{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YPUTI3XZ5VF6KFIIUCYZHH3MUU","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":"8f4a47173d20e432c343390f8f4328b769ccdbdf6f39c7ef77b3b250d9b8219b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-30T03:20:49Z","title_canon_sha256":"7d6caf92229216adabe1957a8dd7b3be14c7cdea3776d4c92fb9bdb927aad7a6"},"schema_version":"1.0","source":{"id":"1608.08311","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08311","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08311v1","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08311","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"pith_short_12","alias_value":"YPUTI3XZ5VF6","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YPUTI3XZ5VF6KFII","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YPUTI3XZ","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:741dabca4ffd7963b2ab76623761d7ba2b1853d1ad1715102655b34c22e21402","target":"graph","created_at":"2026-05-18T00:25:21Z","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":"We study stability criteria for discrete-time switched systems and provide a meta-theorem that characterizes all Lyapunov theorems of a certain canonical type. For this purpose, we investigate the structure of sets of LMIs that provide a sufficient condition for stability. Various such conditions have been proposed in the literature in the past fifteen years. We prove in this note that a family of languagetheoretic conditions recently provided by the authors encapsulates all the possible LMI conditions, thus putting a conclusion to this research effort. As a corollary, we show that it is PSPAC","authors_text":"Amirali Ahmadi, Mardavij Roozbehani, Pablo Parrilo, Raphael M. Jungers","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-30T03:20:49Z","title":"A Characterization of Lyapunov Inequalities for Stability of Switched Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08311","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":"sha256:97b5f1e5f4266d09d6becbb983b0b32fb6a9b9cc83dc35f5f40fa5037f9a6820","target":"record","created_at":"2026-05-18T00:25:21Z","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":"8f4a47173d20e432c343390f8f4328b769ccdbdf6f39c7ef77b3b250d9b8219b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-30T03:20:49Z","title_canon_sha256":"7d6caf92229216adabe1957a8dd7b3be14c7cdea3776d4c92fb9bdb927aad7a6"},"schema_version":"1.0","source":{"id":"1608.08311","kind":"arxiv","version":1}},"canonical_sha256":"c3e9346ef9ed4be51508a0b1939f6ca51c5dbed5e57cc2d9bf2806cd2839d052","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3e9346ef9ed4be51508a0b1939f6ca51c5dbed5e57cc2d9bf2806cd2839d052","first_computed_at":"2026-05-18T00:25:21.316544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:21.316544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hj5oAmPDC2nD49XmNRRk8pAErcThtFujEfnSgj/9g9woy1jWLw97wy9l53gRkfZqdixYaLeS+RkZ1Oos5a5VAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:21.317230Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08311","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97b5f1e5f4266d09d6becbb983b0b32fb6a9b9cc83dc35f5f40fa5037f9a6820","sha256:741dabca4ffd7963b2ab76623761d7ba2b1853d1ad1715102655b34c22e21402"],"state_sha256":"d6c0e6d4b833827504b7e6197e8f30abf9c413d5400f7c9b0cc9903688c3d3f1"}