from research import *
s=begin(653,'Separate Jacob’s two symmetric objects','How do the biographical and death-centered patterns connect?',{'biography':[2006,1936,1929,1859],'death_centered':[1936,1929,1859,1789,1782]},['File70 §5.3; A.5'])
a=[2006,1936,1929,1859]; midpoint=F(a[0]+a[-1],2); gaps=[a[i]-a[i+1] for i in range(3)]
finish(s,{'biography_gaps':gaps,'biography_center':midpoint,'reflection':[2*midpoint-x for x in a],'centers_separation':midpoint-1859},'Jacob’s lifespan path is a different symmetric object:70|7|70 around1932.5, while the later reflection is centered at his death1859. They share sourced nodes1936/1929/1859 but cannot be collapsed into one center.','Test the30/40 subdivision family to see what its junction equality depends on.',{'gaps':gaps==[70,7,70],'symmetry':[2*midpoint-x for x in a]==list(reversed(a)),'total':sum(gaps)==147})