from fractions import Fraction
from itertools import product

def run(load,check):
 reg=load('C286_DATA.json')['target_register'];base=[t for t in reg if (t['Cainan'],t['Terah60'],t['full430'],t['gear'])==(0,0,1,1)]
 noah=[t for t in base if t['tradition']=='SP' and t['role']=='Noah birth'];flood=[t for t in base if t['tradition']=='SP' and t['role'] in ['Flood start','Flood close']]
 phase_register=load('C271_REGISTER.json');phase_sets={r['source_event']['BC_Nisan']:sorted(Fraction(p['reflected_coordinate']) for p in r['phases']) for r in phase_register}
 offsets=[Fraction(-1,4),Fraction(1,4)];rows=[];phase_rows=[]
 for C,N,P in product([5288,5287],noah,flood):
  B=P['center']-650;mt=[t for t in base if t['tradition']=='MT' and t['role']==P['role'] and t['center']==B]
  check('MT frame counterpart'+str(C)+'/'+str(N['center'])+'/'+str(P['center']),len(mt)==1)
  r={'C':C,'Noah':N,'SP_Flood':P,'MT_Flood':mt[0],'Noah_17K_residual':C+N['center']-8993,'fixed2832_residual':C-B-2832,'center_width':N['center']-P['center']}
  r['both_fixed']=r['Noah_17K_residual']==r['fixed2832_residual']==0;rows.append(r)
  for x,y in product(phase_sets[N['center']],phase_sets[P['center']]):
   phase_rows.append({'C':C,'Noah_center':N['center'],'Flood_center':P['center'],'Noah_component':str(x),'Flood_component':str(y),'width':str(x-y),'both_center_interfaces_fixed':r['both_fixed'],'equals600':x-y==600})
 exact=[r for r in rows if r['center_width']==600]
 retained=[p for p in phase_rows if p['both_center_interfaces_fixed']]
 check('actual source phase offsets quarter',all(phase_sets[t['center']]==[t['center']+e for e in offsets] for t in noah+flood))
 check('eight source selector combinations',len(rows)==8)
 check('four center600 alternatives',len(exact)==4)
 check('every600 changes exactly one interface',all(sum(v!=0 for v in [r['Noah_17K_residual'],r['fixed2832_residual']])==1 for r in exact))
 check('changed interface differs one year',all(abs(r['Noah_17K_residual'])+abs(r['fixed2832_residual'])==1 for r in exact))
 check('two joint fixed center cases',len([r for r in rows if r['both_fixed']])==2)
 check('32 exact component comparisons',len(phase_rows)==32)
 check('eight component comparisons retain joint centers',len(retained)==8)
 check('no fixed-center component width600',not any(p['equals600'] for p in retained))
 check('retained phase ranges',sorted({Fraction(p['width']) for p in retained})==[Fraction(1197,2),Fraction(599),Fraction(1199,2),Fraction(1201,2),Fraction(601),Fraction(1203,2)])
 check('eight600 phase rows only alternative bindings',sum(p['equals600'] for p in phase_rows)==8 and all(not p['both_center_interfaces_fixed'] for p in phase_rows if p['equals600']))
 return {'selector_combinations':rows,'exact600_center_alternatives':exact,'actual_component_comparisons':phase_rows,'fixed_pair_phase_comparisons':retained,'phase_method':'Cartesian comparison of the actual reflected source components; translations preserve offsets, Mirror reverses component ancestry.','joint600_solution':False,'changed_equations_are_diagnostics_not_adopted':True}