117 lines
3.8 KiB
TeX
117 lines
3.8 KiB
TeX
%% SCRAP: experiments/campaigns/window_scaling/README
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%% SOURCE: docs/working/experiments/campaigns/window_scaling/README.md
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%% STATUS: CURRENT
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%% FITS: experiments/ch-window-scaling
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%% EDITORIAL: lifted — prose rewritten to press voice
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\section{Window Scaling Experiment: James Law Validation}
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\textbf{Objective:} Empirically validate James Law:
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\[
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\Lambda = \frac{W}{\mathrm{DoF} + 1}
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\]
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where $\Lambda$ is the effective smoothing capacity per degree of freedom,
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$W$ is the rolling window size in bytes, and $\mathrm{DoF}$ is the number
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of active feedback loops (0--7).
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%% PATENT: James Law ($\Lambda = W / (\text{DoF}+1)$) and the window-scaling
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%% invariant are patent-adjacent. Do not draft claims here.
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\subsection{Hypothesis}
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The quantity $K = \Lambda \times (\mathrm{DoF}+1) / W$ should remain
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approximately constant across multiple window sizes, multiple degrees of
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freedom, and diverse workload patterns. $K \approx 1.0$ across all
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conditions validates James Law as a fundamental scaling relationship in
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adaptive computational systems.
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\subsection{Experimental Design}
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\begin{center}
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\begin{tabular}{lll}
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\toprule
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Variable & Levels & Values \\
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\midrule
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DoF & 8 & 0--7 \\
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Window size & 12 & 512, 1{,}024, 1{,}536, 2{,}048, 3{,}072, 4{,}096, \\
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& & 6{,}144, 8{,}192, 16{,}384, 32{,}769, 52{,}153, 65{,}536 \\
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Replicate & 30 & 1--30 \\
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\midrule
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\textbf{Total runs} & & $8 \times 12 \times 30 = 2{,}880$ \\
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\bottomrule
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\end{tabular}
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\end{center}
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Fixed workload: \texttt{init-l8-omni.4th} (the mega-workload combining all
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six L8 workload patterns). Run order is shuffled to eliminate temporal bias.
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Primary metrics: \texttt{ns\_per\_word}, CV. The $K$ statistic is derived
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as $K = \texttt{win\_final\_bytes} / (\mathrm{DoF}+1) / W$.
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\subsection{Validation Criteria}
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\begin{itemize}
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\item $\mathrm{Mean}(K) \in [0.95,\,1.05]$
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\item $\mathrm{Std}(K) < 0.1$
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\item $\max|K - 1.0| < 0.1$
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\end{itemize}
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\subsection{Expected Outcomes}
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\begin{description}
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\item[Scenario A — Law holds.] $K \approx 1.0$ across all conditions.
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James Law validated as a universal scaling relationship. Implication:
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system behavior is predictable and governed by geometric invariants.
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\item[Scenario B — Critical threshold exists.] Law holds for
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$W < W_\text{critical}$, then degrades. A phase transition is
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present (``gravitational collapse''). The prior hypothesis places
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$W_\text{critical} \approx 16{,}384$ bytes ($4 \times W_0$).
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\item[Scenario C — DoF-dependent scaling.] $K$ varies systematically with
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DoF but not randomly. A more complex relationship (logarithmic or
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power-law) governs the system.
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\end{description}
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\subsection{Running the Experiment}
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\begin{lstlisting}[language=bash]
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# Step 1: Generate run matrix
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cd scripts/
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./generate_run_matrix.R
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# Step 2: Pre-build all 96 configurations (~1.5 hours)
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./prebuild_all_configs.sh
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# Step 3: Execute 2,880 runs (~4-5 hours)
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./run_window_sweep.sh
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# Step 4: Analyze
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./analyze_results.R
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\end{lstlisting}
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\subsection{Analysis Plan}
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The R analysis script computes:
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\begin{enumerate}
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\item $K$ for all runs and its distribution by condition (DoF $\times$ window)
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\item ANOVA to assess significance of DoF and window size effects on $K$
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\item The critical window $W_\text{critical}$ where CV exceeds a threshold
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(elbow detection)
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\item Five plots: $K$ vs.\ DoF (faceted by $W$), $K$ vs.\ $W$ (faceted
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by DoF), CV vs.\ $W$ (phase transition), 3D stability surface,
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and $K$-deviation heatmap
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\end{enumerate}
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\subsection{Baseline Validation}
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From prior DoE experiments at the reference window $W_0 = 4{,}096$:
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\[
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\Lambda(\mathrm{DoF}) \times (\mathrm{DoF}+1) = 4{,}096.0 \pm 0.0
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\quad \text{(CV = 0.00\%)}
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\]
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This experiment extends this result to arbitrary window sizes.
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