s1010.py

from research import *
s=begin(1010,'Grand total closes one missing category','Which count remains invisible without the total550?',{},['C1009'])
from algebra import Matrix
p=json.loads((ROOT/'model/esau_joint_measurements.json').read_text());M=Matrix(p['matrix'][:-1]);ns=[list(v) for v in M.nullspace()]
finish(s,{'rank_without_total':M.rank(),'kernel':ns,'missing_category':'male donkeys'},'Without the total, only male donkeys remain unmeasured. The total contributes one independent condition, rather than changing the other eight reconstructed counts.','Choose a square measurement basis and inspect whether it hides fractional reconstruction.',{'rank_eight':M.rank()==8,'one_category_kernel':ns==[[0,0,0,0,0,0,0,0,1]]})