from itertools import combinations
from collections import Counter
def run(load,check):
 reg=load('C286_DATA.json')['target_register'];keys=['tradition','rail','gear','Cainan','Terah60','full430'];roles=['Noah birth','Shem birth','Noah death','Shem death'];groups={}
 for i,r in enumerate(reg):
  if r['role'] not in roles:continue
  k=tuple(r.get(x) for x in keys);groups.setdefault(k,{})[r['role']]=i
 contexts=[]
 for k,rs in sorted(groups.items(),key=lambda x:str(x[0])):
  check('complete profile '+str(k),set(rs)==set(roles));contexts.append({'context':dict(zip(keys,k)),'record_indices':rs,'coordinates':{role:reg[rs[role]]['center'] for role in roles}})
 pairs=[];hits=[];dist=Counter()
 for i,j in combinations(range(len(contexts)),2):
  a,z=contexts[i],contexts[j]
  if a['coordinates']['Noah birth']<z['coordinates']['Noah birth']:i,j=j,i;a,z=z,a
  ds=[a['coordinates'][role]-z['coordinates'][role] for role in roles]
  check('uniform four-station offset '+str((i,j)),len(set(ds))==1)
  d=ds[0];row={'upper_context_index':i,'lower_context_index':j,'offset':d,'same_role_2K':d==1058};pairs.append(row);dist[d]+=1
  if d==1058:hits.append({**row,'upper':a,'lower':z})
 expected=load('PREVIOUS_DATA.json')['profiles'];check('unfiltered result recovers C416 contexts',len(hits)==1 and hits[0]['upper']['context']==expected[0]['context'] and hits[0]['lower']['context']==expected[1]['context'])
 selected=hits[0];variants=[]
 for trad,rail in [('SP','primary'),('LXX',None)]:
  c={**selected['upper']['context'],'tradition':trad,'rail':rail};p=next(x for x in contexts if x['context']==c);diff=p['coordinates']['Noah birth']-selected['lower']['coordinates']['Noah birth'];variants.append({'upper_context':c,'offset_to_same_MT_context':diff});check('primary/native rail control '+trad,diff==1059)
 check('full finite census size',len(contexts)==96 and len(pairs)==4560)
 return {'step':'C417','contexts':contexts,'pair_trials':pairs,'offset_distribution':[{'offset':k,'context_pairs':v} for k,v in sorted(dist.items())],'hits':hits,'rail_controls':variants,'counts':{'contexts':len(contexts),'unordered_context_pairs':len(pairs),'zero_offset_alias_pairs':dist[0],'positive_offset_pairs':sum(v for k,v in dist.items() if k>0),'distinct_offsets':len(dist),'same_role_2K_profiles':len(hits)},'interpretation':'All four person roles share a context offset by source construction; the unfiltered census finds one labelled profile pair at1058. Uniqueness is relative to the frozen96-context menu. Primary SP and LXX coordinates at the chosen upper settings give1059, not1058. No upstream or cumulative Gear is searched.'}