s1049.py

from research import *
s=begin(1049,'Minimal clutch observation basis','Which observed coordinates recover the unrestricted array?',{},['C1048'])
from algebra import Matrix
p=json.loads((ROOT/'model/clutch_array_matrix.json').read_text());rows=p['matrix'];labels=p['labels'];selected=list(range(7))+[21,7];M=Matrix([rows[i] for i in selected]);filtered={'no_Aaron':Matrix([r for r,(i,j,k) in zip(rows,labels) if j==0]).rank(),'no_shift':Matrix([r for r,(i,j,k) in zip(rows,labels) if k==0]).rank(),'one_row_absent':Matrix([r for r,(i,j,k) in zip(rows,labels) if i!=0]).rank()}
finish(s,{'basis_indices':selected,'basis_determinant':M.det(),'incomplete_observation_ranks':filtered},'Seven unshifted Nisan coordinates, one unshifted Aaron coordinate and one half-clutch coordinate form an integer observation basis. Losing a whole phase, all shifts, or an entire source row leaves one parameter undetermined.','Impose exact source phase and repeated-lifespan equalities separately.',{'unimodular':abs(M.det())==1,'all_rank_eight':all(v==8 for v in filtered.values())})