from fractions import Fraction as F
def run(load,read,check):
    reg=load('C286_DATA.json')['target_register'];by={}
    for i,r in enumerate(reg):by.setdefault(r['center'],[]).append(i)
    cases=[]
    for old in load('C434_DATA.json')['cases']:
        g,t=old['gear'],old['Terah60'];N=old['coordinates']['N'];c=N-518
        v={'upper_pivot':c+432,'upper_station':c+18,'center':c,'lower_station':c-18,'lower_pivot':c-432}
        ids={k:by.get(x,[]) for k,x in v.items()}
        check(f'G{g}/T{t} exact old pivots and whole-map fixed point',[v['upper_pivot'],v['lower_pivot'],v['upper_station']]==[old['coordinates'][k] for k in ['P','Q','H']])
        check(f'G{g}/T{t} radii imply E ratio',F(v['upper_pivot']-v['lower_station'],v['upper_pivot']-v['upper_station'])==F(25,23))
        expected=[i for i,r in enumerate(reg) if (r['tradition'],r['role'],r['gear'],r['Cainan'],r['Terah60'],r['full430'])==('MT','Noah birth',g+1,1,t,1)]
        check(f'G{g}/T{t} midpoint membership is next-Gear MT Noah',ids['center']==expected and bool(expected)==(g<=2))
        lower=[i for i,r in enumerate(reg) if (r['tradition'],r['role'],r['gear'],r['Cainan'],r['Terah60'],r['full430']) in [('SP','Flood start',g+2,0,t+1,1),('LXX','Flood start',g+2,0,t+1,1)]]
        check(f'G{g}/T{t} lower station membership is bounded Flood state',ids['lower_station']==lower and bool(lower)==(g==1 and t==0))
        cases.append({'gear':g,'Terah60':t,'N':N,'points':v,'record_indices':ids,'complete':all(ids.values()),'missing':[k for k,z in ids.items() if not z]})
    terms={'upper_pivot':[650,-215,-1,-2],'upper_station':[650,-500,-130,-2],
           'lower_station':[650,-600,-130,60,2],'lower_pivot':[650,-950,-130,-2]}
    check('four source-context equations give exact radii',{k:sum(v) for k,v in terms.items()}=={'upper_pivot':432,'upper_station':18,'lower_station':-18,'lower_pivot':-432})
    check('four existing midpoints and one full profile',sum(bool(r['record_indices']['center']) for r in cases)==4 and sum(r['complete'] for r in cases)==1)
    check('only3188 full profile',[r['points']['center'] for r in cases if r['complete']]==[3188])
    check('no source point introduced',all(i<len(reg) for r in cases for ids in r['record_indices'].values() for i in ids))
    return {'step':'C437','cases':cases,'source_terms_relative_to_center':terms,
            'source_formula':{'center':'N-518 = MT Noah birth(g+1,C1,T,F1)','upper_pivot':'SP companion Noah birth(g,C1,T,F0)',
                              'upper_station':'SP primary/LXX OFF Shem birth(g,C0,T,F1)','lower_station':'SP/LXX OFF Flood start(g+2,C0,T+1,F1)',
                              'lower_pivot':'SP primary/LXX OFF Noah death(g,C0,T,F1)'},
            'counts':{'profiles':6,'sourced_centers':4,'complete_five_point_profiles':1},
            'scope':'Finite local midpoint comparisons, not new global axes or source operators. Formal unavailable Gear/Terah states remain rejected.'}