from research import *
s=begin(681,'Complete the conserved-center2940 corridor','What invariant joins all three source-selected outer endpoint pairs?',{'pairs':[[4326,1416],[4336,1406],[4341,1401]],'final_outward_displacement':5,'source_local_components':[2,3]},['Supplement A §5.1'])
pairs=[[4326,1416],[4336,1406],[4341,1401]]; sums=[sum(x) for x in pairs]; widths=[a-b for a,b in pairs]
finish(s,{'endpoint_sums':sums,'centers':[F(x,2) for x in sums],'widths':widths,'width_increments':[widths[i+1]-widths[i] for i in range(2)]},'Opposed endpoint changes preserve U+L=5742 while widening2910→2930→2940. The final five-year displacement is the source’s local2+3 construction; it supplies generated extremities4341/1401, not new canonical Creation/Conquest anchors or upstream Gear permission.','Express translation and symmetric opening in center/width coordinates.',{'conservation':sums==[5742]*3,'widths':widths==[2910,2930,2940],'increments':[widths[i+1]-widths[i] for i in range(2)]==[20,10]})