s1019.py

from research import *
s=begin(1019,'NT Key-knot constraint rank','Do the one-slot P and six-slot E returns impose independent metric equations?',{},['File43 §3.4','File54 §6','C866–C867'])
from algebra import Matrix
M=Matrix([[P-1,-1],[E-1,-6]])
a=artifact('model/nt_knot_constraints.json',json.dumps(clean({'matrix':M.tolist(),'rank':M.rank(),'kernel':[list(v) for v in M.nullspace()],'unknowns':['Enoch radius w','slot unit u']}),indent=2)+'\n')
finish(s,{'constraint_packet':a,'rank':M.rank(),'row_multiple':6},'The second marked NT return is exactly six times the first equation. The pair has rank one and does not independently determine the70-year metric.','Identify the metric freedom and the additional source constraint that closes it.',{'rank_one':M.rank()==1,'dependent_rows':all(M[1,j]==6*M[0,j] for j in range(2))})