from fractions import Fraction as F

def run(load,check):
    before=load('PREVIOUS_DATA.json'); reg=load('C286_DATA.json')['target_register']
    comp={x['i'] for x in load('C287_DATA.json')['rows'] if x['complete']}
    domain=list(range(3,8)); phases=[F(-1,4),F(1,4)]; rows=[]
    check('five inherited indices',before['parameters']['annual_indices']==domain)
    for old in before['rows']:
        j=old['index']; i=10-j; n=3703+i; s=3213-j; d=s-600
        gear=old['normalized_Shem_birth']['gear']; rail=old['normalized_Shem_birth']['rail']
        records={}
        for role,center in [('Noah birth',n),('Shem birth',s),('Shem death',d)]:
            hits=[r for r in reg if r['tradition']=='SP' and r['gear']==gear and r.get('rail')==rail and r['role']==role and r['center']==center and r['Cainan']==0 and r['Terah60']==0 and r['full430']==1]
            check(f'j{j} unique source {role}',len(hits)==1);records[role]=hits[0]
        check(f'j{j} full biography',n-s==500 and s-d==600 and n-d==1100)
        check(f'j{j} inherited match',records['Noah birth']==old['source_matched_Noah'])
        components=[]
        for e in phases:
            matches=[(k,f) for k in domain for f in phases if F(3703+k)+f-(F(s)-e)==500]
            check(f'j{j} {e} unique reversal',matches==[(i,-e)])
            nc=F(n)-e;sc=F(s)-e;dc=F(d)-e
            check(f'j{j} {e} phase spans',nc-sc==500 and sc-dc==600 and nc-dc==1100)
            check(f'j{j} {e} local involution',(10-i,e)==(j,e) and (-5290+i-e)+(-5290+j+e)==-10570)
            components.append({'Shem_ancestry_phase':str(e),'Noah_ancestry_phase':str(-e),'Noah':str(nc),'Shem_birth':str(sc),'Shem_death':str(dc)})
        rows.append({'j':j,'i':i,'gear':gear,'rail':rail,'biography_BC':[n,s,d],'source_records':records,'components':components,'C287_at_i':i in comp,'C287_at_j':j in comp,'C287_at_both':i in comp and j in comp})
    points={(j,e) for j in domain for e in phases};mapped={(10-j,-e) for j,e in points}
    check('finite closure',points==mapped)
    check('no fixed exact component',all((10-j,-e)!=(j,e) for j,e in points))
    check('full eight-index field is not closed',{10-j for j in range(8)}!=set(range(8)))
    check('both-side C287 only center',[r['j'] for r in rows if r['C287_at_both']]==[5])
    return {'step':'C314','formulas':{'J':'(j,e) -> (10-j,-e)','local_R':'-10570-q','global_axis_unchanged':True},'rows':rows,'counts':{'biographies':5,'phase_biographies':10,'component_comparisons':100,'phase_two_cycles':5,'phase_fixed_points':0,'C287_at_i':sum(r['C287_at_i'] for r in rows),'C287_at_j':sum(r['C287_at_j'] for r in rows),'C287_at_both':sum(r['C287_at_both'] for r in rows)},'interpretation':'Conditional local correspondence on five selected source states, not a source-prescribed selector.'}