from research import *
s=begin(633,'Generate the corresponding Creation–Joseph rail map','Do the two source seven-plus-seven rails require more than one translation?',{'Creation':[4251,4244,4237],'Joseph':[1885,1878,1871]},['File70 §6.3'])
a=[4251,4244,4237];b=[1885,1878,1871];v=[x-y for x,y in zip(a,b)]
finish(s,{'corresponding_spans':v,'rail_gaps':[[a[i]-a[i+1] for i in range(2)],[b[i]-b[i+1] for i in range(2)]],'translation':2366},'One translation of2366 carries all three source nodes and preserves the7+7 partition. The three matches are dependent coordinates of one rigid relation.','Generate every cross-rail span to distinguish the special diagonals from the whole family.',{'translation':v==[2366]*3,'shape':[a[i]-a[i+1] for i in range(2)]==[7,7]==[b[i]-b[i+1] for i in range(2)]})