s975.py

from research import *
s=begin(975,'Check the piecewise-linear response','Does one controlled perturbation agree with the derived response matrix?',{'diagnostic_only':'increase completed Lamech edge by1; retain active-region assumptions'},['C974'])
p=json.loads((ROOT/'model/sp_cap_inputs.json').read_text());b=p['begetting_completed'];d=b.copy();d[-1]+=1;L=p['baseline_lives'];old=[min(l,sum(b[i:])+601) for i,l in enumerate(L)];new=[min(l,sum(d[i:])+601) for i,l in enumerate(L)];changes=[new[i]-old[i] for i in range(9)];cum=[sum(changes[i:]) for i in range(9)];V=json.loads((ROOT/'model/sp_cap_response_matrices.json').read_text())['dC_db']
finish(s,{'lifespan_changes':changes,'cumulative_changes':cum,'status':'unadmitted derivative diagnostic'},'The exact one-unit calculation matches the response matrix while retaining the same active support. The formula’s domain qualification is essential at cap thresholds.','Check the admitted whole-frame change without moving any relative ages.',{'life_response':changes==[0,0,0,0,0,1,0,1,1],'cumulative_response':cum==[row[8] for row in V]})