s1039.py

from research import *
s=begin(1039,'An explicit Covenant dependency circuit','Is the household-middle equality independent of the other source conditions?',{},['C1035–C1038'])
from covenant_model import *
from algebra import Matrix
M=Matrix(coefficient_matrix(claims,KEYS[:13]));rows=M.tolist();combo=[-rows[1][j]+rows[2][j]+rows[3][j]+rows[4][j] for j in range(13)]
finish(s,{'dependency':'A9 = −A2 + A3 + A4 + A5','coefficient_residual':[rows[8][j]-combo[j] for j in range(13)]},'The household-middle equality is forced by the second147 rail, equal lives, twin death arms and Joseph’s double span. It adds no separate constraint after those are retained.','Derive the common-Key landing condition without using its299/276 outputs as inputs.',{'full_coefficient_identity':rows[8]==combo,'nontrivial_circuit':any(combo)})