{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0009559122,0.000695271,0.0007151942,0.0005279186,0.0012783,0.0003565253,0.001214384,0.000495481,0.0003268453],"category_scores_gemma":[0.0005582995,0.0005627557,0.0002838927,0.001436504,0.0002223485,0.0008372417,0.0003077472,0.001046005,0.0003261665],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000294234,"about_ca_system_score_gemma":0.0001018378,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001902958,"about_ca_topic_score_gemma":0.0003845638,"domain_scores_codex":[0.9957339,0.000349743,0.0008439755,0.00112213,0.0009945808,0.0009556913],"domain_scores_gemma":[0.9952915,0.0005330714,0.0003562674,0.002141167,0.000951683,0.0007263356],"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":[0.0004534826,0.000917087,0.03332438,0.0004807178,0.000575192,0.0000330256,0.0026347,0.0001775082,0.01763189,0.915655,0.01308065,0.01503632],"study_design_scores_gemma":[0.003089344,0.0005245571,0.07722639,0.0003316294,0.0003524416,0.0002061576,0.001242041,0.0004057023,0.006452181,0.8555486,0.05221938,0.002401547],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9667443,0.0003921099,0.01486927,0.00243215,0.0002898385,0.006707978,0.0001629192,0.0007950343,0.007606393],"genre_scores_gemma":[0.8982426,0.0000251752,0.09707016,0.0008799601,0.0002624152,0.001761173,0.00002945199,0.0001493916,0.001579699],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08220089,"threshold_uncertainty_score":0.9996824,"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."}}