{"id":"W4414824879","doi":"10.48550/arxiv.2510.02223","title":"Computing Control Lyapunov-Barrier Functions: Softmax Relaxation and Smooth Patching with Formal Guarantees","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Control and Stability of Dynamical Systems","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs","keywords":"Softmax function; Modulo; Lemma (botany); Correctness; Satisfiability; Lyapunov function; Relaxation (psychology); Control theory (sociology); Topology (electrical circuits)","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002597135,0.001088475,0.0007398306,0.0006947675,0.0005383567,0.001677291,0.001458755,0.0009584831,0.005039445],"category_scores_gemma":[0.01021502,0.0006425434,0.001150138,0.0004322603,0.00224982,0.002031825,0.002537226,0.002277269,0.0006382534],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001103501,"about_ca_system_score_gemma":0.001899145,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001618582,"about_ca_topic_score_gemma":0.001871434,"domain_scores_codex":[0.9984646,0.0003554334,0.00008964913,0.0003042263,0.0005432299,0.0002429423],"domain_scores_gemma":[0.9967945,0.001871221,0.000298111,0.000610071,0.0003338854,0.00009211001],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0002487337,0.0001100255,0.0009613255,0.0002877994,0.00004120319,0.0002987973,0.0003704897,0.659642,0.01816895,0.2389049,0.001509478,0.07945634],"study_design_scores_gemma":[0.0000488892,0.0001037953,0.0000863272,0.00004313086,0.00001767405,0.00004141704,0.00005657422,0.8955584,0.01181875,0.09023318,0.001975423,0.00001647082],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.02028384,0.0000474989,0.9766995,0.0001287395,0.00002118292,0.00006437599,0.00004979499,0.0007127601,0.001992344],"genre_scores_gemma":[0.5741606,0.00008823989,0.4224343,0.0001227859,0.00002885979,0.0002369953,0.0001957301,0.0004335029,0.002298968],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.005039445,"threshold_uncertainty_score":0.01685864,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.00836507073125371,"score_gpt":0.2009739948476274,"score_spread":0.1926089241163737,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}