from fractions import Fraction as Q
from collections import Counter
def run(load,check):
 E=Q(25,23);J=Q(300,299);reg=load('C286_DATA.json')['target_register'];keys=['tradition','rail','Cainan','Terah60','full430']
 def family(r):return tuple(r.get(k) for k in keys)
 families=sorted({family(r) for r in reg if r['role']=='Noah birth'})
 def take(f,g,role):
  ff=dict(zip(keys,f));xs=[r for r in reg if r['gear']==g and r['role']==role and all(r.get(k)==v for k,v in ff.items() if k!='rail' or not role.startswith('Flood'))]
  assert len(xs)==1,(f,g,role,len(xs));return xs[0]
 def val(r):return Q(r['center'])
 def apply(a,k,x):return a+k*(x-a)
 trials=[];hits=[];counts=Counter();familiesout=[dict(zip(keys,f)) for f in families]
 for g in [1,2]:
  for fi,src in enumerate(families):
   xr=take(src,g,'Noah birth');yr=take(src,g+1,'Noah birth');x=val(xr);y=val(yr)
   check('source family two-year edge '+str((g,fi)),y-x==2)
   for fj,target in enumerate(families):
    nr=take(target,g,'Noah birth');n1r=take(target,g+1,'Noah birth');zr=take(target,g,'Shem birth');wr=take(target,g+1,'Shem birth');dr=take(target,g+1,'Shem death');N,N1,z,w,D=map(val,[nr,n1r,zr,wr,dr])
    for boundary in ['Flood start','Flood close']:
     ar=take(src,g+1,boundary);A=val(ar);low=apply(A,J,x)==y;up=apply(D,J,z)==w;el=apply(N,E,x)==z;er=apply(N1,E,y)==w;ok=low and up and el and er
     mask=''.join('1' if t else '0' for t in [low,up,el,er]);counts[mask]+=1
     trials.append({'input_Gear':g,'source_family':fi,'target_family':fj,'Flood_boundary':boundary,'J_lower':low,'J_upper':up,'E_left':el,'E_right':er,'complete':ok})
     if ok:
      hits.append({'input_Gear':g,'source_family':dict(zip(keys,src)),'target_family':dict(zip(keys,target)),'Flood_boundary':boundary,'records':{'x':xr,'y':yr,'N':nr,'N_next':n1r,'z':zr,'w':wr,'A':ar,'D':dr},'observed_spans':{'N_minus_x':int(N-x),'N_minus_A':int(N-A),'x_minus_A':int(x-A),'N_minus_z':int(N-z),'w_minus_D':int(w-D)}})
 check('fixed family inventory',len(families)==32 and len(trials)==4096)
 check('complete finite census',len(hits)==8 and sum(t['complete'] for t in trials)==8 and sum(t['E_left'] and t['E_right'] for t in trials)==16 and all(t['J_upper'] for t in trials))
 previous=load('C385_DATA.json')['rows'];old=set()
 for r in previous:
  for lift in r['source_context_lifts']:
   old.add((r['original_tuple'][2],r['original_tuple'][3],lift['tradition'],lift['Noah_input_record']['gear'],lift['Noah_input_record']['full430']))
 new={(h['records']['x']['center'],h['records']['y']['center'],h['target_family']['tradition'],h['input_Gear'],h['target_family']['full430']) for h in hits}
 check('post-census comparison equals earlier positive cases',new==old)
 return {'step':'C390','families':familiesout,'trials':trials,'hits':hits,'outcome_masks_Jlower_Jupper_Eleft_Eright':dict(sorted(counts.items())),'counts':{'source_families':32,'target_families':32,'Gear_transitions':2,'Flood_boundaries':2,'labelled_trials':4096,'two_vertical_E_edges_pass':16,'complete_E_J_squares':8,'complete_coordinate_squares':4,'all_upper_Shem_J_edges_pass':True},'interpretation':'The unconditioned finite coherent-family census recovers exactly the four coordinate squares/eight labelled contexts already found. The original1058 side is an observed output, not a filter. This is selectivity within a defined family motif, not a probability estimate or independent historical corroboration.'}