{"id":"W2100462162","doi":"10.1007/s13348-014-0117-8","title":"Expressing a general form as a sum of determinants","year":2014,"lang":"en","type":"article","venue":"Collectanea mathematica","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Integer (computer science); Combinatorics; Homogeneous; TRACE (psycholinguistics); Matrix (chemical analysis); Integer matrix; Symmetric matrix; Nonnegative matrix; Physics; Eigenvalues and eigenvectors","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":[0.0008395075,0.0002420669,0.0006365625,0.0001586744,0.000170805,0.00003908075,0.0003667556,0.0001316841,0.0007728838],"category_scores_gemma":[0.002240518,0.0002052066,0.0001696606,0.0003950762,0.0001349502,0.0001221668,0.0001249683,0.0001258069,0.0001183694],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003537917,"about_ca_system_score_gemma":0.00006557239,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003989608,"about_ca_topic_score_gemma":0.000002522938,"domain_scores_codex":[0.9982247,0.0001170589,0.0006434189,0.0002583065,0.0003633864,0.000393151],"domain_scores_gemma":[0.9975184,0.001276923,0.0003450187,0.0006437283,0.00009572859,0.0001202206],"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":[0.0002272794,0.0009661986,0.000290023,0.002955171,0.000186851,0.00003869118,0.009708185,0.00000127571,0.02049335,0.9518992,0.007397184,0.005836583],"study_design_scores_gemma":[0.000597039,0.000166196,0.00002595251,0.0003005674,0.00007794926,0.0001702181,0.0002466097,0.002512539,0.05943706,0.9356233,0.0005817515,0.0002608116],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.900748,0.00003116565,0.00838949,0.00003762933,0.0001008536,0.0003304602,0.000003962794,0.0001007545,0.09025776],"genre_scores_gemma":[0.9584946,0.000002911789,0.03230055,0.00005725091,0.0000898744,0.00004695586,0.000001111795,0.00005147022,0.008955305],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08130245,"threshold_uncertainty_score":0.8462535,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02723705845136283,"score_gpt":0.293880774122303,"score_spread":0.2666437156709402,"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."}}