{"id":"W4406279651","doi":"10.1002/mana.202400021","title":"Normal forms and Tyurin degenerations of K3 surfaces polarized by a rank 18 lattice","year":2025,"lang":"en","type":"article","venue":"Mathematische Nachrichten","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Engineering and Physical Sciences Research Council; Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Lattice (music); Rank (graph theory); Pure mathematics; Combinatorics; Physics","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009140653,0.0002363229,0.0005068754,0.0001610095,0.0001869586,0.00004928163,0.000254844,0.0001611004,0.0004022708],"category_scores_gemma":[0.0005795049,0.0001940454,0.00009932434,0.0004897047,0.0001041135,0.0002467426,0.000163752,0.0001976195,0.00002944458],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000185334,"about_ca_system_score_gemma":0.00005143403,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002432261,"about_ca_topic_score_gemma":0.000009432281,"domain_scores_codex":[0.9985255,0.0001172828,0.0005587722,0.0002601146,0.000249331,0.0002890095],"domain_scores_gemma":[0.9982094,0.0009864341,0.0002284884,0.0004015685,0.00009798473,0.00007613833],"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":[0.0001281795,0.0006252787,0.001780393,0.001514763,0.0005993643,0.000004398161,0.001952102,0.000002469515,0.04399187,0.9263363,0.0216119,0.001452966],"study_design_scores_gemma":[0.003850282,0.000135209,0.0008185109,0.0003766702,0.0006741547,0.00004873795,0.001340635,0.001430364,0.1100115,0.8765792,0.004058635,0.0006761102],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9178587,0.001901262,0.0369803,0.0004138288,0.00009206116,0.0005144061,0.00007547174,0.0001307386,0.04203325],"genre_scores_gemma":[0.9642054,0.00004484506,0.02472997,0.000109012,0.00002331154,0.00004270496,0.0000180188,0.0000286941,0.01079805],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06601961,"threshold_uncertainty_score":0.7912942,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01939180826590033,"score_gpt":0.2847433838911054,"score_spread":0.2653515756252051,"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."}}