s1210.py

from research import *
s=begin(1210,'Distinguish cap commutation from strict clipping visibility','Can exact clipping disappear after rounding, and can an unrounded cap change the result?',{},['C1209','C1203'])
def Q(x):return 5*((x+2)//5)
same={'L':721,'c':720,'exact_excess':1,'rounded_input':Q(721),'rounded_capacity':Q(720)}
different={'L':14,'c':11,'Q_min':Q(min(14,11)),'min_Q_exact_c':min(Q(14),11),'min_Q_Qc':min(Q(14),Q(11))}
a=artifact('model/cap_round_visibility_witnesses.json',json.dumps({'hidden_clipping':same,'different_operation_witness':different,'C1209_clarification':'Its12/11 example displayed equal results and was not a distinguishing counterexample;14/11 provides the required contrast.'},indent=2)+'\n')
finish(s,{'witnesses':a},'A one-year excess can disappear inside a rounded cell. Separately, L14 and c11 yield10 when the cap is rounded consistently but11 when only the input is rounded. C1209’s12/11 example did not distinguish the routes; this one does.','State the strict clipping criterion in terms of rounded-cell thresholds.',{'hidden_strictness':same['exact_excess']>0 and same['rounded_input']==same['rounded_capacity'],'distinguished':different['Q_min']==different['min_Q_Qc']==10 and different['min_Q_exact_c']==11})