from research import *
s=begin(568,'Compare the dual490 constructions','Can subset E and whole-span P agree on the source483 partition?',{'parts':[F(805,2),F(161,2)],'total':483},['File62 §§8.6A–C; File63 §1.3'])
a,b=F(805,2),F(161,2);partial=a+E*b;wholeP=P*(a+b);wholeE=E*(a+b)
finish(s,{'partial_E':partial,'whole_P':wholeP,'whole_E':wholeE,'common_day_volume':[partial*360,wholeE*336]},'Expanding only80.5 by E and all483 by P both give490. Whole-span E gives525; the calendar volumes490×360 and525×336 agree. The duration identity needs no deferred endpoint.','Derive the general allocation identity that explains this agreement.',{'dual':partial==wholeP==490,'whole_E':wholeE==525,'volume':490*360==525*336})