{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005762461,0.0003066173,0.0003134978,0.0008726943,0.001391947,0.001375447,0.000479088,0.0006963892,0.004080935],"category_scores_gemma":[0.002166637,0.0002424459,0.0004530084,0.0005158067,0.002782329,0.002626571,0.001366927,0.0010151,0.0003816286],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009429856,"about_ca_system_score_gemma":0.0006329743,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001809273,"about_ca_topic_score_gemma":0.0008871611,"domain_scores_codex":[0.9994022,0.00008891731,0.00003233632,0.0001196971,0.0002028102,0.0001542113],"domain_scores_gemma":[0.9990404,0.0002848608,0.0002185851,0.0001903215,0.0001307049,0.0001351547],"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":[0.00004043962,0.00001519285,0.00112369,0.000022732,0.000005431948,0.0001528736,0.0003862306,0.00344174,0.00160219,0.9888411,0.0005213045,0.003847152],"study_design_scores_gemma":[0.00001074079,0.00003288295,0.001330309,0.0000163859,0.000004153111,0.000153509,0.0001437876,0.01137762,0.001321597,0.984004,0.001579809,0.00002522984],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9279581,0.0002366864,0.03310991,0.0007517223,0.0000413579,0.00002829461,0.0002558613,0.0001571924,0.03746093],"genre_scores_gemma":[0.9924447,0.00008974612,0.004563329,0.00008911117,0.0000366929,0.00001591132,0.00009774868,0.00002170742,0.002640945],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004080935,"threshold_uncertainty_score":0.01365203,"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."}}