{"id":"W2312652594","doi":"10.1112/s0025579316000231","title":"PERFECT POWERS THAT ARE SUMS OF CONSECUTIVE CUBES","year":2016,"lang":"en","type":"article","venue":"Mathematika","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Engineering and Physical Sciences Research Council; Natural Sciences and Engineering Research Council of Canada","keywords":"Perfect power; Logarithm; Euler's formula; Sums of powers; Relation (database)","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0007231842,0.0001823582,0.0004377213,0.000129789,0.00004424356,0.00001367227,0.0003175281,0.00008154301,0.005301805],"category_scores_gemma":[0.001163172,0.0001091412,0.0001520865,0.0001403985,0.0003367399,0.00008246725,0.0001238844,0.00008262883,0.0007685603],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005441776,"about_ca_system_score_gemma":0.00004052299,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007317778,"about_ca_topic_score_gemma":0.00001009151,"domain_scores_codex":[0.9985858,0.0001345317,0.0002804718,0.0002397896,0.0004359977,0.0003234442],"domain_scores_gemma":[0.9972174,0.001738817,0.0002419923,0.0005981576,0.0001031762,0.0001005289],"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":[0.0001017421,0.0003214326,0.01451639,0.000695376,0.0003891454,0.00005100278,0.003026708,9.796417e-8,0.01119791,0.9317434,0.03652709,0.001429703],"study_design_scores_gemma":[0.001142084,0.00009054771,0.0006503335,0.001018608,0.00008165796,0.00005755274,0.003685242,0.00005073476,0.07163086,0.9196132,0.001617833,0.0003612817],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7370913,0.00008865144,0.0132491,0.0006593519,0.00006746248,0.0005617195,0.00004296351,0.0001963629,0.2480431],"genre_scores_gemma":[0.9541832,0.0000132897,0.002107307,0.00001744617,0.00002290661,0.00001984155,3.617151e-7,0.00007142797,0.04356418],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2170919,"threshold_uncertainty_score":0.9956075,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08656458321088152,"score_gpt":0.347010285099643,"score_spread":0.2604457018887615,"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."}}