{"id":"W2604363177","doi":"10.1016/j.jnt.2017.08.024","title":"Triples which are D(n)-sets for several n's","year":2017,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Österreichische Agentur für Internationale Mobilität und Kooperation in Bildung, Wissenschaft und Forschung; Austrian Science Fund; Hrvatska Zaklada za Znanost; Österreichischen Akademie der Wissenschaften","keywords":"Diophantine equation; Mathematics; Square number; Integer (computer science); Conjecture; Combinatorics; Diophantine set; Pythagorean triple; Tuple; Discrete mathematics; Natural number; Set (abstract data type); Diophantine approximation","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":[0.001105521,0.0006047224,0.0008954919,0.002361233,0.006189173,0.004011202,0.00109859,0.001923249,0.0102617],"category_scores_gemma":[0.003498785,0.0006619378,0.00113009,0.001784464,0.002887618,0.004200973,0.003006805,0.001558715,0.001653861],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001706557,"about_ca_system_score_gemma":0.000746434,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001402662,"about_ca_topic_score_gemma":0.002387214,"domain_scores_codex":[0.9988946,0.0001723334,0.000119604,0.0002535714,0.0002404836,0.0003194484],"domain_scores_gemma":[0.9968545,0.001241232,0.0003639681,0.000505404,0.0005781666,0.0004567818],"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":[0.0004151794,0.00009377862,0.003175225,0.0001345199,0.00007017474,0.0009820377,0.0007886442,0.00145907,0.008869638,0.9661976,0.004100876,0.01371328],"study_design_scores_gemma":[0.00005568767,0.00007600257,0.003244137,0.0001252056,0.00006932055,0.00186298,0.00223751,0.007964534,0.01016486,0.9387681,0.03534709,0.00008466063],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6753334,0.0009145083,0.1619566,0.00184526,0.001083522,0.0002489076,0.001940491,0.0005737944,0.1561035],"genre_scores_gemma":[0.8991321,0.0003615947,0.06328652,0.0005466954,0.00011328,0.0003472602,0.001641585,0.0001864052,0.03438454],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0102617,"threshold_uncertainty_score":0.03432888,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07064788094550187,"score_gpt":0.3833443446932516,"score_spread":0.3126964637477497,"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."}}