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% UNITED STATES PATENT APPLICATION
% SOLID STATE MACHINE FOR SELF-REGULATING COMPUTATIONAL SYSTEMS
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% Inventor: Robert A. James
% Filing Date: December 2025
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\begin{center}
\Large\textbf{UNITED STATES PATENT APPLICATION}
\vspace{2em}

\LARGE\textbf{STEADY STATE MACHINE FOR}\\[0.3em]
\LARGE\textbf{SELF-REGULATING COMPUTATIONAL SYSTEMS}
\vspace{1em}

\large\textit{An Adaptive Runtime System Exhibiting}\\
\large\textit{Autonomous Workload Optimization and Deterministic Convergence}
\vspace{2em}

\normalsize
\begin{tabular}{ll}
\textbf{Inventor:} & Robert A. James \\
\textbf{Assignee:} & [To Be Determined] \\
\textbf{Filing Date:} & December 2025 \\
\textbf{Application Type:} & Utility Patent Application \\
\end{tabular}
\end{center}

\vspace{2em}

\noindent\textbf{Technical Field:} Adaptive Virtual Machines, Self-Regulating Computational Systems, Feedback-Loop Control Architectures, Runtime Optimization

\vspace{1em}

\noindent\textbf{Related Systems:} Virtual Machine Runtimes, Adaptive Execution Environments, Embedded Systems, Microkernel Subsystems

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\tableofcontents
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\input{sections/02_field.tex}
\input{sections/03_background.tex}
\input{sections/04_summary.tex}

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% DRAWINGS AND FIGURES
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\FloatBarrier
\section{Brief Description of the Drawings}

The following figures illustrate representative embodiments and experimental
validation of the Solid State Machine architecture. The drawings depict
configuration distributions, mode selection behavior, feedback loop effects,
workload-shape invariance, and performance comparisons between adaptive and
static configurations.

\subsection{Configuration Space Analysis}

\begin{figure}[H]
	\centering
	\includegraphics[width=\textwidth]{ch1_config_distribution.png}
	\caption{\textbf{FIG. 1 -- Configuration Space Distribution.} Performance
	distribution across the static configuration space, illustrating the wide
	variance in execution behavior when feedback loops are configured manually.
	The distribution demonstrates that static configurations produce highly
	variable performance outcomes, motivating the need for autonomous mode
	selection.}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=\textwidth]{ch1_config_ranking.png}
	\caption{\textbf{FIG. 2 -- Configuration Ranking.} Ranking of static
	configurations by mean performance and stability metrics. This analysis
	identifies candidate high-performance configurations that form the basis
	for validated execution modes in the Solid State Machine.}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=\textwidth]{ch1_main_effects.png}
	\caption{\textbf{FIG. 3 -- Main Effects Analysis.} Main effects plot showing
	the influence of individual feedback loops (L1--L7) on overall system
	performance. This factorial analysis reveals which loops contribute most
	significantly to performance improvement and stability.}
\end{figure}

\subsection{Mode Selection and Optimization}

\begin{figure}[H]
	\centering
	\includegraphics[width=\textwidth]{ch2_runoff_boxplot.png}
	\caption{\textbf{FIG. 4 -- Configuration Runoff Comparison.} Box plot
	comparison of candidate top-performing configurations under identical
	workload conditions. This runoff analysis validates that the selected
	execution modes represent genuine performance optima rather than
	statistical artifacts.}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=\textwidth]{ch2_optimality_scores.png}
	\caption{\textbf{FIG. 5 -- Optimality Analysis.} Multi-objective optimality
	scores across configuration candidates, balancing throughput, variance
	reduction, and convergence speed. The Solid State Machine's mode selector
	uses similar multi-criteria evaluation to select appropriate execution modes.}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=\textwidth]{phase_space_portrait.png}
	\caption{\textbf{FIG. 6 -- Optimality Analysis.} Execution heat versus performance parameter traced through configuration space
		during adaptive convergence. The non-retracing path demonstrates state-dependent
		conductance characteristic of memristive dynamics, with approximately 180-degree
		reversals at architectural cache boundaries. Horizontal spreads indicate bimodal
		distributions over dual attractor states at resonance windows.}
\end{figure}
\subsection{Workload Shape Invariance}

\begin{figure}[H]
	\centering
	\includegraphics[width=\textwidth]{ch3_shape1_performance.png}
	\caption{\textbf{FIG. 7 -- Workload Shape Performance (Set I).} Performance
	measurements across the first family of workload shapes, including
	sinusoidal, triangular, and burst-like patterns. The Solid State Machine
	maintains consistent performance regardless of input waveform characteristics.}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=\textwidth]{ch5_shape2_performance.png}
	\caption{\textbf{FIG. 8 -- Workload Shape Performance (Set II).} Performance
	validation across additional workload waveforms demonstrating shape-invariant
	behavior. The system achieves stable throughput across square-wave, sawtooth,
	and compound mixed-pattern workloads.}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=\textwidth]{ch5_cv_comparison.png}
	\caption{\textbf{FIG. 9 -- Coefficient of Variation Analysis.} Comparison
	of coefficient of variation (CV) across workload families, demonstrating
	that the adaptive system maintains low variance regardless of workload
	shape. Low CV indicates predictable, stable execution behavior.}
\end{figure}

\subsection{Adaptive Mode Behavior}

\begin{figure}[H]
	\centering
	\includegraphics[width=\textwidth]{ch4_mode_usage_stacked.png}
	\caption{\textbf{FIG. 10 -- Mode Usage Distribution.} Stacked distribution
	showing how the supervisory mode selector (L8) allocates time across
	different execution modes for various workload families. The Solid State
	Machine autonomously selects appropriate modes without manual intervention.}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=\textwidth]{ch4_l8_vs_static.png}
	\caption{\textbf{FIG. 11 -- Adaptive vs. Static Performance.} Direct
	comparison between the Solid State Machine's adaptive behavior and
	equivalent static configurations. The adaptive system matches or exceeds
	static performance while providing automatic workload adaptation.}
\end{figure}

\subsection{State Vector Dynamics}

\begin{figure}[H]
	\centering
	\includegraphics[width=0.9\textwidth]{fig1_snake_trajectory.pdf}
	\caption{\textbf{FIG. 12 -- State Vector Trajectory.} Representative
	trajectory of the runtime state vector through the execution heat--entropy
	phase space. The hysteresis-like behavior demonstrates that the system
	exhibits memory effects: the current state depends not only on instantaneous
	workload but also on recent execution history. This memristive characteristic
	enables stable convergence to appropriate operating points.}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=0.9\textwidth]{fig2_K_vs_window.pdf}
	\caption{\textbf{FIG. 13 -- Performance Scaling Relationship.} Relationship
	between the stability constant K and the observation window size W, showing
	the scaling law that governs system behavior. The periodic structure reveals
	fundamental resonances in the adaptive architecture.}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=0.9\textwidth]{fig3_FFT_spectrum.pdf}
	\caption{\textbf{FIG. 14 -- Spectral Analysis.} Fast Fourier Transform
	spectrum of state vector dynamics, revealing the characteristic frequencies
	and periodic structures inherent in the Solid State Machine's feedback
	architecture. Dominant spectral peaks correspond to fundamental control
	loop frequencies.}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=0.9\textwidth]{fig4_golden_ratio_penalties.pdf}
	\caption{\textbf{FIG. 15 -- Golden Ratio Interference Pattern.} Performance
	variations showing interference effects at window sizes related to the
	golden ratio $\varphi \approx 1.618$. These patterns demonstrate that the
	system exhibits cache-like resonance behavior governed by mathematical
	constants.}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=0.9\textwidth]{fig5_bimodal_distributions.pdf}
	\caption{\textbf{FIG. 16 -- Bimodal State Distributions.} Distribution of
	state vector measurements showing quantum-analog bimodal behavior. Under
	certain conditions, the system exhibits discrete stable states rather than
	continuous distributions, analogous to quantized energy levels.}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=0.9\textwidth]{fig6_performance_vs_k.pdf}
	\caption{\textbf{FIG. 17 -- Performance Correlation with K.} Correlation
	between the stability constant K and measured performance metrics. This
	relationship enables the mode selector to predict performance outcomes
	based on state vector measurements.}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=0.9\textwidth]{fig7_performance_by_regime.pdf}
	\caption{\textbf{FIG. 18 -- Performance by Operating Regime.} Performance
	breakdown across different operating regimes identified by the workload
	characterization subsystem. Each regime corresponds to distinct feedback
	loop configurations and mode selections.}
\end{figure}


\begin{figure}[H]
	\centering
	\includegraphics[width=0.9\textwidth]{architecture.png}
	\caption{\textbf{FIG. 19 -- System Architecture.} }
\end{figure}

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% DETAILED DESCRIPTION
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\input{sections/06_detailed_description.tex}

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% CLAIMS
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% ABSTRACT OF THE DISCLOSURE
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\section*{Abstract of the Disclosure}
\addcontentsline{toc}{section}{Abstract of the Disclosure}

\begin{center}
\textbf{A STEADY STATE MACHINE FOR SELF-REGULATING COMPUTATIONAL SYSTEMS}
\end{center}

A Steady State Machine (SSM) is disclosed that provides autonomous, self-regulating
control of computational workloads through coordinated feedback loops operating
within a virtual or physical execution environment. The SSM continuously measures
internal runtime metrics and external workload characteristics, derives stability-oriented control signals, and dynamically adjusts system parameters to maintain
an optimized operational state. Unlike conventional virtual machines or runtime
systems that rely on static configuration, manual tuning, or heuristic rules,
the SSM employs a structured state vector, multi-loop feedback controllers, and
a supervisory mode-selection mechanism to converge toward a stable operating
point aligned with the workload's intrinsic behavior. The architecture produces
deterministic, repeatable steady-state behavior while accommodating workload
variability, pipeline turbulence, cache effects, and temporal fluctuations.
Experimental validation across 38,400 runs demonstrates zero variance across
replicates within each configuration, and an exact equilibrium relationship
(K = 1.0) governing resource allocation. The disclosed system can be implemented
in software, firmware, or hardware, and applies to virtual machines, microkernels,
embedded runtimes, or adaptive control subsystems.

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