{"id":"W4396723964","doi":"10.1007/s00209-024-03507-7","title":"Filtered deformations of commutative algebras of Krull dimension two","year":2024,"lang":"de","type":"article","venue":"Mathematische Zeitschrift","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Krull dimension; Global dimension; Commutative property; Pure mathematics; Dimension (graph theory); Commutative algebra; Dimension theory (algebra); Algebra over a field; Noetherian","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":[0.0008611505,0.0008341277,0.000892488,0.002309588,0.002388207,0.003437398,0.001038029,0.001083143,0.006222758],"category_scores_gemma":[0.001366086,0.0005258808,0.0008930464,0.001362833,0.00311627,0.005244025,0.002044335,0.001868472,0.0006336597],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001754673,"about_ca_system_score_gemma":0.0006372978,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001469162,"about_ca_topic_score_gemma":0.001374384,"domain_scores_codex":[0.9993823,0.0001210605,0.00003629421,0.0001198264,0.000164846,0.0001756503],"domain_scores_gemma":[0.9990882,0.000211671,0.0001817313,0.00011306,0.00009885921,0.0003065077],"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":[0.00007471744,0.00003241765,0.0002013068,0.00001426389,0.00001075244,0.0001349887,0.0003731827,0.0006451095,0.001701441,0.9950558,0.0003002714,0.001455795],"study_design_scores_gemma":[0.00002913887,0.00004211191,0.0007490287,0.000007740423,0.00001285064,0.0002241602,0.0002217683,0.002509774,0.0009217772,0.9933335,0.001917968,0.00003017529],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8991845,0.0007525867,0.03606486,0.001075944,0.0003226666,0.00003685303,0.000234467,0.0003023726,0.06202587],"genre_scores_gemma":[0.9813049,0.0002055067,0.003854134,0.0001595494,0.0002078579,0.00002266597,0.0001240514,0.00005426732,0.01406704],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006222758,"threshold_uncertainty_score":0.02081716,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02645203766645201,"score_gpt":0.3084575585273314,"score_spread":0.2820055208608794,"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."}}