from research import *
s=begin(1040,'Primitive common-Key landing condition','Which relation among source paths makes the two expanded points agree?',{},['File60 common1566 comparison','C1032','C1039'])
from covenant_model import *
v={k:F(x) for k,x in json.loads((ROOT/'model/covenant_source_inputs.json').read_text()).items()};r=regular(v);u=v['Q']-r['Levi_death'];w=v['Q']-r['Joseph_death'];res=13*w-12*u;pointJ=v['Q']-J*u;pointE=v['Q']-E*w
finish(s,{'generated_radii':[u,w],'primitive_residual':res,'generated_points':[pointJ,pointE],'difference_formula':'pointE−pointJ = −25/299 · (13w−12u)'},'The two routes agree exactly when13 times the Joseph radius equals12 times the Levi radius. The radii299/276 and common1566 point are generated from the local source paths.','Measure the additional constraint that this cycle imposes.',{'radii':[u,w]==[299,276],'common':pointJ==pointE==1566,'identity':pointE-pointJ==-F(25,299)*res})