{"id":"W7128633611","doi":"10.1109/focs63196.2025.00038","title":"Direct Product Theorems for Randomized Query Complexity","year":2025,"lang":"","type":"article","venue":"","topic":"Complexity and Algorithms in Graphs","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Direct product; Product (mathematics); Bounded function; Measure (data warehouse); Function (biology); Boolean function","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.01064664,0.002446964,0.002736873,0.002847408,0.001711616,0.007187327,0.005321934,0.002672085,0.01607118],"category_scores_gemma":[0.07323436,0.001321865,0.004294677,0.003819812,0.007526041,0.02750391,0.008012805,0.01013891,0.003060869],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.006421655,"about_ca_system_score_gemma":0.002717343,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001781735,"about_ca_topic_score_gemma":0.001125608,"domain_scores_codex":[0.9840685,0.004254344,0.0009143724,0.00410036,0.005476909,0.00118563],"domain_scores_gemma":[0.877719,0.09800123,0.004174784,0.011618,0.006527376,0.001959533],"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":[0.0001590255,0.00009393218,0.0009669974,0.0002622362,0.00005957406,0.0001085542,0.0003000113,0.01608525,0.00145196,0.9521853,0.003295874,0.02503125],"study_design_scores_gemma":[0.00005198964,0.00009679746,0.0003819497,0.00003424917,0.0000453204,0.0002063902,0.00003447147,0.1199705,0.001845947,0.8742264,0.003061326,0.00004464323],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03488996,0.001853958,0.9317103,0.002792791,0.0001831165,0.0002237955,0.0008571622,0.0006759202,0.02681308],"genre_scores_gemma":[0.7284162,0.002590282,0.245106,0.002365282,0.001532577,0.001881947,0.001577587,0.00119379,0.01533625],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01607118,"threshold_uncertainty_score":0.05630547,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03415585052121464,"score_gpt":0.2938558317782489,"score_spread":0.2596999812570343,"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."}}