2a"},"schema_version":"1.0","source":{"id":"1511.00265","kind":"arxiv","version":1}},"canonical_sha256":"d31d63b794616c5e72c712fbcd6041ae609a3043f453d5c91045c7c158dbd88c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d31d63b794616c5e72c712fbcd6041ae609a3043f453d5c91045c7c158dbd88c","first_computed_at":"2026-05-18T01:20:18.906030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:18.906030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ywQ0e0xOoUKpudsCK9JEil2birPNAQslTTM9xG98dA00he0JBBVZsdEHhx5hSg77myUfMIygoPuX43bqaHkDCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:18.906680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.00265","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:875bd886830dc3103944a896734bcfc46f78d7dee059fd87c7c5cb536c932102","sha256:d4feb5dbc15530dc44f3a3ce6def9348e34f25004b473369809e3a415d693e92"],"state_sha256":"71b4b5b644a5a55c985cc83103c16e395307e8734faa37ecd7b49f0e030df318"}