{"id":"W2912554709","doi":"10.4171/jems/1108","title":"Sums of squares and quadratic persistence on real projective varieties","year":2021,"lang":"en","type":"preprint","venue":"Journal of the European Mathematical Society","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Subvariety; Invariant (physics); Projective test; Quadratic equation; Homogeneous; Projective space; Combinatorics; Variety (cybernetics); Homogeneous coordinates; Pencil (optics); Integer (computer science); Pure mathematics; Discrete mathematics; Geometry; Computer science","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000654856,0.0008120871,0.0005507497,0.002178313,0.0008166743,0.00204323,0.000750786,0.0003214638,0.003645041],"category_scores_gemma":[0.00341668,0.0002896523,0.0004214602,0.001415521,0.003971157,0.004032457,0.002975546,0.001865247,0.0004518968],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007119512,"about_ca_system_score_gemma":0.0002559527,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002750648,"about_ca_topic_score_gemma":0.0002003565,"domain_scores_codex":[0.9993184,0.0001107248,0.00003816016,0.0001940861,0.0002201829,0.0001185501],"domain_scores_gemma":[0.997573,0.001041588,0.0006256358,0.0002400293,0.0001265265,0.0003932922],"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":[0.0003352626,0.00007905141,0.007841809,0.0002083265,0.00004555044,0.0003676884,0.0006328079,0.01276892,0.01168938,0.923684,0.001635834,0.04071138],"study_design_scores_gemma":[0.00003569319,0.0002026966,0.005246198,0.00003624293,0.00003847047,0.0005357104,0.0002482617,0.03969479,0.01001361,0.9390989,0.004791082,0.00005834557],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9081033,0.001042656,0.07069051,0.0005868292,0.00006645307,0.00002178251,0.0001617384,0.0001952822,0.01913135],"genre_scores_gemma":[0.9915558,0.0003097567,0.005369831,0.0000251644,0.0001255942,0.00002153154,0.0001350174,0.00003913909,0.002418028],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003645041,"threshold_uncertainty_score":0.01219386,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02895796854314601,"score_gpt":0.2443786010166939,"score_spread":0.2154206324735479,"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."}}