s1050.py

from research import *
s=begin(1050,'Exact-phase and lifespan constraints','How do source equalities reduce the array without merging distinct phase policies?',{},['C1048','C1049','File62 §1.3'])
from algebra import Matrix
phase=[0]*7+[-2,1];life=[0,0,0,1,-1,-1,1,0,0];M=Matrix([phase,life])
finish(s,{'dimension_phase_only':9-Matrix([phase]).rank(),'dimension_equal_lives_only':9-Matrix([life]).rank(),'dimension_both':9-M.rank(),'exact_phase_residual':7-2*F(7,2),'whole_year_phase_residual':7-2*3},'The exact7=2×3.5 link and repeated137 life each remove one degree of freedom; together they leave seven. The whole-year phase3 does not satisfy the same equality and stays a separate model.','Generate the seven base boundaries from the source lifespan path.',{'independent_constraints':M.rank()==2,'exact_vs_whole':7-2*F(7,2)==0 and 7-2*3==1})