{"id":"W1861085200","doi":"10.1090/s0025-5718-2013-02706-8","title":"Fundamental invariants for the action of $SL_3(\\mathbb {C}) \\times SL_3(\\mathbb {C}) \\times SL_3(\\mathbb {C})$ on $3 \\times 3 \\times 3$ arrays","year":2013,"lang":"en","type":"article","venue":"Mathematics of Computation","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University; University of Saskatchewan","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Monomial; Combinatorics; Lie algebra; Homogeneous; Action (physics); Lie group; Group (periodic table); Algebra over a field; Pure mathematics; Physics","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":[0.0002746573,0.000611248,0.0003207533,0.001450945,0.001067208,0.001405531,0.0007771908,0.0006132922,0.01053527],"category_scores_gemma":[0.0003935392,0.0001858113,0.0009486543,0.0005507904,0.002341077,0.001450161,0.0009572402,0.001197846,0.00173815],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001528161,"about_ca_system_score_gemma":0.0009861238,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00195257,"about_ca_topic_score_gemma":0.002374584,"domain_scores_codex":[0.9997576,0.00001737119,0.000007518387,0.00003559208,0.00006441734,0.0001174625],"domain_scores_gemma":[0.9998336,0.00002436626,0.00005437415,0.00002107819,0.00002231751,0.00004425919],"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":[0.00004473996,0.00006445836,0.0003786398,0.00002240497,0.000005510627,0.00008417288,0.0004316609,0.003122044,0.007811484,0.9753729,0.001333213,0.01132877],"study_design_scores_gemma":[0.00002647277,0.0001071436,0.001321832,0.00002311684,0.00001318869,0.0001362974,0.0003617771,0.02110631,0.01310482,0.9538233,0.009903896,0.00007186862],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8307453,0.0002457558,0.07534881,0.0006123717,0.000353017,0.00007139254,0.0003677594,0.0004232447,0.09183229],"genre_scores_gemma":[0.968839,0.0002229721,0.01282139,0.0001685508,0.0001976748,0.00006783494,0.0003609793,0.000256709,0.0170649],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01053527,"threshold_uncertainty_score":0.03524399,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05942020334877784,"score_gpt":0.3388176848776243,"score_spread":0.2793974815288464,"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."}}