{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2WFN3VBGIDC7M2AQPDJ4JCIWRJ","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":"18d3c0159d8de547f83a45dc93143f98129eb0f2a9a5c592314170b1ec2dae8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-23T20:21:17Z","title_canon_sha256":"bc5d356cc57ed6e9448a4929d5428bbdfa039dc54014aa99dcfa3493111d39a4"},"schema_version":"1.0","source":{"id":"2607.21794","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.21794","created_at":"2026-07-27T00:20:21Z"},{"alias_kind":"arxiv_version","alias_value":"2607.21794v1","created_at":"2026-07-27T00:20:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21794","created_at":"2026-07-27T00:20:21Z"},{"alias_kind":"pith_short_12","alias_value":"2WFN3VBGIDC7","created_at":"2026-07-27T00:20:21Z"},{"alias_kind":"pith_short_16","alias_value":"2WFN3VBGIDC7M2AQ","created_at":"2026-07-27T00:20:21Z"},{"alias_kind":"pith_short_8","alias_value":"2WFN3VBG","created_at":"2026-07-27T00:20:21Z"}],"graph_snapshots":[{"event_id":"sha256:369a54de9461ba7d3a59ff440610349572a8cfbad48026afaf7ed5205c657a9b","target":"graph","created_at":"2026-07-27T00:20:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.21794/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Control barrier functions (CBFs) have become an important controller design tool for autonomous systems subject to safety constraints. Despite their popularity, recent works have shown that CBF-based controllers can destabilize the internal dynamics of the system. In this paper, we consider linear systems with affine safety constraints and design linear feedback controllers that satisfy high-order CBF (HOCBF) constraints while rendering the origin globally exponentially stable. We first characterize the exact class of all linear gain matrices that globally satisfy the HOCBF constraints, includ","authors_text":"Aaron D. Ames, Pio Ong, Pol Mestres, Shima Sadat Mousavi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-23T20:21:17Z","title":"Safe Stabilizing Linear Feedback: Necessary and Sufficient Conditions, Optimality, and Margins"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21794","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:ae3b59f70d9ee8bef2f139d66e19551322fbb94262653691928caefe1578413f","target":"record","created_at":"2026-07-27T00:20:21Z","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":"18d3c0159d8de547f83a45dc93143f98129eb0f2a9a5c592314170b1ec2dae8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-23T20:21:17Z","title_canon_sha256":"bc5d356cc57ed6e9448a4929d5428bbdfa039dc54014aa99dcfa3493111d39a4"},"schema_version":"1.0","source":{"id":"2607.21794","kind":"arxiv","version":1}},"canonical_sha256":"d58addd42640c5f6681078d3c489168a67d36fa4a72f7290101912ca0a07a368","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d58addd42640c5f6681078d3c489168a67d36fa4a72f7290101912ca0a07a368","first_computed_at":"2026-07-27T00:20:21.349881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-27T00:20:21.349881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KOIhBw8xuB1jsWGGjXJNLxJrfdm/LfRQoGIEBghsy2IpIUA5yQHa16LDykIxMGtGL+KZZEMW+nQFyRUFTF+7BA==","signature_status":"signed_v1","signed_at":"2026-07-27T00:20:21.350735Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.21794","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae3b59f70d9ee8bef2f139d66e19551322fbb94262653691928caefe1578413f","sha256:369a54de9461ba7d3a59ff440610349572a8cfbad48026afaf7ed5205c657a9b"],"state_sha256":"925da89b0027050155a1d589e76677fd5f56bbdf770283c8701b8f4495aab45c"}