from fractions import Fraction as Q

def run(load,check):
 K=529;rows=[]
 for r in load('C287_DATA.json')['rows']:
  i=r['i'];a=r['S']+13*K;b=r['F']+13*K;R=r['R'];N=r['Noah_required']
  needR=8*K-b;needN=8*K-a
  check(f'fixed reflection residual i{i}',R-needR==N-needN==2*i)
  check(f'row midpoint i{i}',Q(a+N,2)==Q(b+R,2)==4*K+i)
  for e in [Q(-1,4),Q(1,4)]:check(f'reversed phase residual i{i} {e}',(R-e)-(8*K-(b+e))==2*i and (N-e)-(8*K-(a+e))==2*i)
  rows.append({'i':i,'translated_S':a,'translated_F':b,'R':R,'N_required':N,'N_present':r['complete'],'fixed8K_required_R':needR,'fixed8K_required_N':needN,'residual':2*i,'inner_fixed_pair':i==0,'complete_fixed_four_node_row':i==0 and r['complete']})
 check('only opening inner pair',[r['i'] for r in rows if r['inner_fixed_pair']]==[0])
 check('no complete fixed-axis row',not any(r['complete_fixed_four_node_row'] for r in rows))
 return {'rows':rows,'reflection':'J(y)=4232-y = T8K after global Mirror','fixed_comparison_center':2116,'row_midpoint':'2116+i','new_axis_adopted':False,'exact_inner_comparison_pair':[1587,2645],'first_inner_member_status':'generated13K image of admitted cumulative Flood opening','missing_outer_partner':3703}