\section{Related Work}\label{sec:related}

\paragraph{Reflective-evolution prompt optimization.}
GEPA~\cite{agrawal2025gepa} evolves text components via
reflection-driven mutation over a Pareto front.  Earlier work on
prompt-optimization for LLMs (OPRO~\cite{yang2024opro},
APE~\cite{zhou2022ape}) uses scalar reward or rank-based comparison
as the primary evaluator signal; feedback is either absent or
free-form output from a grading LLM.  Our paper tests whether
replacing that scalar channel with a constrained, formal-predicate
verifier changes mutation efficiency in the reflective branch.

\paragraph{Verifier-guided LLM generation.}  Outcome verification has
been used to filter, rerank, or constrain LLM outputs in program
synthesis, math, and theorem proving.  The signal there is typically
used \emph{outside} the optimization loop --- as a final gate or as
part of best-of-$N$ selection.  Our work differs in using verifier
output as the optimizer's \emph{inner-loop} score, driving which
candidates the reflection model sees and how.

\paragraph{Operon certificates.}  The Operon project~\cite{banu2026operon}
exposes a registry of theorems with associated verify functions
(e.g.\ \texttt{behavioral\_stability\_windowed},
\texttt{behavioral\_quality}) over structural and behavioral
predicates drawn from biological agent designs.  A certificate
records the theorem name, parameters, a conclusion, and a source
trace; \texttt{verify()} re-derives the predicate from parameters and
returns \texttt{(holds, evidence)}.  The evidence dictionary is what
this paper's treatment arm feeds to GEPA's reflection LM as
obligation text.

\paragraph{DSPy and GEPA integration.}  DSPy~\cite{khattab2024dspy}
provides a compile abstraction for LLM programs that can host
GEPA-evolved components via the \texttt{DSPyFullProgramAdapter}.  We
do not use DSPy here --- our candidate is a single text component
rather than a program --- but the same certificate mechanism could
bind to DSPy compile artifacts in a follow-up experiment (Theorem~2
of the companion memo).

\paragraph{Agent2Agent (A2A) protocol.}  The A2A
specification~\cite{a2a2025} is a JSON-RPC-2.0 interoperability
layer that defines \texttt{Message} objects with polymorphic
\texttt{Part} payloads.  The companion memo proposes a canonical
\texttt{DataPart} schema for Operon certificates.  The paper-6
experiment does not exchange certificates over A2A wire, but every
candidate score reported here is in principle serializable as such a
\texttt{Part}.
