from research import *
s=begin(642,'Reconstruct the no-Cainan companion','Which relations survive when the Creation rail alone moves130?',{'standard_Creation':[4121,4114,4107],'Joseph':[1885,1878,1871],'standard_exposure':4108},['File70 §§6.1,6.6'])
T=4121-1885;v=[T-26,T-14,T,T+14];counts=[F(v[0],180),F(v[1],168),F(T,182)]
finish(s,{'span_family':v,'corresponding_spans':[4121-1885,4114-1878,4107-1871],'calendar_half_counts':counts,'shift_from_restored':130},'Removing130 preserves both7+7 rails and all their relative diagonals, giving2236 as the corresponding translation. It changes the calendar counts to nonintegers, so the restored state’s13/14/13 specialization is not automatic from rail shape alone.','Ask whether the fixed standard state and three-calendar conditions select130 as the least nonnegative correction.',{'companion':T==2236 and v==[2210,2222,2236,2250],'shape':4121-1885==4114-1878==4107-1871,'counts_changed':all(x.denominator!=1 for x in counts)})