{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3GGE564XMZ6VEPKWRRJ5IGLCBA","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":"a747251b568a7148832ad6d5bc8f6542ec22fb296f96019a387c3bb12a917e23","cross_cats_sorted":["math.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-03-28T15:45:28Z","title_canon_sha256":"7e43f8b6fca25b964705e1c380da8ff00dafb99c6bd98376e9bad19232addc37"},"schema_version":"1.0","source":{"id":"1803.10689","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10689","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10689v1","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10689","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"pith_short_12","alias_value":"3GGE564XMZ6V","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3GGE564XMZ6VEPKW","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3GGE564X","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:2c4ace02b3766aae98b0642d36d2e77d04987cd168f2e3f73fabe6104c9780d6","target":"graph","created_at":"2026-05-18T00:19:54Z","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":"Merging two Control Lyapunov Functions (CLFs) means creating a single \"new-born\" CLF by starting from two parents functions. Specifically, given a \"father\" function, shaped by the state constraints, and a \"mother\" function, designed with some optimality criterion, the merging CLF should be similar to the father close to the constraints and similar to the mother close to the origin. To successfully merge two CLFs, the control-sharing condition is crucial: the two functions must have a common control law that makes both Lyapunov derivatives simultaneously negative. Unfortunately, it is difficult","authors_text":"Filippo Fabiani, Franco Blanchini, Sergio Grammatico","cross_cats":["math.DS","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-03-28T15:45:28Z","title":"On merging constraint and optimal control-Lyapunov functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10689","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":"sha256:8b140da65144fa0959171092fb410b99f0d4d2fdc4a8b917fa6a7b863f53b490","target":"record","created_at":"2026-05-18T00:19:54Z","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":"a747251b568a7148832ad6d5bc8f6542ec22fb296f96019a387c3bb12a917e23","cross_cats_sorted":["math.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-03-28T15:45:28Z","title_canon_sha256":"7e43f8b6fca25b964705e1c380da8ff00dafb99c6bd98376e9bad19232addc37"},"schema_version":"1.0","source":{"id":"1803.10689","kind":"arxiv","version":1}},"canonical_sha256":"d98c4efb97667d523d568c53d41962081df62747270ed44801e947ea96a8273f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d98c4efb97667d523d568c53d41962081df62747270ed44801e947ea96a8273f","first_computed_at":"2026-05-18T00:19:54.449771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:54.449771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J+nItCA4nTSCksyUScgqjhUrRPqvTHqu9cmmLf/vpBb7r/hGCJq4nYvLm0qMLWxhTrxGw0SVL69k9bnXdTuABg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:54.450497Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.10689","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b140da65144fa0959171092fb410b99f0d4d2fdc4a8b917fa6a7b863f53b490","sha256:2c4ace02b3766aae98b0642d36d2e77d04987cd168f2e3f73fabe6104c9780d6"],"state_sha256":"ac582bc045db588b42c16ca1cde21d34bde6c3ce18f0b9a62158fb35c7948e7f"}