{"id":"W4414972727","doi":"10.48550/arxiv.2510.04943","title":"The NPA hierarchy does not always attain the commuting operator value","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Computability, Logic, AI Algorithms","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Banff International Research Station for Mathematical Innovation and Discovery; Villum Fonden","keywords":"Undecidable problem; Operator (biology); Hierarchy; Value (mathematics); Property (philosophy); Constraint (computer-aided design); Turing machine","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":[0.001382947,0.000385511,0.0009936317,0.0006478152,0.002184086,0.002626381,0.001248445,0.001297935,0.006899178],"category_scores_gemma":[0.008673177,0.0004404553,0.00121829,0.0004766451,0.003511283,0.006496863,0.002414481,0.004484619,0.0006669486],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0019245,"about_ca_system_score_gemma":0.001842077,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003080919,"about_ca_topic_score_gemma":0.003818522,"domain_scores_codex":[0.9981072,0.0004010478,0.00009532308,0.0004690971,0.000478815,0.0004485602],"domain_scores_gemma":[0.9921417,0.005090875,0.0004326678,0.0008367519,0.0007403236,0.0007577793],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00009598996,0.00005473481,0.001002248,0.0001101178,0.00002441529,0.0001806138,0.0003304658,0.00284084,0.004394703,0.9834347,0.001316212,0.006214757],"study_design_scores_gemma":[0.00002628055,0.00002973926,0.0003495219,0.00001542302,0.00001499374,0.0001111925,0.0001105138,0.02317408,0.002564328,0.9718397,0.0017484,0.00001586012],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6007457,0.0003799236,0.3175392,0.003449898,0.0001181572,0.0001412095,0.0005585605,0.001065635,0.07600173],"genre_scores_gemma":[0.9661749,0.00009759633,0.02812684,0.0003919461,0.00004912926,0.00009281126,0.0002032023,0.0001038115,0.004759663],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006899178,"threshold_uncertainty_score":0.02308005,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04010095455430727,"score_gpt":0.2880831119645439,"score_spread":0.2479821574102366,"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."}}