from fractions import Fraction as Q

def run(load,check):
 # Affine expressions in the free common translation u are pairs(constant,u_coefficient).
 rows=[];K=529
 for r in load('C287_DATA.json')['rows']:
  i=r['i'];F=(r['F']+10*K,1);H=(r['S']+12*K,1);RF=(5*K-r['R'],-1)
  check(f'cumulative coincidence i{i}',F==H==(i,1))
  check(f'global reflected pair i{i}',RF==(-i,-1))
  for e in [Q(-1,4),Q(1,4)]:check(f'phase reflection i{i} {e}',(5*K-(r['R']+e),-1)==(-(i+e),-1))
  if r['complete']:
   RN=(r['Noah_required']-7*K,1);check(f'Noah same image i{i}',RN==F)
  rows.append({'i':i,'F_image':[i,1],'H_ON_image':[i,1],'regular_Flood_image':[-i,-1],'regular_Noah_image':[i,1] if r['complete'] else None})
 old=load('C270_MAPS.json')
 check('C270 coefficient binding',int(old['cumulative_Flood_map'][1])==10*K and -int(old['cumulative_reflected_Shem_map'][1])+460==12*K and int(old['regular_reflected_Flood_map'][1])-460==5*K and -int(old['regular_reflected_Noah_map'][1])==7*K)
 check('retained state lift',5290==10*K and 5888+460==12*K and 3105-460==5*K and 3703==7*K)
 check('mixed increment',12*K-10*K==1058 and 1058-460==598)
 check('common-translation null direction',[(1)-(1),(-1)+(1),1-1]==[0,0,0])
 check('K intercept congruence only',all((b+n*K)%K==0 for b in [10*K,12*K,7*K,5*K] for n in [-1,0,1]))
 return {'rows':rows,'maps':{'F_OFF':'q+10K+u','H_ON':'q+12K+u','G_ON':'-q-12K-u','RN_SP':'y-7K+u','RF_MT_restored':'5K-u-y'},'freedom':'u remains arbitrary; integer u preserves annual centers','all_intercepts_in_KZ':'u in KZ, not uniquely zero','baseline':'u=0 is retained, not derived anew','mixed_increment':1058}