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David H. Friedel Jr. 2025-07-21 18:12:20 -04:00
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@ -55,7 +55,7 @@ Once published on arXiv:
1. **Quick Overview**: Read `executive_summary.md` (2 pages) 1. **Quick Overview**: Read `executive_summary.md` (2 pages)
2. **Technical Summary**: Read `two_page_summary.tex` (2 pages, compile to PDF) 2. **Technical Summary**: Read `two_page_summary.tex` (2 pages, compile to PDF)
3. **Full Paper**: Read `main.tex` (24 pages, compile to PDF) 3. **Full Paper**: Read `main.tex` (25 pages, compile to PDF)
4. **Try It Yourself**: Visit the [experiments repository](https://github.com/sqrtspace/sqrtspace-experiments) 4. **Try It Yourself**: Visit the [experiments repository](https://github.com/sqrtspace/sqrtspace-experiments)
## Contact ## Contact

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@ -505,6 +505,13 @@ Chunked $\sqrt{n}$ & 54.10 $\pm$ 2.71s & 2.41 MB & 122 & 18.3× \\
The 18.3× slowdown aligns more closely with theoretical predictions than our simulated results, demonstrating that real models exhibit the expected space-time tradeoffs when processing is dominated by model inference rather than memory bandwidth. The 18.3× slowdown aligns more closely with theoretical predictions than our simulated results, demonstrating that real models exhibit the expected space-time tradeoffs when processing is dominated by model inference rather than memory bandwidth.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.75\textwidth]{figures/ollama_sqrt_validation.png}
\caption{Validation that our Ollama context chunking follows the theoretical $\sqrt{n}$ pattern. For 14,750 characters of input, we use 122 chunks of 121 characters each, precisely following $\sqrt{n}$ chunking.}
\label{fig:ollama_sqrt}
\end{figure}
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=0.95\textwidth]{figures/ollama_spacetime_results.png} \includegraphics[width=0.95\textwidth]{figures/ollama_spacetime_results.png}

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