{"id":"W1988834806","doi":"10.5539/jmr.v1n2p21","title":"The Packing Spheres Constant for a Class of Separable Orlicz Function Spaces","year":2009,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Advanced Banach Space Theory","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; SPHERES; Conjecture; Separable space; Norm (philosophy); Space (punctuation); Constant (computer programming); Pure mathematics; Mathematical analysis; Function space; Ideal (ethics); Class (philosophy); Combinatorics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.007780672,0.000154708,0.0005031755,0.0002181451,0.0003240813,0.0001051216,0.000510153,0.00009502572,0.00004910524],"category_scores_gemma":[0.005961713,0.00009397231,0.0002191267,0.0003571015,0.0002951396,0.0002076529,0.00005760956,0.0005613299,0.000005270181],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001406479,"about_ca_system_score_gemma":0.0002356833,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001587118,"about_ca_topic_score_gemma":0.00002976629,"domain_scores_codex":[0.9969757,0.0002511955,0.0009073071,0.0001195574,0.001242525,0.0005037414],"domain_scores_gemma":[0.988856,0.00814671,0.0009379728,0.0004434958,0.001504279,0.0001115532],"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":[0.0006299322,0.0005969804,0.00003154443,0.0005895402,0.0002167062,0.00001277982,0.001641796,0.0001513624,0.02304908,0.9450135,0.02120076,0.006865974],"study_design_scores_gemma":[0.0007444739,0.0009727133,0.000009126317,0.0004588061,0.00005845003,0.00006167586,0.0129748,0.00142973,0.009037302,0.9697981,0.004357924,0.0000968646],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6036349,0.003726155,0.3650854,0.00519093,0.0004979369,0.002359249,0.00002113937,0.00006720609,0.01941707],"genre_scores_gemma":[0.8839763,0.0003695864,0.113006,0.00002695359,0.0002859676,0.00001483523,4.158824e-7,0.00005448186,0.002265476],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2803414,"threshold_uncertainty_score":0.7137158,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1399061827223733,"score_gpt":0.4506545462631893,"score_spread":0.310748363540816,"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."}}