from fractions import Fraction as Q

def run(load,check):
 rows=[]
 for name,B in [('LXX_OFF_Flood',5290),('LXX_ON_Shem',6350)]:
  for j in range(8):rows.append({'group':name,'index':j,'BC_base':B-j,'kind':'cumulative annual boundary'})
 targets=load('C286_DATA.json')['target_register']
 for t in targets:
  mt=t['tradition']=='MT' and t['role'].startswith('Flood') and (t['Cainan'],t['Terah60'],t['full430'])==(1,1,1)
  sp=t['tradition']=='SP' and t['role']=='Noah birth' and (t['Cainan'],t['Terah60'],t['full430'])==(0,0,1)
  if mt or sp:rows.append({'group':'MT_restored_Flood' if mt else 'SP_Noah','BC_base':t['center'],'source':t,'kind':'regular'})
 check('28 admitted source records',len(rows)==28)
 for ix,r in enumerate(rows):
  B=r['BC_base'];W=2*B;r.update({'self_Mirror_width':W,'K_multiple':W//529 if W%529==0 else None,'source_pair':f'{B+1}t/{B}n BC','reflected_pair':f'AD {B}t/{B+1}n'})
  for e in [Q(-1,4),Q(1,4)]:check(f'paired-set mirror ix{ix} {e}',-B+e+W==-(-B-e))
  check(f'divisibility equivalence ix{ix}',(W%529==0)==(B%529==0))
 hits=[r for r in rows if r['K_multiple'] is not None]
 check('exact three selfMirror K widths',{(r['group'],r['BC_base'],r['K_multiple']) for r in hits}=={('LXX_OFF_Flood',5290,20),('LXX_ON_Shem',6348,24),('MT_restored_Flood',2645,10)})
 check('14K Noah absent',not any(r['group']=='SP_Noah' and r['BC_base']==3703 for r in rows))
 return {'rows':rows,'exact_K_hits':hits,'phase_qualification':'Translation and Mirror give the same paired set at W=2B, with opposite input-component ancestry; they are not identical maps of each component.','nominal_Noah14K_width':7406,'Noah_source_at3703_present':False}