from research import *
s=begin(638,'Explain the Priestly minimum by factor structure','Why does subtracting the14-year rail width from13×182 produce14×168?',{'corresponding_count':13,'Enochian_half':182,'rail_width':14},['File70 §§6.2–6.5'])
T=13*182;minimum=T-14
finish(s,{'corresponding_factorization':[14,13**2],'minimum_factorization':[14,13**2-1],'Priestly_half':168,'identity':'13×182−14=14(169−1)=14×168'},'The Priestly minimum follows from182=14×13 and168=13²−1. The common14-year width turns the corresponding vector into fourteen Priestly halves. This explains the change from13 to14 calendar units through the rail geometry.','Test whether the combined half-calendar conditions select a unique count or a congruence family.',{'factorization':T==14*169,'minimum':minimum==2352==14*168,'difference_of_squares':168==12*14})