{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QJWCVLZ4OHCHW7BOPMVEYGPJH7","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":"87f0992891b19a242ee459f5bdd1e2c1fb65d39c4e16b9bb7caf48b59427f65a","cross_cats_sorted":["cs.SY","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2024-11-27T13:15:50Z","title_canon_sha256":"091058e951195e35124c09ab90f62fff99a762826fbaddbe9ceb93af4c75886b"},"schema_version":"1.0","source":{"id":"2411.18318","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18318","created_at":"2026-07-05T10:47:33Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18318v2","created_at":"2026-07-05T10:47:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18318","created_at":"2026-07-05T10:47:33Z"},{"alias_kind":"pith_short_12","alias_value":"QJWCVLZ4OHCH","created_at":"2026-07-05T10:47:33Z"},{"alias_kind":"pith_short_16","alias_value":"QJWCVLZ4OHCHW7BO","created_at":"2026-07-05T10:47:33Z"},{"alias_kind":"pith_short_8","alias_value":"QJWCVLZ4","created_at":"2026-07-05T10:47:33Z"}],"graph_snapshots":[{"event_id":"sha256:78dc9c4734c23df696d06f98305ddb2e30214ebc59dc1ef9ba478e3d1bd05596","target":"graph","created_at":"2026-07-05T10:47:33Z","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/2411.18318/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems. However, we show that the current SRG analysis suffers from a pitfall that limit its applicability in analyzing practical nonlinear systems. We overcome this pitfall by modifying the SRG of a linear time invariant operator, combining the SRG with the Nyquist criterion, and apply our result to Lur'e systems. We thereby obtain a generalization of the celebrated circle criterion, which deals with a broader class of nonlinearities, and provides (incremental) $L_2$-gain performance","authors_text":"Amritam Das, Julius P.J. Krebbekx, Roland T\\'oth","cross_cats":["cs.SY","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2024-11-27T13:15:50Z","title":"Scaled Relative Graph Analysis of Lur'e Systems and the Generalized Circle Criterion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18318","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":"sha256:0b067b8c997bf57cd4acf3e2862bfb5ad49a45a9a14f76ad89fdfbe098448766","target":"record","created_at":"2026-07-05T10:47:33Z","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":"87f0992891b19a242ee459f5bdd1e2c1fb65d39c4e16b9bb7caf48b59427f65a","cross_cats_sorted":["cs.SY","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2024-11-27T13:15:50Z","title_canon_sha256":"091058e951195e35124c09ab90f62fff99a762826fbaddbe9ceb93af4c75886b"},"schema_version":"1.0","source":{"id":"2411.18318","kind":"arxiv","version":2}},"canonical_sha256":"826c2aaf3c71c47b7c2e7b2a4c19e93fe881b555669715cf24533c56d55724ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"826c2aaf3c71c47b7c2e7b2a4c19e93fe881b555669715cf24533c56d55724ea","first_computed_at":"2026-07-05T10:47:33.957627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:47:33.957627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9jujPGMs/MaHHzLNC9mN1D7ctw1fZnKab/ES0JcWSYLIMzeP4QZJzwWobltmpzoClwDBCNrE/bFOQOKp/phPCg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:47:33.958095Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.18318","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b067b8c997bf57cd4acf3e2862bfb5ad49a45a9a14f76ad89fdfbe098448766","sha256:78dc9c4734c23df696d06f98305ddb2e30214ebc59dc1ef9ba478e3d1bd05596"],"state_sha256":"a88e541eee62fecfe6d5a035afd11cc639f4e88de37c1e6d55fdc206d62f8d8c"}