{"id":"W2950365644","doi":"","title":"Rational decomposition of dense hypergraphs and some related eigenvalue estimates","year":2011,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Hypergraph; Eigenvalues and eigenvectors; Decomposition; Mathematics; Combinatorics; Scheme (mathematics); Discrete mathematics; Mathematical analysis; Physics","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":[0.0002061567,0.0002601844,0.0003954357,0.0002691369,0.0001756501,0.00001455831,0.0002922028,0.0003644628,0.0001011896],"category_scores_gemma":[0.00008311693,0.0002663295,0.0001947067,0.0001395388,0.0003193898,0.0001361187,0.0005233407,0.0003487124,0.00000325625],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003748454,"about_ca_system_score_gemma":0.00004121055,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003410908,"about_ca_topic_score_gemma":0.000005922231,"domain_scores_codex":[0.9988753,0.0001133243,0.0002896942,0.0004758584,0.00007166943,0.000174175],"domain_scores_gemma":[0.9986504,0.0002909632,0.0003580594,0.0004822222,0.0001302875,0.00008802296],"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":[0.00009396774,0.00007007294,0.004084233,0.0002188988,0.0002709979,0.00004395019,0.0005156681,0.001583438,0.0002779143,0.9927325,0.00005600872,0.00005237609],"study_design_scores_gemma":[0.000396349,0.000043958,0.003181876,0.0001485807,0.0003401624,0.00001594686,0.0000568393,0.006433017,0.001328095,0.987785,0.000004252273,0.0002659248],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9940868,0.0002784736,0.003012069,0.000008073443,0.0002919434,0.0002416152,0.00003781198,0.00008018544,0.001963005],"genre_scores_gemma":[0.9962031,0.0003327216,0.00316411,0.00001543674,0.000026297,6.591256e-7,0.00002496288,0.00002574794,0.000206985],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004947476,"threshold_uncertainty_score":0.9999789,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07312652253199978,"score_gpt":0.2212816094189095,"score_spread":0.1481550868869097,"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."}}