{"id":"W3153008905","doi":"10.4064/aa210419-4-7","title":"A new diophantine equation involving fifth powers","year":2021,"lang":"en","type":"preprint","venue":"Acta Arithmetica","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Lakeshore General Hospital","funders":"","keywords":"Diophantine equation; Elliptic curve; Mathematics; Diophantine set; Parametric statistics; Parametric equation; Thue equation; Legendre's equation; Diophantine geometry; Pure mathematics; Mathematical analysis; Geometry; Statistics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000280942,0.0004627976,0.00052992,0.0005886108,0.00101943,0.001772774,0.0007509664,0.001313733,0.006223504],"category_scores_gemma":[0.0008644699,0.0002278503,0.0006185548,0.0007470677,0.001592031,0.001954284,0.001435607,0.001897993,0.000738672],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000735934,"about_ca_system_score_gemma":0.0004936751,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002725223,"about_ca_topic_score_gemma":0.0003020154,"domain_scores_codex":[0.9998191,0.00003026665,0.00001106513,0.00003442425,0.00006177177,0.00004341191],"domain_scores_gemma":[0.9998597,0.00003693019,0.00002498121,0.00002795408,0.00002005062,0.00003030905],"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":[0.00003431812,0.00002611816,0.0002535427,0.00006775814,0.00001188447,0.0004688537,0.000355506,0.003271671,0.008722093,0.978737,0.0006857317,0.007365522],"study_design_scores_gemma":[0.0000732181,0.0001024719,0.0004736945,0.00006395015,0.00003054677,0.001248051,0.0006424476,0.04604375,0.01198119,0.9199221,0.01934845,0.00007004493],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6727188,0.001065611,0.1832004,0.002891793,0.0007314748,0.00009174582,0.0002044458,0.0001572772,0.1389385],"genre_scores_gemma":[0.936971,0.0004195847,0.02813084,0.0002625247,0.0001093454,0.0000423275,0.00009376707,0.00004093924,0.03392966],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006223504,"threshold_uncertainty_score":0.02081966,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04777195643873293,"score_gpt":0.298251601251326,"score_spread":0.2504796448125931,"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."}}