from research import *
s=begin(844,'Derive the equal-marginal constraint','What exactly must be true for purity and sex totals to coincide?',{},['C843'])
a,b,c,d=440,50,50,10
family={'clean_minus_female':b-c,'unclean_minus_male':c-b,'fixed_margin_family':'[[490−t,t],[t,60−t]], 0≤t≤60','source_t':50,'constraint_count':1,'independence_determinant':a*d-b*c}
finish(s,family,'The double490/60 display imposes one cross-category balance, b=c. Given those margins, one cell parameter remains; the source selects50. Distinct category definitions and equal marginals do not establish statistical independence.','Recover the exact rank of the nine-row measurement map.',{'equal_marginals':b==c,'source_family':[[490-50,50],[50,60-50]]==[[a,b],[c,d]],'not_product_table':a*d!=b*c})