{"id":"W4320728553","doi":"10.4153/s0008439523000140","title":"Perfectly packing a cube by cubes of nearly harmonic sidelength","year":2023,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Northern British Columbia","funders":"","keywords":"Cube (algebra); Mathematics; Combinatorics; Integer (computer science); Volume (thermodynamics); Harmonic; Physics; Thermodynamics; Computer science; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0009651104,0.0002475129,0.0005310685,0.0004430142,0.0001461643,0.00007796566,0.0003555954,0.0001571574,0.008081364],"category_scores_gemma":[0.003922412,0.0002234843,0.0001587732,0.000918477,0.0001301302,0.00005351769,0.00006503289,0.0002378257,0.004832195],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001099787,"about_ca_system_score_gemma":0.0002510175,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001603481,"about_ca_topic_score_gemma":0.0003982758,"domain_scores_codex":[0.9978114,0.00007366041,0.0006344021,0.0002941944,0.0004074752,0.0007788067],"domain_scores_gemma":[0.997321,0.00150921,0.0001411542,0.0004127953,0.0001583971,0.0004574546],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001421031,0.0001351093,0.0001430034,0.00277653,0.0001549481,0.00009362615,0.003589798,0.000003315142,0.0003686773,0.4335731,0.5557446,0.003403105],"study_design_scores_gemma":[0.000754675,0.0002393643,0.00008872475,0.0006372888,0.0001276421,0.00005080921,0.003777109,0.001850578,0.003789413,0.8270507,0.1607831,0.0008505892],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9613214,0.0004122934,0.001542175,0.006177325,0.000111114,0.0004702224,0.000237052,0.0002864588,0.02944195],"genre_scores_gemma":[0.9870365,0.00005092532,0.001791134,0.0003543667,0.00007654336,0.00005119961,0.00002282256,0.00007024687,0.01054622],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3949614,"threshold_uncertainty_score":0.9959427,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0471675462639286,"score_gpt":0.2906617693506551,"score_spread":0.2434942230867265,"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."}}