{"id":"W4411615336","doi":"10.1017/s0305004125000325","title":"On the $\\mathfrak{M}_H(G)$-property","year":2025,"lang":"en","type":"article","venue":"Mathematical Proceedings of the Cambridge Philosophical Society","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Property (philosophy); Combinatorics; Mathematics; Philosophy; Epistemology","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":[0.002165995,0.0005993036,0.0009078636,0.001644767,0.001853342,0.002802381,0.0008305447,0.000981465,0.007585514],"category_scores_gemma":[0.0071018,0.0002900253,0.0009326577,0.0009233214,0.005376331,0.005833768,0.003464668,0.002452816,0.000964953],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001151946,"about_ca_system_score_gemma":0.0005772267,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001044502,"about_ca_topic_score_gemma":0.0005551401,"domain_scores_codex":[0.9988905,0.0002209294,0.00004473606,0.0002862634,0.0001619331,0.0003956947],"domain_scores_gemma":[0.991994,0.004551127,0.0009155324,0.0009947445,0.0005394609,0.001005123],"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":[0.0008346414,0.00008844382,0.0097952,0.0001506688,0.00003226718,0.0004899435,0.0005484223,0.004862277,0.005107409,0.9630364,0.004091438,0.01096293],"study_design_scores_gemma":[0.0001401784,0.000252375,0.007551482,0.0001031725,0.00005275518,0.0007139812,0.0004640273,0.03557514,0.01561053,0.9316735,0.007775474,0.0000875039],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9054971,0.0006559032,0.0334502,0.002196133,0.0001089665,0.00004444361,0.0004894967,0.0003524503,0.05720537],"genre_scores_gemma":[0.9948658,0.0001279804,0.002566923,0.0001441506,0.0001149847,0.00002286352,0.0002243958,0.00004266184,0.00189023],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007585514,"threshold_uncertainty_score":0.02537608,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03320954308873525,"score_gpt":0.2729216330618708,"score_spread":0.2397120899731356,"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."}}