{"id":"W3034848674","doi":"10.3336/gm.55.1.04","title":"Perfect powers in an alternating sum of consecutive cubes","year":2020,"lang":"en","type":"article","venue":"Glasnik Matematicki","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Diophantine equation; Perfect power; Combinatorics; Prime (order theory); Discrete mathematics","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":[],"consensus_categories":[],"category_scores_codex":[0.000729324,0.000200448,0.0005462319,0.0001051302,0.00004229189,0.00002574661,0.0003125138,0.00008128673,0.0004765809],"category_scores_gemma":[0.001219187,0.0001805049,0.00009005556,0.0003171498,0.0001135435,0.000211544,0.00009893284,0.0001877053,0.0000903188],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000273088,"about_ca_system_score_gemma":0.00003703015,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000230868,"about_ca_topic_score_gemma":0.000009048333,"domain_scores_codex":[0.9982585,0.0002679109,0.0006477652,0.0002621992,0.0002834865,0.0002801785],"domain_scores_gemma":[0.9984544,0.0007593976,0.0002796928,0.000306614,0.00007182311,0.0001281004],"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":[0.0008890023,0.00154414,0.07748753,0.01739557,0.000580679,0.0003542412,0.1471968,0.0002244131,0.02999206,0.7203658,0.002802488,0.001167282],"study_design_scores_gemma":[0.004988129,0.00177026,0.005069169,0.002534056,0.0002904768,0.0001079912,0.06392898,0.01908601,0.1455773,0.7547453,0.0001787132,0.001723617],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9920955,0.00005512257,0.0007862327,0.0002350033,0.00009826733,0.0003426539,0.00001518094,0.00008889617,0.006283143],"genre_scores_gemma":[0.9964217,0.000004212831,0.00320605,0.0002052624,0.00004648882,0.00001466288,0.000005227097,0.00003172364,0.00006465492],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1155852,"threshold_uncertainty_score":0.7360777,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04775073028518333,"score_gpt":0.3114059904010625,"score_spread":0.2636552601158792,"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."}}