from research import *
s=begin(1041,'Common landing adds one cycle condition','Does the common-Key relation add information beyond the same-side Covenant rails?',{},['C1038–C1040'])
from covenant_model import *
from algebra import Matrix
rows=coefficient_matrix(claims,KEYS[:13]);r5=Matrix(rows[:5]).rank();r6=Matrix(rows[:6]).rank()
finish(s,{'rank_first_five':r5,'rank_with_Key_cycle':r6,'added_constraint':'13w=12u'},'The common-Key cycle adds one constraint in the declared variable source model. Introducing its landing coordinate does not create a second independent equality.','Test how fixed source lifespans alter apparent independence of the radius progression.',{'one_extra':r6==r5+1,'ranks':(r5,r6)==(5,6)})