from fractions import Fraction as Q
def run(load,check):
 reg=load('C286_DATA.json')['target_register'];coords={r['center'] for r in reg};strip=load('C388_DATA.json')['strips'][0];rat={'E':Q(25,23),'P':Q(70,69),'J':Q(300,299)}
 def aff(k,c):return(k,(1-k)*c)
 def comp(a,b):return(a[0]*b[0],a[0]*b[1]+a[1])
 def inv(a):return(1/a[0],-a[1]/a[0])
 def val(a,t):return(a[0]*t+a[1])
 vs=strip['MT_Noah_vertices'];zs=list(map(Q,strip['SP_LXX_Shem_vertices']));ns=strip['Noah_centers'];charts={u:aff(rat['E'],n) for u,n in zip(vs,ns)};images=dict(zip(vs,zs));rows=[];phases=[]
 for i,e in enumerate(load('C400_DATA.json')['edges']):
  op,u,v,p=e['operator'],e['input'],e['output'],e['pivot'];k=rat[op];z,w=images[u],images[v];V=(k*z-w)/(k-1);T=comp(charts[v],comp(aff(k,p),inv(charts[u])));hits=[r for r in reg if r['center']==V]
  check('transported whole affine arrow '+str(i),T==aff(k,V) and val(T,z)==w and V==p-40)
  check('target endpoints sourced '+str(i),z in coords and w in coords)
  rows.append({'edge':i,'operator':op,'Noah_input':u,'Noah_output':v,'Shem_input':str(z),'Shem_output':str(w),'original_pivot':p,'required_Shem_pivot':str(V),'source_pivot_records':hits,'transported_affine':list(map(str,T))})
  for eps in [-Q(1,4),Q(1,4)]:
   charts_phase={a:aff(rat['E'],n+eps) for a,n in zip(vs,ns)};TT=comp(charts_phase[v],comp(aff(k,p+eps),inv(charts_phase[u])));Vp=(k*(z+eps)-(w+eps))/(k-1)
   check('matched phase whole arrow '+str((i,eps)),TT==aff(k,Vp) and Vp==V+eps)
   phases.append({'edge':i,'offset':str(eps),'required_pivot':str(Vp),'same_phase_source_pivot':bool(hits)})
 check('only two J arrows sourced',[r['operator'] for r in rows if r['source_pivot_records']]==['J','J'])
 check('new E pivot obstruction',[r['required_Shem_pivot'] for r in rows if r['operator']=='E']==['3016','3018'])
 check('P obstruction retained',[r['required_Shem_pivot'] for r in rows if r['operator']=='P']==['2853','2855'])
 paths=load('C400_DATA.json')['path_trials'];tests=[]
 for t in paths:
  u,v=t['start'],t['end'];F=tuple(map(Q,t['affine_coefficients']));T=comp(charts[v],comp(F,inv(charts[u])));m=F[0]
  check('path conjugation '+str((u,tuple(t['edge_indices']))),T==(m,images[v]-m*images[u]))
  admitted=all(bool(rows[i]['source_pivot_records']) for i in t['edge_indices']);tests.append({'start':u,'end':v,'word':t['operators_in_execution_order'],'transported_affine':list(map(str,T)),'all_primitive_pivots_sourced':admitted})
 admitted=[t for t in tests if t['all_primitive_pivots_sourced']]
 check('J subgraph paths only',len(admitted)==6 and sorted(t['word'] for t in admitted)==['','','','J','J','JJ'])
 return {'step':'C404','Noah_vertices':vs,'Shem_vertices':list(map(str,zs)),'vertical_Noah_pivots':ns,'edge_transport':rows,'matched_phase_trials':phases,'path_transport':tests,'counts':{'primitive_arrows':6,'sourced_transported_arrows':2,'missing_E_pivots':2,'missing_P_pivots':2,'matched_phase_arrow_trials':12,'paths_checked':len(tests),'source_admitted_transported_paths':len(admitted),'nonempty_source_admitted_closed_paths':0},'general_form':'Transport through the existing E charts retains each path slope and sends its two endpoint labels to their Shem images. Primitive E and P pivots are absent; only the finite J subgraph is source-qualified.','interpretation':'Formal conjugation is exact but cannot supply missing source pivots. Same-phase component comparisons do not make one physical-time seasonal action. No new source or canonical graph edit.'}