{"id":"W2401643816","doi":"10.5539/jmr.v8n3p112","title":"Products of Admissible Monomials in the Polynomial Algebra as a Module over the Steenrod Algebra","year":2016,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Monomial; Combinatorics; Quotient; Degree (music); Polynomial; Vector space; Steenrod algebra; Basis (linear algebra); Algebra over a field; Pure mathematics; Geometry; Physics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.01434562,0.0003038862,0.000894826,0.0005297947,0.0001783147,0.0001135036,0.002287429,0.0001767908,0.0001806063],"category_scores_gemma":[0.02130278,0.0001352273,0.0002569738,0.0009715668,0.0004271861,0.0004205447,0.0003799039,0.0009377027,0.00005145256],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002574594,"about_ca_system_score_gemma":0.0007230609,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001499132,"about_ca_topic_score_gemma":0.000009363263,"domain_scores_codex":[0.9933372,0.0009725431,0.002009475,0.000266695,0.002684998,0.0007291174],"domain_scores_gemma":[0.9851152,0.0107719,0.001379408,0.001448525,0.001131388,0.0001535702],"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":[0.0004326308,0.00431671,0.0002674165,0.001809916,0.0003870535,0.0001385206,0.01727664,0.00001908738,0.03513265,0.8932281,0.04328304,0.003708259],"study_design_scores_gemma":[0.001843396,0.0005806796,0.0001528023,0.000913949,0.00005698139,0.0002217795,0.002758419,0.0001123047,0.02983729,0.9617893,0.001541457,0.0001916221],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9892889,0.0003061341,0.001529027,0.005024255,0.0003428924,0.00125627,0.000008529314,0.0000158942,0.002228084],"genre_scores_gemma":[0.978853,0.000181117,0.01917315,0.00004186123,0.0006174825,0.00005158064,2.098968e-7,0.0000894979,0.0009921358],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06856124,"threshold_uncertainty_score":0.9869412,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1342022592218145,"score_gpt":0.4225922846954431,"score_spread":0.2883900254736286,"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."}}