from research import *
s=begin(689,'Explain the normalized13440 register','What added quantity separates PhaseNorm40 from the calibrated micro completion?',{'E_count':F(75,2),'normalized_count':40,'Priestly_calendar':336},['Supplement A §§4.3,6'])
base=F(75,2)*336; completed=40*336; residual=(40-F(75,2))*336
finish(s,{'calibrated_volume':base,'normalized_volume':completed,'residual_volume':residual,'identity':'40×336 = E(34.5)×336 + 2.5×336'},'The normalized13440 body adds exactly840 to12600, because the source’s2.5 residual is measured in336-day units. This explains the extra completion without assigning it to a new event or applying another Key.','Compare these scalar registers with the source’s retained2940 cumulative partition.',{'volumes':[base,completed,residual]==[12600,13440,840],'additivity':base+residual==completed,'residual_count':40-F(75,2)==F(5,2)})