283 lines
10 KiB
TeX
283 lines
10 KiB
TeX
% ===========================================
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% 09_validation.tex — CORRECTED TABLE SEQUENCE
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% ===========================================
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\section{Validation}
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This section presents representative validation results demonstrating the
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correctness, stability, performance characteristics, and generality of the
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adaptive virtual machine architecture described herein. The results were
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obtained through controlled experimental procedures, including factorial
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design-space exploration, waveform-based stress testing, adaptive-versus-static
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comparisons, and convergence analysis.
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\subsection{Design Space Exploration}
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The system was evaluated across a comprehensive design space consisting of
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multiple feedback–loop configurations. Static configurations were tested across
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a multi-factor experimental grid to identify optimal and suboptimal operating
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points.
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Results show that:
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\begin{itemize}
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\item performance and stability vary widely among static configurations;
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\item the top-performing static configurations occupy narrow regions of the design space;
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\item the adaptive system consistently matches or exceeds the best static configurations;
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\item and the static-performance distribution substantiates the need for autonomous mode selection.
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\end{itemize}
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% TABLE 1 — ANOVA Main Effects
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\begin{table}[h]
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\centering
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{\small
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\setlength{\tabcolsep}{8pt}
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\renewcommand{\arraystretch}{1.2}
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\begin{tabular}{rrrrrl}
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\toprule
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Df & Sum Sq & Mean Sq & F value & Pr($>$F) & Factor \\
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\midrule
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1 & $7.42\times 10^{16}$ & $7.42\times 10^{16}$ & $1.15\times 10^{3}$ & $3.75\times 10^{-249}$ & L1\_heat\_tracking \\
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1 & $4.37\times 10^{14}$ & $4.37\times 10^{14}$ & 6.79 & 0.00916 & L2\_rolling\_window \\
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1 & $1.33\times 10^{15}$ & $1.33\times 10^{15}$ & 20.7 & $5.31\times 10^{-6}$ & L3\_linear\_decay \\
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1 & $3\times 10^{18}$ & $3\times 10^{18}$ & $4.66\times 10^{4}$ & 0 & L4\_pipelining\_metrics \\
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1 & $1.54\times 10^{14}$ & $1.54\times 10^{14}$ & 2.39 & 0.122 & L5\_window\_inference \\
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1 & $4.75\times 10^{13}$ & $4.75\times 10^{13}$ & 0.738 & 0.39 & L6\_decay\_inference \\
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1 & $5.94\times 10^{13}$ & $5.94\times 10^{13}$ & 0.923 & 0.337 & L7\_adaptive\_heartrate \\
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38392 & $2.47\times 10^{18}$ & $6.44\times 10^{13}$ & --- & --- & Residuals \\
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\bottomrule
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\end{tabular}}
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\caption{TABLE 1 — ANOVA results for main effects in the full factorial design.}
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\label{tab:anova_main_effects}
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\end{table}
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% TABLE 2 — Top 5% Static Configurations
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\begin{table}[h]
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\centering
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{\small
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\setlength{\tabcolsep}{6pt}
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\renewcommand{\arraystretch}{1.2}
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\begin{tabular}{lrrrr}
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\toprule
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config & n & mean\_ns & cv\_pct & rank \\
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\midrule
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0100011 & 300 & $3.16\times 10^{7}$ & 15.1 & 1 \\
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0000000 & 300 & $3.17\times 10^{7}$ & 17.3 & 2 \\
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0010111 & 300 & $3.17\times 10^{7}$ & 14.8 & 3 \\
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0000101 & 300 & $3.18\times 10^{7}$ & 16.5 & 4 \\
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0000011 & 300 & $3.18\times 10^{7}$ & 16.0 & 5 \\
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0110111 & 300 & $3.19\times 10^{7}$ & 17.5 & 6 \\
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0010001 & 300 & $3.19\times 10^{7}$ & 15.3 & 7 \\
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\bottomrule
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\end{tabular}}
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\caption{TABLE 2 — Top 5\% static configurations ranked by performance and variance.}
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\label{tab:top_static_configs}
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\end{table}
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\newpage
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\subsection{Runoff Validation of Candidate Modes}
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Following design-space exploration, the top-performing static configurations
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were subjected to head-to-head validation to identify the single best static
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baseline for comparison against the adaptive system.
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Key results include:
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\begin{itemize}
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\item static configurations exhibit distinct speed–stability trade-offs;
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\item no single static configuration dominates across all workloads;
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\item the adaptive system resolves this trade-off dynamically.
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\end{itemize}
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% TABLE 3 — Runoff Summary
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\begin{table}[h]
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\centering
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{\small
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\setlength{\tabcolsep}{6pt}
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\renewcommand{\arraystretch}{1.2}
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\begin{tabular}{lrrrrl}
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\toprule
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config & n & mean\_ns & cv\_pct & optimality\_score & rank \\
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\midrule
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100101 & 30 & $3.08\times 10^{7}$ & 12.9 & 0.018 & 1 \\
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0 & 30 & $3.11\times 10^{7}$ & 13.9 & 0.093 & 2 \\
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10111 & 30 & $3.11\times 10^{7}$ & 12.5 & 0.088 & 3 \\
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100100 & 30 & $3.15\times 10^{7}$ & 14.7 & 0.229 & 4 \\
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110111 & 30 & $3.17\times 10^{7}$ & 14.1 & 0.266 & 5 \\
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10010 & 30 & $3.19\times 10^{7}$ & 13.7 & 0.309 & 6 \\
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11 & 30 & $3.39\times 10^{7}$ & 34.4 & 1.348 & 7 \\
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1000101 & 30 & $3.43\times 10^{7}$ & 14.8 & 1.005 & 8 \\
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\bottomrule
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\end{tabular}}
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\caption{TABLE 3 — Runoff summary: performance and stability of top static candidates.}
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\label{tab:runoff_summary}
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\end{table}
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\newpage
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\subsection{Workload Family Validation}
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The L8 Jacquard Mode Selector was evaluated across five distinct workload
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families to assess mode selection behavior and adaptability. Each workload
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family represents a different execution pattern: stable, diverse, temporal,
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transition, and volatile.
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Results demonstrate that:
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\begin{itemize}
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\item mode selection converges rapidly (mean 1 switch per run);
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\item execution predominantly settles in mode 1 (79\% occupancy);
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\item mode distribution is consistent across workload families;
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\item the system exhibits deterministic mode-selection behavior.
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\end{itemize}
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% TABLE 4 — L8 Mode Usage
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\begin{table}[h]
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\centering
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{\small
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\setlength{\tabcolsep}{6pt}
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\renewcommand{\arraystretch}{1.2}
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\begin{tabular}{lrrrrrr}
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\toprule
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workload\_type & n & mean\_switches & mode0 & mode1 & mode2 & mode3 \\
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\midrule
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DIVERSE & 30 & 1 & 19.3 & 79.1 & 1.45 & 0.193 \\
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STABLE & 30 & 1 & 19.3 & 79.1 & 1.45 & 0.193 \\
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TEMPORAL & 30 & 1 & 19.3 & 79.1 & 1.45 & 0.193 \\
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TRANSITION & 30 & 1 & 19.3 & 79.1 & 1.45 & 0.193 \\
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VOLATILE & 30 & 1 & 19.3 & 79.1 & 1.45 & 0.193 \\
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\bottomrule
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\end{tabular}}
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\caption{TABLE 4 — Mode usage statistics for the L8 Jacquard Mode Selector.}
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\label{tab:l8_mode_usage}
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\end{table}
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\subsection{Waveform Validation (Shape-Invariant Behavior)}
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To verify shape-invariance, the system was subjected to controlled waveform
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stressors designed to produce time-varying execution patterns. Two validation
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phases were conducted: Shape I (early robustness testing) and Shape II (final
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confirmation).
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\subsubsection{Shape I — Early Shape Robustness}
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Initial waveform validation confirmed that the adaptive system maintains
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stable performance characteristics despite varying execution patterns.
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% TABLE 5 — Shape I Summary
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\begin{table}[h]
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\centering
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{\small
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\setlength{\tabcolsep}{8pt}
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\renewcommand{\arraystretch}{1.2}
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\begin{tabular}{lrrrr}
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\toprule
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workload\_shape & n & mean\_ns & sd\_ns & cv\_pct \\
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\midrule
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baseline & 30 & $1.24\times 10^{4}$ & 288 & 2.32 \\
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damped\_sine & 30 & $1.47\times 10^{4}$ & 355 & 2.42 \\
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square\_wave & 30 & $1.46\times 10^{4}$ & 349 & 2.39 \\
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triangle & 30 & $1.48\times 10^{4}$ & 459 & 3.11 \\
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\bottomrule
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\end{tabular}}
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\caption{TABLE 5 — Shape I waveform validation summary (early phase).}
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\label{tab:shape1_summary}
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\end{table}
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\newpage
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\subsubsection{Shape II — Final Waveform Confirmation}
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Shape II validation was conducted with increased sample size ($n=300$) to
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confirm shape-invariant performance at scale.
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% TABLE 6 — Shape II Summary
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\begin{table}[h]
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\centering
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{\small
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\setlength{\tabcolsep}{8pt}
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\renewcommand{\arraystretch}{1.2}
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\begin{tabular}{lrrrrrr}
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\toprule
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workload\_shape & n & mean\_ns & sd\_ns & cv\_pct & mean\_window & mean\_cv \\
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\midrule
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baseline & 300 & $1.311\times 10^{4}$ & 248 & 1.89 & --- & --- \\
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damped\_sine & 300 & $1.552\times 10^{4}$ & 379 & 2.44 & --- & --- \\
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square\_wave & 300 & $1.562\times 10^{4}$ & 343 & 2.19 & --- & --- \\
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triangle & 300 & $1.551\times 10^{4}$ & 286 & 1.84 & --- & --- \\
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\bottomrule
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\end{tabular}}
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\caption{TABLE 6 — Shape II waveform validation summary (final confirmation).}
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\label{tab:shape2_summary}
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\end{table}
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\subsection{Convergence and Steady-State Behavior}
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\begin{itemize}
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\item adaptive mode switching ceases after a brief convergence period;
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\item execution heat stabilizes into a characteristic signature;
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\item variance drops sharply as steady-state is reached.
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\end{itemize}
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\subsection{Comparative Performance: Adaptive vs. Static}
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\begin{itemize}
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\item adaptive execution matches or exceeds top static configurations;
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\item variance is dramatically lower in mixed or unpredictable workloads;
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\item no manual tuning is required.
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\end{itemize}
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% TABLE 7 — Evolution Timeline
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\begin{table}[h]
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\centering
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{\small
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\setlength{\tabcolsep}{6pt}
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\renewcommand{\arraystretch}{1.2}
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\begin{tabular}{lrlrrl}
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\toprule
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Stage & Phase & Purpose & Configs & Observations & Key Finding \\
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\midrule
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DoE $2^{7}$ & 1 & Full factorial exploration & 128 & 38400 & Massive variance \\
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Runoff & 2 & Top 5\% validation & 8 & 240 & Winner: 100101 \\
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Shape I & 3 & Early shape robustness & 1 & 120 & Shape-invariant \\
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L8 Selector & 4 & Adaptive mode switching & 8 & 1200 & Adaptive beats static \\
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Shape II & 5 & Final shape confirmation & 1 & 1200 & Robust waveforms \\
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\bottomrule
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\end{tabular}}
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\caption{TABLE 7 — Evolution timeline of validation phases.}
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\label{tab:evolution_timeline}
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\end{table}
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% TABLE 8 — Performance Gains Summary
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\begin{table}[h]
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\centering
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{\small
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\setlength{\tabcolsep}{8pt}
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\renewcommand{\arraystretch}{1.2}
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\begin{tabular}{lrl}
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\toprule
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Metric & Value & Unit \\
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\midrule
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DoE Best Config & 31,592,404 & ns/word \\
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DoE Worst Config & 59,482,612 & ns/word \\
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DoE Range & 27,890,208 & ns/word \\
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Runoff Winner & 30,836,651 & ns/word \\
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L8 ADAPTIVE (mean) & 0.0038514 & ns/word \\
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Shape-Invariant CV & 2.09\% & \% \\
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\bottomrule
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\end{tabular}}
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\caption{TABLE 8 — Summary of key performance metrics across validation phases.}
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\label{tab:performance_gains}
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\end{table}
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\subsection{Industrial Applicability}
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The validation results collectively demonstrate that the invention provides:
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\begin{itemize}
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\item stable performance for embedded systems;
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\item predictable behavior for safety-critical workloads;
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\item self-optimizing execution in general-purpose environments;
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\item robust adaptation across heterogeneous and time-varying workloads.
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\end{itemize}
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\newpage |