from research import *
s=begin(958,'Greatest feasible lifespan field','Why does the minimum represent shortening only as required?',{'constraints':['x_i≤baseline_i','x_i≤capacity_i'],'objective':'maximize sum(x_i)'},['C956','C957'])
proof={'coordinate_bound':'Every feasible x_i is at most min(L_i,C_i).','feasibility':'The coordinatewise minimum satisfies both upper bounds.','uniqueness':'If any coordinate is smaller, the sum is smaller because no other coordinate can exceed its bound.','qualification':'Conditional on the two upper bounds and fixed row meanings.'}
finish(s,proof,'The cap is the unique coordinatewise greatest feasible vector and uniquely minimizes total reduction. This states the model’s mechanism without inventing an optimization history.','Recover death labels with each branch’s own counting convention.',{'upper_bound_logic':min(962,847)==847,'no_increase':all(x<=y for x,y in zip(json.loads((ROOT/'model/sp_cap_prediction.json').read_text())['lifespans'],json.loads((ROOT/'model/sp_cap_inputs.json').read_text())['baseline_lives']))})