{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:LGB4JT6EOVT3AF65Z3V6BZOIAL","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":"9625c6d25ad8cc576527583a6535ea985abae06db17b522130d0bbde045f89ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-14T19:03:09Z","title_canon_sha256":"1f5bb2d06a9dbfae7e822bec759ec3c762aeaea0b785cc23fdc0d83b3b9986ba"},"schema_version":"1.0","source":{"id":"2008.06546","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.06546","created_at":"2026-07-05T01:53:38Z"},{"alias_kind":"arxiv_version","alias_value":"2008.06546v2","created_at":"2026-07-05T01:53:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.06546","created_at":"2026-07-05T01:53:38Z"},{"alias_kind":"pith_short_12","alias_value":"LGB4JT6EOVT3","created_at":"2026-07-05T01:53:38Z"},{"alias_kind":"pith_short_16","alias_value":"LGB4JT6EOVT3AF65","created_at":"2026-07-05T01:53:38Z"},{"alias_kind":"pith_short_8","alias_value":"LGB4JT6E","created_at":"2026-07-05T01:53:38Z"}],"graph_snapshots":[{"event_id":"sha256:c7fa3a587c05ac4265c56f99d6fb3ab6b1958d60ff727688106a3ad7a9a06d8e","target":"graph","created_at":"2026-07-05T01:53:38Z","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/2008.06546/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a learning-based method for Lyapunov stability analysis of piecewise affine dynamical systems in feedback with piecewise affine neural network controllers. The proposed method consists of an iterative interaction between a learner and a verifier, where in each iteration, the learner uses a collection of samples of the closed-loop system to propose a Lyapunov function candidate as the solution to a convex program. The learner then queries the verifier, which solves a mixed-integer program to either validate the proposed Lyapunov function candidate or reject it with a counterexample, ","authors_text":"George J. Pappas, Mahyar Fazlyab, Manfred Morari, Shaoru Chen, Victor M. Preciado","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-14T19:03:09Z","title":"Learning Lyapunov Functions for Piecewise Affine Systems with Neural Network Controllers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.06546","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":"sha256:801da677bbba5b7427154dfc8d0e0151c39cf42a3e225bf6c24fe7be75acfb70","target":"record","created_at":"2026-07-05T01:53:38Z","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":"9625c6d25ad8cc576527583a6535ea985abae06db17b522130d0bbde045f89ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-14T19:03:09Z","title_canon_sha256":"1f5bb2d06a9dbfae7e822bec759ec3c762aeaea0b785cc23fdc0d83b3b9986ba"},"schema_version":"1.0","source":{"id":"2008.06546","kind":"arxiv","version":2}},"canonical_sha256":"5983c4cfc47567b017ddceebe0e5c802eae926104077e100a16462d1c4e2e34f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5983c4cfc47567b017ddceebe0e5c802eae926104077e100a16462d1c4e2e34f","first_computed_at":"2026-07-05T01:53:38.767326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:53:38.767326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SrIoF6ByNL9zBSLBjL9yfQE1cqZMIF52VM1iUsixT4WSEyUKpRm++otQwxfBe1Mh+KOsqT4VIBkE2mrim9FpBw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:53:38.767801Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.06546","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:801da677bbba5b7427154dfc8d0e0151c39cf42a3e225bf6c24fe7be75acfb70","sha256:c7fa3a587c05ac4265c56f99d6fb3ab6b1958d60ff727688106a3ad7a9a06d8e"],"state_sha256":"79ec50dc129b43677f79fa0ef94ddf273ca8d6a53600b577d7c0372f6c2616f2"}