{"id":"W6891547493","doi":"10.4230/lipics.itcs.2025.37","title":"A Lower Bound on the Trace Norm of Boolean Matrices and Its Applications","year":2025,"lang":"en","type":"article","venue":"DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)","topic":"Complexity and Algorithms in Graphs","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria; University of Toronto; McGill University","funders":"University of Toronto; Natural Sciences and Engineering Research Council of Canada; University of Rochester","keywords":"Boolean function; Logarithm; Parity function; Binary decision diagram; Exponential function; Norm (philosophy); Upper and lower bounds; Integer (computer science); Binary number","routes":{"ca_aff":true,"ca_fund":true,"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":[],"consensus_categories":[],"category_scores_codex":[0.000439541,0.0002213991,0.0002590023,0.0002449806,0.0004674684,0.0003280744,0.001268813,0.00009373287,0.00001071494],"category_scores_gemma":[0.00005536899,0.0001641052,0.0001482784,0.0006204765,0.0001471981,0.000666658,0.0004160457,0.0002641539,0.00002551291],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003395344,"about_ca_system_score_gemma":0.00006209358,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006920707,"about_ca_topic_score_gemma":0.00001068507,"domain_scores_codex":[0.9984871,0.0000233787,0.0006326229,0.0002126457,0.0002996396,0.0003445782],"domain_scores_gemma":[0.9983004,0.0004525472,0.000266411,0.0007190155,0.0001870281,0.00007462749],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00004304828,0.0003673873,0.0002872482,0.0005270564,0.0001335994,8.540374e-7,0.003260506,0.00004301908,0.00004086843,0.9518067,0.003376594,0.04011313],"study_design_scores_gemma":[0.003327862,0.0006882442,0.002452229,0.0006705222,0.0001135855,0.00004346962,0.002002899,0.3079787,0.00512788,0.07159177,0.605009,0.0009938383],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.216581,0.001061189,0.7352095,0.006630545,0.001314631,0.004309589,0.000649274,0.000367905,0.03387638],"genre_scores_gemma":[0.9834276,0.0001847735,0.01321926,0.001960818,0.00007704123,0.000327227,0.00002987911,0.00001725788,0.0007561344],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8802149,"threshold_uncertainty_score":0.6692018,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01565305313479278,"score_gpt":0.2603466745017213,"score_spread":0.2446936213669285,"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."}}