{"id":"W4414581253","doi":"10.61091/jcmcc127-19","title":"Integer partitions of zero and compositional structures in finite groups","year":2025,"lang":"en","type":"article","venue":"Journal of Combinatorial Mathematics and Combinatorial Computing","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Enumeration; Partition (number theory); Integer (computer science); Type (biology); Zero (linguistics); Algebraic number; Value (mathematics)","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002171609,0.0002392557,0.0008707405,0.0005497884,0.0001567294,0.0001065806,0.0003193544,0.0001724702,0.00001253644],"category_scores_gemma":[0.001849342,0.0002151771,0.0001307685,0.0004813897,0.0002478098,0.0001627507,0.0003087983,0.0006414306,3.824818e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007537317,"about_ca_system_score_gemma":0.0001454634,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000658453,"about_ca_topic_score_gemma":0.000001055199,"domain_scores_codex":[0.9973485,0.0002328348,0.001399987,0.0001849125,0.0005464445,0.000287351],"domain_scores_gemma":[0.9938605,0.004541441,0.0007444807,0.0002157478,0.0005257198,0.0001120796],"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":[0.0001747476,0.0005410121,0.0007579076,0.0005613563,0.0001099449,0.00001521995,0.0009971812,0.000028447,0.0007219836,0.9955744,0.0001986314,0.0003192408],"study_design_scores_gemma":[0.003704516,0.0003694083,0.0005340972,0.0008777063,0.00007466339,0.00004144157,0.0003902668,0.001744693,0.0009580286,0.9910851,0.00005822273,0.0001619241],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9853563,0.0002786939,0.009560307,0.0001687591,0.003034197,0.0002844461,0.000006864693,0.00001612021,0.001294301],"genre_scores_gemma":[0.9924962,0.00002990539,0.00721192,0.00001674733,0.0002127597,0.000002446768,0.000001504961,0.00002117285,0.000007342909],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00713989,"threshold_uncertainty_score":0.8774667,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02657844331968861,"score_gpt":0.3173679497274808,"score_spread":0.2907895064077922,"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."}}