{"id":"W3099338996","doi":"","title":"3 Linear Dependencies in Weyl-Heisenberg Orbits","year":2016,"lang":"en","type":"article","venue":"","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":20,"is_retracted":false,"has_abstract":true,"ca_institutions":"Perimeter Institute","funders":"","keywords":"Mathematics; Algebraic number; Eigenvalues and eigenvectors; Dimension (graph theory); Pure mathematics; Unitary state; Vector space; Clifford algebra; Subspace topology; Matrix (chemical analysis); Linear map; Algebra over a field; Mathematical analysis; Quantum mechanics; Physics","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":[0.0001275421,0.0000979082,0.0001472427,0.00009662681,0.00002266196,0.000005071214,0.0001164896,0.00006098357,0.0009039197],"category_scores_gemma":[0.0004955849,0.00005555877,0.00003839445,0.0001896174,0.00002872502,0.0001478375,0.00005767637,0.00006072661,0.000448595],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002782719,"about_ca_system_score_gemma":0.00001847807,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002916749,"about_ca_topic_score_gemma":0.0001573497,"domain_scores_codex":[0.9992661,0.00001684002,0.0001897513,0.0001598736,0.0001424444,0.0002249699],"domain_scores_gemma":[0.9992434,0.0004075606,0.00003679165,0.0002278715,0.00003232012,0.00005200397],"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":[0.0000355523,0.0002353981,0.02135796,0.0000742649,0.00002841828,0.00006864628,0.0002840609,0.000004007957,0.01094568,0.9223009,0.005287826,0.03937732],"study_design_scores_gemma":[0.0008812012,0.00004215969,0.002063117,0.00008734121,0.000006746997,0.00001385169,0.0001744289,0.00003775506,0.03333943,0.9557709,0.007322148,0.0002609399],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9407716,0.00005812413,0.03119555,0.0008213622,0.0001311549,0.0001730961,0.000003823267,0.0001537493,0.02669149],"genre_scores_gemma":[0.9551529,0.00002769698,0.01638474,0.0001244436,0.00008263929,0.00001425206,3.682843e-7,0.00001845126,0.02819451],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03911638,"threshold_uncertainty_score":0.9897287,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04965882848669682,"score_gpt":0.3323070756844216,"score_spread":0.2826482471977248,"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."}}