{"id":"W7000867149","doi":"","title":"Hypergraph Capacity with Applications to Matrix Multiplication","year":2013,"lang":"en","type":"article","venue":"Scholarship - Claremont (Claremont Colleges)","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Hypergraph; Upper and lower bounds; Set (abstract data type); Matrix multiplication; Matrix (chemical analysis); Multiplication (music)","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":[0.001259113,0.0005557415,0.0006359103,0.002886244,0.001546165,0.003319522,0.001207635,0.001216193,0.008122338],"category_scores_gemma":[0.01060899,0.0004180905,0.0006368066,0.003567355,0.005074032,0.007100152,0.003041663,0.003029125,0.000692313],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003658638,"about_ca_system_score_gemma":0.0009998616,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002277613,"about_ca_topic_score_gemma":0.001679142,"domain_scores_codex":[0.9986367,0.0004529142,0.00005323847,0.0002864282,0.00037555,0.0001952282],"domain_scores_gemma":[0.9885244,0.008560379,0.0007208098,0.0008982304,0.000675097,0.0006210572],"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":[0.0000139851,0.00001206797,0.0002237561,0.00004733564,0.000004143166,0.00004427717,0.0001259355,0.008506784,0.0004822524,0.9837299,0.001572957,0.005236529],"study_design_scores_gemma":[0.000004160604,0.00001004889,0.0001601441,0.00003372483,0.000004633603,0.00008443603,0.00006559675,0.04403446,0.000820905,0.9476793,0.00708819,0.00001446989],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1580181,0.008665054,0.5798234,0.01233631,0.0005721429,0.0001610536,0.001024092,0.000855122,0.2385446],"genre_scores_gemma":[0.9126665,0.004027971,0.06707472,0.0005392062,0.0008818049,0.0002385531,0.0002518513,0.0001697362,0.01414971],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008122338,"threshold_uncertainty_score":0.02717191,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0415896441113883,"score_gpt":0.3011813436100197,"score_spread":0.2595916994986314,"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."}}