def run(load,check):
 d=load('C286_DATA.json');pairs=d['source_pairs'];reg=d['target_register'];left=[];right=[]
 for z in pairs:
  s,f,j,i=z['Shem_Cainan'],z['Flood_Cainan'],z['Shem_index'],z['Flood_index'];gap=z['F']-z['S'];expected=600+460*(s-f)+i-j
  check(f'cumulative {s}{f}/{j}/{i}',gap==expected and (gap==1058)==(s==1 and f==0 and j==i+2))
  if gap==1058:left.append({'i':i,'j':j,'S':z['S'],'q':z['F'],'source_pair':z})
 ns=[z for z in reg if z['tradition']=='SP' and z['role']=='Noah birth' and z['Cainan']==z['Terah60']==0 and z['full430']==1]
 rs=[z for z in reg if z['tradition']=='MT' and z['role'] in ['Flood start','Flood close'] and z['full430']==1]
 controls=[]
 for N in ns:
  for R in rs:
   e=int(N['rail']=='companion');k=int(R['role']=='Flood close');h=R['gear']-N['gear'];c,t=R['Cainan'],R['Terah60'];gap=N['center']-R['center'];want=1250-130*c-60*t-2*h-e+k;criterion=c==t==1 and h==1 and e==k
   tag=f'{N["gear"]}/{e}-{R["gear"]}/{k}/{c}{t}'
   check(tag+' right factorization',gap==want and (gap==1058)==criterion)
   controls.append({'SP_gear':N['gear'],'MT_gear':R['gear'],'c':c,'t':t,'e':e,'k':k,'gap':gap,'is2K':gap==1058})
   if gap==1058:right.append({'i':2*N['gear']+1-e,'N':N,'R':R,'h':h,'e':e,'k':k})
 left.sort(key=lambda x:x['i']);right.sort(key=lambda x:x['i']);joined=[]
 for l in left:
  for r in right:
   il,ir=l['i'],r['i'];S,q,R,N=l['S'],l['q'],r['R']['center'],r['N']['center'];delta=ir-il
   check(f'join {il}/{ir}',R-S==N-q==8993+delta and N-S==10051+delta and R-q==7935+delta)
   joined.append({'left_i':il,'right_i':ir,'S':S,'q':q,'R':R,'N':N,'cross_span':N-q,'two17K':delta==0,'allK':all(x%529==0 for x in [q-S,N-R,R-S,N-q,N-S,R-q])})
 aligned=[x for x in joined if x['two17K']];old=[x for x in load('C287_DATA.json')['rows'] if x['complete']]
 check('left6 right4 join24 aligned4',(len(left),len(right),len(joined),len(aligned))==(6,4,24,4))
 check('exact C287 reconciliation',[(x['left_i'],x['S'],x['q'],x['R'],x['N']) for x in aligned]==[(x['i'],x['S'],x['F'],x['R'],x['Noah_required']) for x in old])
 check('17K exactly equal annual index',all(x['allK']==x['two17K']==(x['left_i']==x['right_i']) for x in joined))
 return {'step':'C337','left_2K_pairs':left,'right_2K_pairs':right,'right_context_controls':controls,'joins24':joined,'aligned4':aligned,'source_conditions':{'left':'ON-Shem j=i+2 and OFF-Flood i','right':'restored MT CainanON/Terah60; MT Gear one above SP; SP primary/start or companion/close','cross':'equal left and right i'},'formulas':{'left':'600+460(s-f)+i-j','right':'1250-130c-60t-2h-e+k','cross':'8993+i_right-i_left'},'counts':{'left_source_pairs_tested':len(pairs),'right_source_pairs_tested':len(controls),'left2K':6,'right2K':4,'independent_pairings':24,'two17K':4},'interpretation':'Conditional factorization of existing source domain, not a prescribed selection or statistical independence claim.'}