{"id":"W2171365210","doi":"10.1112/plms/pdq038","title":"A positive Monk formula in the <i>S</i> <sup>1</sup>-equivariant cohomology of type <i>A</i> Peterson varieties","year":2011,"lang":"en","type":"article","venue":"Proceedings of the London Mathematical Society","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":32,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"","keywords":"Schubert calculus; Cohomology ring; Cohomology; Flag (linear algebra); Schubert variety; Quantum cohomology; Schubert polynomial; Type (biology); Generalized flag variety; Class (philosophy)","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":[0.001559189,0.0003646742,0.0008475314,0.00004312977,0.0001297664,0.00002670682,0.001322364,0.0002710914,0.00005115894],"category_scores_gemma":[0.001766988,0.0002148824,0.000481071,0.0006687616,0.0005892871,0.0002430163,0.0004494155,0.0005438545,0.000007834384],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008319248,"about_ca_system_score_gemma":0.00005158162,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001590828,"about_ca_topic_score_gemma":5.65728e-7,"domain_scores_codex":[0.9973561,0.00004433805,0.001027121,0.0003160264,0.0007453365,0.0005111379],"domain_scores_gemma":[0.9969055,0.001337298,0.000782506,0.0004437005,0.0004647884,0.00006617966],"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":[0.0001007914,0.0008412745,0.000277119,0.001401908,0.0001235268,0.000001153527,0.05314445,0.000003170335,0.002420052,0.9401988,0.001454378,0.00003340686],"study_design_scores_gemma":[0.0007453878,0.0002713431,0.00007334659,0.0003417381,0.0001963884,0.00005004387,0.006328079,0.001738329,0.01925007,0.9707501,0.00003172002,0.0002234625],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.970812,0.00009615851,0.002948847,0.0006423543,0.0001338921,0.001981419,0.00001933149,0.00009733695,0.02326861],"genre_scores_gemma":[0.9402651,0.00002637796,0.05912426,0.0002172227,0.00006015821,0.00007410728,7.849838e-7,0.00006061484,0.0001713877],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05617541,"threshold_uncertainty_score":0.876265,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0376142608029878,"score_gpt":0.2683737033294723,"score_spread":0.2307594425264845,"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."}}