{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RQPWNUBOMWDAEFGOMGA7JE4GK6","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":"dffed32340a45b8d90cc9ac5e2cbf36d4b6fa3306c89be21a93013be13dfb70a","cross_cats_sorted":["cs.LG","cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2026-03-20T00:58:51Z","title_canon_sha256":"af1a90d19c9f86ee1bc08d1047f835b21c61e7b471eb3fb0ffd518c9207b88f2"},"schema_version":"1.0","source":{"id":"2603.19545","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.19545","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"2603.19545v2","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.19545","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"RQPWNUBOMWDA","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"pith_short_16","alias_value":"RQPWNUBOMWDAEFGO","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"pith_short_8","alias_value":"RQPWNUBO","created_at":"2026-05-21T01:04:24Z"}],"graph_snapshots":[{"event_id":"sha256:c0ddd178dbbf609af5b6c820245ed6c2a71de0496a137e5044691632044b8ad4","target":"graph","created_at":"2026-05-21T01:04:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2603.19545/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many core problems in nonlinear systems analysis and control can be recast as solving partial differential equations (PDEs) such as Lyapunov and Hamilton-Jacobi-Bellman (HJB) equations. Physics-informed neural networks (PINNs) have emerged as a promising mesh-free approach for approximating their solutions, but in most existing works there is no rigorous guarantee that a small PDE residual implies a small solution error. This paper develops verifiable error bounds for approximate solutions of Lyapunov and HJB equations, with particular emphasis on PINN-based approximations. For both the Lyapun","authors_text":"Jun Liu","cross_cats":["cs.LG","cs.SY","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2026-03-20T00:58:51Z","title":"Verifiable Error Bounds for Physics-Informed Neural Network Solutions of Lyapunov and Hamilton-Jacobi-Bellman Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.19545","kind":"arxiv","version":2},"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:d10b4b2b228aad5591f19cebfe3bed87b5dd74af9dc878521bc6d3b15589bfdd","target":"record","created_at":"2026-05-21T01:04:24Z","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":"dffed32340a45b8d90cc9ac5e2cbf36d4b6fa3306c89be21a93013be13dfb70a","cross_cats_sorted":["cs.LG","cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2026-03-20T00:58:51Z","title_canon_sha256":"af1a90d19c9f86ee1bc08d1047f835b21c61e7b471eb3fb0ffd518c9207b88f2"},"schema_version":"1.0","source":{"id":"2603.19545","kind":"arxiv","version":2}},"canonical_sha256":"8c1f66d02e65860214ce6181f4938657961966f8a958f6decf88eacd3faadf90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c1f66d02e65860214ce6181f4938657961966f8a958f6decf88eacd3faadf90","first_computed_at":"2026-05-21T01:04:24.831422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:24.831422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vWnAIXvltrtLUTI8JFF0GT3B5ewCyoxUAp6WV7MAKXps7Q/cIZMcmfhVXEsescEloiPMTw6VRIhPXLF+k3NPAg==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:24.832078Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.19545","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d10b4b2b228aad5591f19cebfe3bed87b5dd74af9dc878521bc6d3b15589bfdd","sha256:c0ddd178dbbf609af5b6c820245ed6c2a71de0496a137e5044691632044b8ad4"],"state_sha256":"b09636946ab79eacce48947beffa3f38572ca55753819d214e12a4338a9bf6e1"}