{"id":"W3184660658","doi":"10.1007/s00208-022-02404-w","title":"On the squarefree values of $$a^4+b^3$$","year":2022,"lang":"de","type":"preprint","venue":"Mathematische Annalen","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","keywords":"Square-free integer; Mathematics; Combinatorics; BETA (programming language); Product (mathematics); Alpha (finance); Statistics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001290173,0.001115984,0.0006000066,0.001987108,0.001671419,0.003160186,0.001474582,0.001221377,0.01400795],"category_scores_gemma":[0.006499714,0.0004200531,0.0004138752,0.001140074,0.004502172,0.004384168,0.00200029,0.002631949,0.00159361],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001274786,"about_ca_system_score_gemma":0.0007215532,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008726365,"about_ca_topic_score_gemma":0.0009878696,"domain_scores_codex":[0.9993541,0.0001843263,0.00002106306,0.0001420333,0.0001729626,0.0001254894],"domain_scores_gemma":[0.9975243,0.001564164,0.000235984,0.0001726416,0.0002378979,0.0002649981],"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":[0.000135349,0.00001585524,0.0001926038,0.00005215314,0.000007487842,0.00009480928,0.0001815168,0.001004115,0.001807819,0.9880962,0.001975345,0.006436584],"study_design_scores_gemma":[0.0000127261,0.000007911594,0.0002707107,0.00001830104,0.000005093666,0.00007698366,0.00006508058,0.003184201,0.0009311377,0.9937357,0.001676218,0.00001585273],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5629966,0.001968954,0.07941011,0.006778423,0.001416077,0.00004750364,0.0005065086,0.0003436888,0.3465321],"genre_scores_gemma":[0.961573,0.0007472702,0.01192804,0.0006379519,0.000469128,0.00006703008,0.0001715707,0.0003042078,0.02410181],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01400795,"threshold_uncertainty_score":0.04686129,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1053661112679716,"score_gpt":0.3649862026881679,"score_spread":0.2596200914201964,"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."}}