{"id":"W4405029179","doi":"10.48550/arxiv.2411.15449","title":"A Representation theoretic perspective of Koszul theory","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Philosophy, Science, and History","field":"Arts and Humanities","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Perspective (graphical); Representation (politics); Representation theory; Mathematics; Mathematical economics; Epistemology; Computer science; Algebra over a field; Sociology; Pure mathematics; Political science; Artificial intelligence; Philosophy","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001324491,0.0004870205,0.0006071939,0.001853872,0.001774517,0.004182159,0.001258958,0.001435995,0.006583681],"category_scores_gemma":[0.001306874,0.0002707134,0.0009383713,0.001208424,0.008337122,0.009915191,0.00222277,0.003366841,0.0007851211],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002678271,"about_ca_system_score_gemma":0.0008287904,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001237191,"about_ca_topic_score_gemma":0.0007504208,"domain_scores_codex":[0.9990116,0.000394212,0.00003393828,0.000183296,0.0002048306,0.0001720213],"domain_scores_gemma":[0.9992711,0.000282478,0.00008332937,0.000130416,0.0001369053,0.00009570456],"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":[0.000001085389,0.000002430912,0.00001921847,0.00000595634,8.571345e-7,0.0000125559,0.0001245323,0.00007892754,0.0000912134,0.9989328,0.0001467497,0.000583803],"study_design_scores_gemma":[0.000002980592,0.000005526673,0.00004389252,0.000008882549,0.000001326085,0.00003940835,0.0000768855,0.0008254097,0.00008801275,0.9928864,0.006018049,0.000003227451],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.1454821,0.01264023,0.3729095,0.02633747,0.0008602331,0.00005327718,0.0004060242,0.0003899171,0.4409212],"genre_scores_gemma":[0.922895,0.003053242,0.04345624,0.001731391,0.001248533,0.0000924678,0.0002394005,0.0001114661,0.02717235],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006583681,"threshold_uncertainty_score":0.02202463,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08222381701074488,"score_gpt":0.2005619431331845,"score_spread":0.1183381261224396,"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."}}