{"id":"W4415076176","doi":"10.1007/978-3-032-00155-9_6","title":"Hunter’s Positivity Theorem and Random Vector Norms","year":2025,"lang":"en","type":"book-chapter","venue":"Operator theory","topic":"Rough Sets and Fuzzy Logic","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université Laval","funders":"","keywords":"Degree (music); Interpretation (philosophy); Probabilistic logic; Homogeneous; Type (biology); Square (algebra); Fundamental theorem","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0007449035,0.0004388279,0.0005613144,0.0001307384,0.0002380928,0.0003977624,0.0008897585,0.0003078435,0.0001859086],"category_scores_gemma":[0.0000392767,0.000320568,0.0001698022,0.00004813681,0.0001964425,0.0002531254,0.0006513268,0.0004195846,0.0001163389],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005212629,"about_ca_system_score_gemma":0.0001169105,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005749086,"about_ca_topic_score_gemma":0.000005353274,"domain_scores_codex":[0.9983192,0.000131379,0.0002851836,0.0007357289,0.0002338477,0.0002946382],"domain_scores_gemma":[0.9984139,0.0003650915,0.000101985,0.0009044979,0.00008129488,0.0001332949],"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":[0.00006407208,0.0000143086,0.000004159897,0.00002961301,0.00007538366,0.00005743816,0.0002186274,8.07151e-7,0.00003828973,0.94538,0.00092681,0.05319051],"study_design_scores_gemma":[0.00235365,0.0002833892,0.0001362762,0.0005518471,0.0001192121,0.00008047478,0.00002021796,0.0009363801,0.0003290704,0.8001702,0.1936475,0.001371687],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.0001254199,0.002631229,0.0309989,0.000422396,0.0008623589,0.0004411392,0.00007000302,0.0001753216,0.9642732],"genre_scores_gemma":[0.1298142,0.001260504,0.00761446,0.006155599,0.0007831783,0.00006399921,0.00005062008,0.0001171609,0.8541403],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.1927207,"threshold_uncertainty_score":0.9999247,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.00727054050201154,"score_gpt":0.2072198721256548,"score_spread":0.1999493316236433,"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."}}