s1043.py

from research import *
s=begin(1043,'Complete Covenant constraint basis','How many independent equations remain in the nine selected claims?',{},['C1035–C1042'])
from covenant_model import *
from algebra import Matrix
M=Matrix(coefficient_matrix(claims,KEYS[:13]));v={k:F(x) for k,x in json.loads((ROOT/'model/covenant_source_inputs.json').read_text()).items()};a=artifact('model/covenant_claim_basis.json',json.dumps(clean({'parameters':KEYS[:13],'matrix':M.tolist(),'rank':M.rank(),'basis_rows':list(range(8)),'source_residuals':claims(v),'left_kernel':[list(x) for x in M.T.nullspace()],'qualification':'rank under declared variable local parameters; not probability or historical independence'}),indent=2)+'\n')
finish(s,{'constraint_basis':a,'rank':M.rank(),'free_dimensions':13-M.rank()},'Nine selected claims reduce to eight equations in the variable local model. Path identities and fixed-source-dependent equivalences are classified separately.','Identify what the prominent numerical normalizations add beyond these relations.',{'rank_eight':M.rank()==8,'first_eight_basis':Matrix(M.tolist()[:8]).rank()==8,'all_source_residuals':claims(v)==[0]*9})