s1165.py

from research import *
from algebra import Matrix
s=begin(1165,'Compress the SP-to-LXX lifespan edge by its disjoint supports','Which part of the three-tradition pattern is common to every final-edge row?',{},['C1164','C1154'])
names=['Shem','Arphaxad','Shelah','Eber','Peleg','Reu','Serug','Nahor','Terah']
M=Matrix([[0,0,0],[0,0,1],[0,0,1],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[0,1,0],[0,1,0]])
v=list(M*Matrix([100,60,27]))
a=artifact('model/SP_LXX_disjoint_life_pattern.json',json.dumps(clean({'names':names,'parameters':['u','t','a'],'matrix':M.tolist(),'rank':M.rank(),'values':v,'support_sizes':[4,2,2],'total_formula':'4u+2t+2a','source_total':sum(v),'nonnegative_cone':'u,t,a>=0 gives coordinatewise LXX>=SP while regular begetting values are equal'}),indent=2)+'\n')
finish(s,{'disjoint_life_pattern':a,'rank':M.rank(),'source_total':sum(v)},'The final lifespan edge is a disjoint4/2/2 pattern with amplitudes100,60,27. It explains a common regular birth path alongside a cumulative surplus574, with no need to assign a different birth transformation to each row.','Determine how the pattern propagates through the complete cumulative path rather than just its total.',{'rank3':M.rank()==3,'total574':sum(v)==574,'nonnegative_values':min(v)>=0})