{"id":"W3014654089","doi":"10.1007/s00454-020-00252-6","title":"On Arithmetic Progressions in Model Sets","year":2021,"lang":"en","type":"article","venue":"Discrete & Computational Geometry","topic":"Quasicrystal Structures and Properties","field":"Materials Science","cited_by":6,"is_retracted":false,"has_abstract":false,"ca_institutions":"MacEwan University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Van der Waerden's theorem; Mathematics; Arithmetic; Arithmetic progression; Point (geometry); Space (punctuation); Second-order arithmetic; Type (biology); Euclidean space; Discrete mathematics; Combinatorics; Computer science; Peano axioms; Geometry","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":[0.001371869,0.001108861,0.001356449,0.002397263,0.002436588,0.00429259,0.001746658,0.001666605,0.01508573],"category_scores_gemma":[0.005203137,0.0006307326,0.001564708,0.002752336,0.005220252,0.009313061,0.003248632,0.004062909,0.001491576],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002276639,"about_ca_system_score_gemma":0.0008591523,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001720699,"about_ca_topic_score_gemma":0.001393147,"domain_scores_codex":[0.9990619,0.0003159826,0.00005738901,0.0001481221,0.0002612802,0.000155345],"domain_scores_gemma":[0.997614,0.001588574,0.0001823355,0.0002705941,0.0001943506,0.0001501411],"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":[0.000004091503,0.000003013716,0.00001317941,0.000007679151,8.272622e-7,0.000009260176,0.00004851439,0.0004631175,0.00003405078,0.9983468,0.0002713032,0.0007981759],"study_design_scores_gemma":[0.000003359763,0.000003458693,0.00001560771,0.000007318262,0.000001123369,0.00001296773,0.00002063265,0.00166657,0.00003573754,0.9972434,0.000986882,0.000002902147],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2250233,0.004400009,0.4058239,0.007536854,0.001328715,0.0001694085,0.000997479,0.0005911668,0.3541291],"genre_scores_gemma":[0.9057586,0.002307487,0.04522437,0.0008854473,0.0007260785,0.0002103434,0.0006510928,0.0002816841,0.04395488],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01508573,"threshold_uncertainty_score":0.05046678,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.016726087211784,"score_gpt":0.280398203943213,"score_spread":0.263672116731429,"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."}}