s968.py

from research import *
s=begin(968,'The inverse image of a capped life','What does a capped output reveal about its input lifespan?',{},['C955','C956'])
C=json.loads((ROOT/'model/sp_capacity_field.json').read_text())['capacities']; Y=json.loads((ROOT/'model/sp_cap_prediction.json').read_text())['lifespans']; field=[{'row':i,'output':y,'input_condition':('equals '+str(y)) if y<c else ('at least '+str(c))} for i,(c,y) in enumerate(zip(C,Y))]
finish(s,{'inverse_conditions':field,'exactly_recovered_rows':[i for i,(c,y) in enumerate(zip(C,Y)) if y<c]},'Six uncapped inputs are recoverable exactly; each clipped input is only bounded below. Clipping loses the original excess.','Test whether even a supplied ancestral multiset restores the three lost row placements.',{'six_exact':sum(y<c for y,c in zip(Y,C))==6,'three_bounds':sum(y==c for y,c in zip(Y,C))==3})