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@@ -55,7 +55,7 @@ Once published on arXiv:
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1. **Quick Overview**: Read `executive_summary.md` (2 pages)
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1. **Quick Overview**: Read `executive_summary.md` (2 pages)
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2. **Technical Summary**: Read `two_page_summary.tex` (2 pages, compile to PDF)
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2. **Technical Summary**: Read `two_page_summary.tex` (2 pages, compile to PDF)
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3. **Full Paper**: Read `main.tex` (24 pages, compile to PDF)
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3. **Full Paper**: Read `main.tex` (25 pages, compile to PDF)
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4. **Try It Yourself**: Visit the [experiments repository](https://github.com/sqrtspace/sqrtspace-experiments)
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4. **Try It Yourself**: Visit the [experiments repository](https://github.com/sqrtspace/sqrtspace-experiments)
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## Contact
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## Contact
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figures/ollama_sqrt_validation.png
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main.tex
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main.tex
@@ -505,6 +505,13 @@ Chunked $\sqrt{n}$ & 54.10 $\pm$ 2.71s & 2.41 MB & 122 & 18.3× \\
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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.
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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.
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\begin{figure}[htbp]
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\centering
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\includegraphics[width=0.75\textwidth]{figures/ollama_sqrt_validation.png}
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\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.}
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\label{fig:ollama_sqrt}
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\end{figure}
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\begin{figure}[htbp]
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\begin{figure}[htbp]
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\centering
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\centering
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\includegraphics[width=0.95\textwidth]{figures/ollama_spacetime_results.png}
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\includegraphics[width=0.95\textwidth]{figures/ollama_spacetime_results.png}
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ubiquity.pdf
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