{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.00540507,0.0006605794,0.001943956,0.0005085,0.001108565,0.0009035548,0.002512705,0.0001571834,0.0003283675],"category_scores_gemma":[0.001397555,0.0005512995,0.001396678,0.001800842,0.002333797,0.0005675174,0.001126019,0.0003752137,0.00004126495],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009380634,"about_ca_system_score_gemma":0.000563829,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004420245,"about_ca_topic_score_gemma":0.00009933147,"domain_scores_codex":[0.9943877,0.001023371,0.001297224,0.001759078,0.0004854442,0.001047142],"domain_scores_gemma":[0.9932775,0.003590898,0.0003165481,0.002033571,0.000592223,0.0001892342],"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":[0.008312781,0.0003943674,0.00001477503,0.0002374402,0.0004109443,0.000002477634,0.0005464296,0.00003192028,0.00004487747,0.8993775,0.008737137,0.08188941],"study_design_scores_gemma":[0.07179439,0.00007637965,0.0000618868,0.000203296,0.0001527698,0.000004862207,0.00006021022,0.3140012,0.00417212,0.5896336,0.01926601,0.0005732633],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0002978562,0.003025088,0.8416632,0.009664679,0.006588527,0.004605915,0.00004319916,0.0004315909,0.1336799],"genre_scores_gemma":[0.5989696,0.0006371189,0.35027,0.004322906,0.00102145,0.001117342,0.00003161892,0.00005248588,0.04357739],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.5986718,"threshold_uncertainty_score":0.9996939,"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."}}