s978.py

from research import *
s=begin(978,'Rounding the cap counts','Does nearest-five rounding commute with the source minimum?',{},['C953','C955','C956','File51a nearest-five policy'])
q=lambda n:5*((n+2)//5)
L=json.loads((ROOT/'model/sp_cap_inputs.json').read_text())['baseline_lives'];C=json.loads((ROOT/'model/sp_capacity_field.json').read_text())['capacities'];left=[q(min(l,c)) for l,c in zip(L,C)];right=[min(q(l),q(c)) for l,c in zip(L,C)]
a=artifact('model/sp_cap_rounded_counts.json',json.dumps({'rounded_lives':left,'rounded_baseline':[q(x) for x in L],'rounded_capacities':[q(x) for x in C]},indent=2)+'\n')
finish(s,{'field':a,'rounded_lives':left,'proof':'A monotone map on a total order preserves binary minima.'},'Count rounding commutes with the cap across all nine rows because the rounding map is monotone. This does not yet define Rounded date labels.','Check whether this source field keeps the same strict active support.',{'commutes_all_rows':left==right,'expected_counts':left==[930,910,905,910,895,845,365,720,655]})