{"id":"W2104191500","doi":"10.1007/s11786-014-0186-9","title":"The 3 ×  3 ×  3 Hyperdeterminant as a Polynomial in the Fundamental Invariants for $${{SL_3(\\mathbb{C}) \\times SL_3(\\mathbb{C}) \\times SL_3(\\mathbb{C})}}$$ S L 3 ( C ) × S L 3 ( C ) × S L 3 ( C )","year":2014,"lang":"en","type":"article","venue":"Mathematics in Computer Science","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"Simon Fraser University; University of Saskatchewan","funders":"","keywords":"Invariant theory; Invariant (physics); Polynomial; Algebra over a field; Action (physics); Alternating polynomial; Invariant polynomial; Group theory","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":[0.000967685,0.0009686148,0.0005671105,0.003129902,0.001825894,0.00305457,0.001426922,0.001842137,0.01035679],"category_scores_gemma":[0.001927512,0.0004967954,0.001078359,0.001211958,0.00400392,0.003654477,0.001723216,0.002609267,0.001061675],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002032924,"about_ca_system_score_gemma":0.001313955,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001817397,"about_ca_topic_score_gemma":0.002044701,"domain_scores_codex":[0.9991527,0.0001525143,0.00002772055,0.0001776417,0.0002152036,0.000274204],"domain_scores_gemma":[0.9988865,0.0003008705,0.0002197459,0.0001040285,0.0001383532,0.0003504968],"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":[0.00008558988,0.00005072634,0.0003013948,0.0000213859,0.000007262419,0.0001726003,0.0003208423,0.0009513272,0.003891113,0.9857653,0.001333173,0.007099157],"study_design_scores_gemma":[0.00004279715,0.00007014487,0.001768472,0.00002226211,0.00001791262,0.0004036936,0.0001827732,0.01990808,0.003705213,0.9689738,0.004807341,0.00009746521],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8524008,0.0003482726,0.07513252,0.002309277,0.0007793486,0.00007512272,0.0003547143,0.0006288125,0.0679711],"genre_scores_gemma":[0.9805813,0.0001671868,0.007043435,0.0003301681,0.000349499,0.00003654514,0.0001563959,0.0003254578,0.01100988],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01035679,"threshold_uncertainty_score":0.03464687,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05852512899978808,"score_gpt":0.3559044107329234,"score_spread":0.2973792817331353,"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."}}