from research import *
s=begin(994,'An equal total can hide internal change','What is the vector defect when partial and uniform transformations share one total?',{'S':483,'selected_fraction':'1/6','selected_factor':'25/23'},['C993','File63 §1.3','C609 inherited example'])
S=F(483);f=F(1,6);k=E;r=1+f*(k-1);v=[(1-f)*S,f*S];partial=[v[0],k*v[1]];uniform=[r*x for x in v];defect=[a-b for a,b in zip(partial,uniform)]
finish(s,{'source_parts':v,'partial':partial,'uniform':uniform,'defect':defect,'general_selected_first_defect':'(k−1)f(1−f)S·(1,−1)'},'The inherited490 equality loses an internal displacement of35/6 in opposite directions. The general zero-sum defect explains why equal totals do not identify the same path.','Find a complete nonredundant measurement basis for retained-part families.',{'same_total':sum(partial)==sum(uniform)==490,'nonzero_shape':defect==[-F(35,6),F(35,6)],'criterion_fails':k!=1})