from research import *
s=begin(688,'Explain the two completed volume registers','What operation distinguishes12600 from12740 at the same35 count?',{'count':35,'calendar_lengths':[360,364],'root_volume':12558},['Supplement A §6'])
a,b=35*360,35*364; common=[a*364,b*360]
finish(s,{'volumes':[a,b],'difference':b-a,'calendar_ratio':F(b,a),'cross_products':common,'root_outputs':[J*12558,P*12558]},'The12600/12740 pair uses the same completed count35 with360/364 calendar lengths. Their ratio91/90 and shared cross-product follow from this construction; the product is a register equality, not an additional chronology or independent witness.','Account for the PhaseNorm40 volume and its residual relative to12600.',{'outputs':[a,b]==[J*12558,P*12558]==[12600,12740],'difference':b-a==35*4==140,'cross_products':common==[4586400]*2})