from research import *
s=begin(939,'Classify the regular total without choosing its split','What follows from2700 and two three-digit nonzero-ended cores alone?',{'scaled_total':270,'H_range':[2,18],'T_range':[0,18],'U_range':[2,18]},['C938 fixed register'])
poss=[(H,T,U) for H in range(2,19) for T in range(19) for U in range(2,19) if 100*H+10*T+U==270]
proof=['last digit forces U=10 within2..18','10H+T=26','H>=2 and0<=T<=18 force H2,T6']
a=artifact('model/regular_total_register_theorem.json',json.dumps({'aggregate_solutions':poss,'proof':proof,'reversed_total':10620,'scope':'diagnostic register class, not additional chronology partitions'},indent=2)+'\n')
finish(s,{'aggregate_solutions':poss,'theorem':a},'The regular total2700 forces aggregate digits(2,6,10) throughout the specified two-component register class, hence transformed total10620. The source Flood breakpoint is not needed to determine this outer total, although it still determines the internal path.','Classify the cumulative12600 total on the same declared register class.',{'unique':poss==[(2,6,10)],'outer':10*(2+10*6+100*10)==10620})