%% SCRAP: experiments/02-experiments/heartbeat-doe/design
%% SOURCE: docs/working/experiments/02-experiments/heartbeat-doe/design.md
%% STATUS: WORKING
%% FITS: experiments/ch-heartbeat
%% EDITORIAL: lifted — prose rewritten to press voice
%% NOTE: This is the initial design document, superseded by corrected-design.tex.
%%       Kept as the historical record of Stage 2 design intent.

\section{Heartbeat DoE — Initial Design}
\label{sec:heartbeat-doe-design}

\subsection{Overview}

The heartbeat design-of-experiments experiment constitutes Stage~2 of the
StarForth factorial campaign. Where Stage~1 (3{,}200 runs, six factors, no
heartbeat thread) measured static final-performance metrics, Stage~2
incorporates heartbeat observability to capture \emph{temporal stability}
characteristics: convergence speed, jitter envelope, load-response coupling,
and decay-slope tracking.

\subsection{Design Points}

Stage~2 focuses on the five elite configurations identified by Stage~1
analysis:

\begin{center}
\begin{tabular}{llp{6cm}}
\toprule
\# & Configuration & Key Characteristics \\
\midrule
1 & \texttt{1\_0\_1\_1\_1\_0} & Heat + Decay + Pipelining + Window Inference \\
2 & \texttt{1\_0\_1\_1\_1\_1} & Config~1 plus Decay Inference \\
3 & \texttt{1\_1\_0\_1\_1\_1} & Heat + Rolling Window + Pipelining + both Inferences \\
4 & \texttt{1\_0\_1\_0\_1\_0} & Heat + Decay + Window Inference (lean) \\
5 & \texttt{0\_1\_1\_0\_1\_1} & Rolling Window + Decay + both Inferences (no heat) \\
\bottomrule
\end{tabular}
\end{center}

\subsection{New Metrics}

Stage~2 extends the \texttt{DoeMetrics} struct with approximately 20
heartbeat-specific fields, raising the CSV column count from 38 to
approximately 60:

\begin{center}
\begin{tabular}{llll}
\toprule
Metric & Type & Purpose & Target \\
\midrule
\texttt{tick\_interval\_cv} & double & Jitter coefficient of variation & $< 0.15$ \\
\texttt{tick\_outlier\_ratio} & double & Fraction of ticks $> 3\sigma$ & $< 0.02$ \\
\texttt{decay\_slope\_convergence\_rate} & double & Ticks to slope convergence & $> 50$ \\
\texttt{load\_interval\_correlation} & double & Workload--heartbeat coupling & $> 0.75$ \\
\texttt{settling\_time\_ticks} & double & Ticks to 10\% settling band & $< 1{,}000$ \\
\texttt{overall\_stability\_score} & double & Composite 0--100 score & $> 75$ \\
\bottomrule
\end{tabular}
\end{center}

\subsection{Execution Plan}

Five configurations at 50 replicates each yield 250 total runs, randomised
into a single test matrix to eliminate ordering bias. The experiment is
designed to complete in 2--4~hours.

The composite stability score weights jitter, convergence, and load coupling
equally:

\[
  S = \tfrac{1}{3}\bigl(S_{\text{jitter}} + S_{\text{convergence}}
      + S_{\text{coupling}}\bigr) \in [0, 100]
\]

The configuration with the highest~$S$ becomes the \emph{golden
configuration} for use as the MamaForth production baseline.

\subsection{Note on Subsequent Correction}

This initial design assumed a fixed $\sim$1~ms heartbeat interval and framed
the primary metric as jitter in a fixed tick. A subsequent design review
identified a critical gap: the heartbeat tick interval \texttt{tick\_ns} is
dynamically modulated by the inference engine. The corrected design measures
load-to-heartrate coupling rather than fixed-interval jitter.
See Section~\ref{sec:heartbeat-doe-corrected-design}.