from research import *
s=begin(508,'SP equal-gain rectangle','Can the calendar grammar reconstruct the Strategy’s separately declared SP rectangle?',{'Strategy_ReportIV_comparison_heads':[4206,13406],'Exodus':1446,'Conquest':1406,'state_note':'historical Strategy SP−215 rectangle; not the File18 completion pair used in C483'},['Strategy §4.3'])
x,y=4206-1446,13406-1446
finish(s,{'input_radii':[x,y],'P_and_J_outputs':[P*x,J*y],'gains':[P*x-x,J*y-y],'preserved_difference':[y-x,J*y-P*x],'E_difference':E*(y-x),'general_rule':'69m ->70m and299m ->300m; common gain m and preserved separation230m'},
 'At m=40, two distinct Keys add the same40, preserving9200 while terminating at the shared1406 target with the two heads held. This is a reusable equal-gain construction, separate from the newer File18 completion comparison.',
 'Derive how anchor changes affect otherwise identical expansions, needed to relate the14726 family’s two presentations.',{'radii':[x,y]==[2760,11960],'gain':P*x-x==J*y-y==40,'difference':y-x==J*y-P*x==9200,'E':E*(y-x)==10000})