s974.py

from research import *
s=begin(974,'Local regular-to-cumulative response','What map transmits a begetting change through fixed active caps?',{'active_indices':[5,7,8],'condition':'fixed Noah/Flood relation, baseline lives and active support'},['C954','C956','C972'])
U=[[int(j>=i) for j in range(9)] for i in range(9)]; AU=[[int(i in [5,7,8])*x for x in row] for i,row in enumerate(U)]; V=[[sum(U[i][k]*AU[k][j] for k in range(9)) for j in range(9)] for i in range(9)]
a=artifact('model/sp_cap_response_matrices.json',json.dumps({'dB_db':U,'dL_db':AU,'dC_db':V,'domain':s['inputs']['condition']},indent=2)+'\n')
finish(s,{'matrices':a,'last_begetting_response_regular':[row[8] for row in U],'last_begetting_response_cumulative':[row[8] for row in V]},'Within one active region, the maps are U, A·U, and U·A·U. A regular-row change can alter three capped lives and hence several cumulative coordinates; this is a sensitivity model, not an admitted variant.','Test the local formula against a controlled one-unit perturbation.',{'upper_rows_accumulate_three':V[0][8]==3,'last_row_one':V[8][8]==1,'masked_unchanged_rows':all(AU[i]==[0]*9 for i in [0,1,2,3,4,6])})