{"id":"W2057305711","doi":"10.4153/cjm-2009-046-2","title":"The Face Semigroup Algebra of a Hyperplane Arrangement","year":2009,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":74,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Mathematics; Hyperplane; Cellular algebra; Algebra over a field; Filtered algebra; Cohomology; Pure mathematics; Algebra representation; Combinatorics","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":[0.0005910494,0.0001478896,0.0003603622,0.00009472458,0.0001485985,0.00005286462,0.0005060247,0.00007722728,0.00005098648],"category_scores_gemma":[0.0004950918,0.0000951676,0.0001566305,0.0001317759,0.00007682217,0.00006392892,0.000009548225,0.0002103783,0.000003032594],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008294127,"about_ca_system_score_gemma":0.0003674681,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007583325,"about_ca_topic_score_gemma":0.0006891869,"domain_scores_codex":[0.9985883,0.00003613698,0.0006833658,0.00007130104,0.0003364676,0.0002844445],"domain_scores_gemma":[0.9982246,0.0003619685,0.0005871663,0.0003283675,0.0002007277,0.0002971412],"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":[0.00001041626,0.00005320268,0.00005719589,0.00007253893,0.0001227067,0.00003633447,0.00441822,0.00002573982,0.0001439711,0.9821118,0.01002479,0.002923127],"study_design_scores_gemma":[0.0003723608,0.0002119286,0.0001222623,0.0001531087,0.00008530894,0.0001726719,0.002250756,0.00009146554,0.0006074316,0.9926852,0.003128766,0.0001187631],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9902105,0.001244999,0.00330049,0.001586502,0.000736892,0.0002410094,0.000008358143,0.000009115537,0.002662134],"genre_scores_gemma":[0.9949422,0.00003558441,0.004543058,0.00009301315,0.0001586244,9.254271e-7,3.568327e-7,0.0000157001,0.0002104695],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01057342,"threshold_uncertainty_score":0.3880822,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02311424620319197,"score_gpt":0.2567048004703096,"score_spread":0.2335905542671177,"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."}}