from research import *
s=begin(963,'Aggregate cap identification','Can the complete lifespan sum identify k after support is fixed?',{'source_total':7137,'active':[5,7,8]},['C953','C954','C962'])
L=json.loads((ROOT/'model/sp_cap_inputs.json').read_text())['baseline_lives']; u=json.loads((ROOT/'model/sp_birth_regeneration.json').read_text())['suffixes']; a=s['inputs']['active']; intercept=sum(L[i] if i not in a else u[i] for i in range(9)); k=F(s['inputs']['source_total']-intercept,len(a))
finish(s,{'sum_equation':'total = 5334 + 3k','intercept':intercept,'recovered_k':k},'Within the fixed support region, the sum7137 identifies601. It is an alternative coordinate for the same data, retaining support and order assumptions.','Recover the changed begetting inputs from the individual cap equations.',{'intercept':intercept==5334,'k':k==601,'support_valid':584<=k<716})