{"id":"W4415692432","doi":"10.4153/s0008439525101331","title":"A division algorithm for the Gaussian integers’ minimal Euclidean function","year":2025,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University of Cambridge","keywords":"Euclidean domain; Euclidean geometry; Euclidean algorithm; Euclidean distance; Euclidean shortest path; Non-Euclidean geometry; Division (mathematics); Euclidean distance matrix","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0003729694,0.0001241456,0.0001402749,0.0001329113,0.0003097502,0.0002121726,0.0005500044,0.00006297342,0.0003658249],"category_scores_gemma":[0.0001978849,0.00008753105,0.00009893197,0.0002536831,0.00005784686,0.00005122436,0.00008420907,0.0001161516,0.0008308928],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001016679,"about_ca_system_score_gemma":0.0002168342,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004313523,"about_ca_topic_score_gemma":0.0003063818,"domain_scores_codex":[0.999009,0.00003582206,0.000234277,0.0002684454,0.0001195744,0.0003328471],"domain_scores_gemma":[0.9987574,0.0006244353,0.00004200514,0.0003186152,0.0000544572,0.0002030811],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00000267435,0.00001829821,0.000002839695,0.00001826484,0.00002188883,0.000003157327,0.0001610927,0.000008477834,0.00001237802,0.3389975,0.04200662,0.6187468],"study_design_scores_gemma":[0.0003839128,0.00008887401,0.0007922548,0.0001011728,0.00002180328,0.000006314734,0.000104325,0.4369807,0.00007634872,0.2115823,0.3496678,0.000194188],"study_design_candidate":"design_other","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0005183453,0.00008351679,0.9584302,0.03509469,0.0004116002,0.0003569816,0.00000600348,0.0000639716,0.005034662],"genre_scores_gemma":[0.8679941,0.000005008965,0.112571,0.009974089,0.0002748336,0.0002269867,0.00001331653,0.00002366539,0.008916992],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8674757,"threshold_uncertainty_score":0.9999471,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009926549685176879,"score_gpt":0.2278070699930849,"score_spread":0.217880520307908,"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."}}