{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:FGIL67TIFNJLIGDDRJKI3Q6JSD","short_pith_number":"pith:FGIL67TI","schema_version":"1.0","canonical_sha256":"2990bf7e682b52b418638a548dc3c990f77f660e48ebf2c5afd444959dea596e","source":{"kind":"arxiv","id":"2409.20528","version":1},"attestation_state":"computed","paper":{"title":"Formally Verified Physics-Informed Neural Control Lyapunov Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.SY","math.OC"],"primary_cat":"eess.SY","authors_text":"Jun Liu, Maxwell Fitzsimmons, Ruikun Zhou, Yiming Meng","submitted_at":"2024-09-30T17:27:56Z","abstract_excerpt":"Control Lyapunov functions are a central tool in the design and analysis of stabilizing controllers for nonlinear systems. Constructing such functions, however, remains a significant challenge. In this paper, we investigate physics-informed learning and formal verification of neural network control Lyapunov functions. These neural networks solve a transformed Hamilton-Jacobi-Bellman equation, augmented by data generated using Pontryagin's maximum principle. Similar to how Zubov's equation characterizes the domain of attraction for autonomous systems, this equation characterizes the null-contro"},"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":"2409.20528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2024-09-30T17:27:56Z","cross_cats_sorted":["cs.LG","cs.SY","math.OC"],"title_canon_sha256":"114bf2aa134f14769be2563cd87518776f69c24594fcac6eda15a4e33ea10090","abstract_canon_sha256":"52ac6e1c8a6310c9ba3d06ab2bb7167b07df17e138a8c266ea802517d368c14f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:13:44.862129Z","signature_b64":"C5MfBTs+SpRt3gPJ5ZLGJ+NAVVsT9QXoGq39Up8MbkNtbJ3gy0agVejPwsRh6F0OKWPjFtcW+4Djo2ThLjwOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2990bf7e682b52b418638a548dc3c990f77f660e48ebf2c5afd444959dea596e","last_reissued_at":"2026-07-05T09:13:44.861713Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:13:44.861713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Formally Verified Physics-Informed Neural Control Lyapunov Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.SY","math.OC"],"primary_cat":"eess.SY","authors_text":"Jun Liu, Maxwell Fitzsimmons, Ruikun Zhou, Yiming Meng","submitted_at":"2024-09-30T17:27:56Z","abstract_excerpt":"Control Lyapunov functions are a central tool in the design and analysis of stabilizing controllers for nonlinear systems. Constructing such functions, however, remains a significant challenge. In this paper, we investigate physics-informed learning and formal verification of neural network control Lyapunov functions. These neural networks solve a transformed Hamilton-Jacobi-Bellman equation, augmented by data generated using Pontryagin's maximum principle. Similar to how Zubov's equation characterizes the domain of attraction for autonomous systems, this equation characterizes the null-contro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.20528","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.20528/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2409.20528","created_at":"2026-07-05T09:13:44.861767+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.20528v1","created_at":"2026-07-05T09:13:44.861767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.20528","created_at":"2026-07-05T09:13:44.861767+00:00"},{"alias_kind":"pith_short_12","alias_value":"FGIL67TIFNJL","created_at":"2026-07-05T09:13:44.861767+00:00"},{"alias_kind":"pith_short_16","alias_value":"FGIL67TIFNJLIGDD","created_at":"2026-07-05T09:13:44.861767+00:00"},{"alias_kind":"pith_short_8","alias_value":"FGIL67TI","created_at":"2026-07-05T09:13:44.861767+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.03932","citing_title":"A Physics-Informed Scenario Approach with Data Mitigation for Safety Verification of Nonlinear Systems","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FGIL67TIFNJLIGDDRJKI3Q6JSD","json":"https://pith.science/pith/FGIL67TIFNJLIGDDRJKI3Q6JSD.json","graph_json":"https://pith.science/api/pith-number/FGIL67TIFNJLIGDDRJKI3Q6JSD/graph.json","events_json":"https://pith.science/api/pith-number/FGIL67TIFNJLIGDDRJKI3Q6JSD/events.json","paper":"https://pith.science/paper/FGIL67TI"},"agent_actions":{"view_html":"https://pith.science/pith/FGIL67TIFNJLIGDDRJKI3Q6JSD","download_json":"https://pith.science/pith/FGIL67TIFNJLIGDDRJKI3Q6JSD.json","view_paper":"https://pith.science/paper/FGIL67TI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.20528&json=true","fetch_graph":"https://pith.science/api/pith-number/FGIL67TIFNJLIGDDRJKI3Q6JSD/graph.json","fetch_events":"https://pith.science/api/pith-number/FGIL67TIFNJLIGDDRJKI3Q6JSD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FGIL67TIFNJLIGDDRJKI3Q6JSD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FGIL67TIFNJLIGDDRJKI3Q6JSD/action/storage_attestation","attest_author":"https://pith.science/pith/FGIL67TIFNJLIGDDRJKI3Q6JSD/action/author_attestation","sign_citation":"https://pith.science/pith/FGIL67TIFNJLIGDDRJKI3Q6JSD/action/citation_signature","submit_replication":"https://pith.science/pith/FGIL67TIFNJLIGDDRJKI3Q6JSD/action/replication_record"}},"created_at":"2026-07-05T09:13:44.861767+00:00","updated_at":"2026-07-05T09:13:44.861767+00:00"}