s1190.py

from research import *
s=begin(1190,'Specify the joint Rounded-row observation','What exact data remain after begetting and remaining years are rounded separately?',{'Q':'nearest multiple of5 on integer nonnegative durations'},['C1189','File51a','File52c_latest.md','C1131 inherited rounding analysis'])
def Q(x):return 5*((x+2)//5)
cells={str(q):[x for x in range(max(0,q-3),q+4) if Q(x)==q] for q in [0,5,10]}
a=artifact('model/joint_rounding_observation.json',json.dumps({'observed':['B=Q(b)','R=Q(r)','exact L=b+r'],'hidden':['u=b-B','v=r-R'],'bounds':'u,v in {-2,-1,0,1,2}, plus b,r>=0','constraint':'u+v=L-B-R','zero_cell_truncation':cells,'independence':'This is a conditional observation problem; current R values calculated from source rows are not new independent testimony.'},indent=2)+'\n')
finish(s,{'observation':a,'cells':cells},'Joint Rounded observations restrict two hidden residuals to a bounded line u+v=L−B−R. Nonnegative durations truncate the cell at zero; current derived remainders do not supply independent evidence.','Derive and verify the exact size of that bounded line for interior cells.',{'zero_cell':cells['0']==[0,1,2],'interior_cell':cells['5']==[3,4,5,6,7]})