{"id":"W3093667119","doi":"10.4153/s0008439520000855","title":"Relations between modular invariants of a vector and a covector in dimension two","year":2020,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Modular design; Invariant (physics); Dimension (graph theory); Pure mathematics; Algebra over a field; Computer science","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0004365189,0.0001497697,0.0004126744,0.0001285906,0.00005366174,0.00001480005,0.0001353689,0.0001098097,0.00496578],"category_scores_gemma":[0.002553649,0.0001444153,0.00004561126,0.0002598031,0.0001046583,0.00003185146,0.00005117946,0.000217884,0.0009770546],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005652098,"about_ca_system_score_gemma":0.0001085172,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004350234,"about_ca_topic_score_gemma":0.0002626013,"domain_scores_codex":[0.9987631,0.0001251031,0.0004377854,0.0002301415,0.0001598363,0.0002840239],"domain_scores_gemma":[0.9981868,0.0009579251,0.00008891484,0.0002026369,0.00003577938,0.0005279183],"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":[0.00004061156,0.0001113084,0.009643965,0.000792923,0.0001003672,0.0001066974,0.005237435,0.000009523152,0.0009190656,0.9769055,0.005776018,0.000356553],"study_design_scores_gemma":[0.001859491,0.0001677543,0.01052383,0.0004613542,0.000107911,0.00002217134,0.0006229017,0.000793687,0.001088199,0.9798043,0.00403071,0.0005177085],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9844853,0.0000602179,0.003855968,0.007432201,0.00001721942,0.0003713446,0.00005028643,0.0000305996,0.003696857],"genre_scores_gemma":[0.9942615,0.000001101359,0.005137169,0.0003452735,0.00004507577,0.00001149553,0.000005762535,0.00002572394,0.0001668778],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009776215,"threshold_uncertainty_score":0.9998008,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03462910609405485,"score_gpt":0.2582360379985734,"score_spread":0.2236069319045186,"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."}}