from research import *
s=begin(697,'Derive directional convergence from the Key gap','What source offset makes the paired anchored outputs equal?',{'span':690,'held_forward':[3626,3576],'held_reverse':[2216,2166]},['C696; Supplement A §8'])
gap=(E-P)*690; forward_difference=(3626-3576)-(E-P)*690; reverse_difference=(2216-2166)+(P-E)*690
finish(s,{'Key_output_gap':gap,'forward_residual':forward_difference,'reverse_residual':reverse_difference,'individual_gains':[(P-1)*690,(E-1)*690]},'The50 source offset equals(E−P)×690. With the declared direction and assignment, that one equality forces both convergences. The four outputs are structured consequences of the offset and operators, not four independent confirmations.','Recover the complete70-wide quartet and its supplied1470 translation.',{'gap':gap==50,'residuals':forward_difference==reverse_difference==0,'gains':[(P-1)*690,(E-1)*690]==[10,60]})