from research import *
s=begin(1022,'NT placement as an alternative basis','Can the two supplied co-registrations recover both hinge and unit?',{'slot_indices':[55,20],'BC_coordinates':[3856,1406]},['File54','C1021'])
from algebra import Matrix
M=Matrix([[1,55],[1,20]]);sol=M.gauss_jordan_solve(Matrix([3856,1406]))[0]
finish(s,{'determinant':M.det(),'hinge_and_unit':list(sol),'ceiling':'already constructed source co-registrations; consistency basis, not independent origin proof'},'The co-registrations recover the6BC hinge and70-year unit. Since those positions belong to the existing schematic display, this is an equivalent parameterization, not a new historical derivation or Nativity revision.','Test how Toledot grouping changes the measured object itself.',{'unique':M.det()==-35,'source_basis':list(sol)==[6,70]})