s971.py

from research import *
s=begin(971,'Bidirectional cap equation packet','How much independent information do forward and inverse reconstructions require?',{'variables':['bJ','bE','bM','bL','lifeJ','lifeM','lifeL','k']},['C964','C965','C970'])
M=[[1,1,1,1,-1,0,0,1],[0,0,1,1,0,-1,0,1],[0,0,0,1,0,0,-1,1]]
finish(s,{'equations':M,'rank':3,'unconstrained_dimension':5,'after_k_and_Enoch_held':3},'The late-row relation has three independent equations on eight variables. Holding k and Enoch leaves equivalent three-number choices: the changed begettings or the capped lives. This is bidirectional constraint, not double evidence.','Propagate the cap-derived reductions into the cumulative field.',{'unique_life_columns':[row[4:7] for row in M]==[[-1,0,0],[0,-1,0],[0,0,-1]],'dimension':8-3-2==3})