\section{Convergence: Integrating External Agent Frameworks}\label{sec:convergence}

The preceding sections develop Operon's structural analysis, epistemic topology,
and formal verification foundations. This section summarizes how these tools
extend to external agent orchestration systems through a typed adapter
architecture. A standalone companion paper provides the full treatment, including
implementation details, all 107 examples, and complete TLA+ specification
listings; this section is self-contained but deliberately concise.

\begin{center}
\begin{tikzpicture}[
  layer/.style={draw, minimum width=10cm, minimum height=0.8cm, font=\small},
  >=latex
]
\node[layer, fill=blue!8]  (L5) at (0,3.2) {A-Evolve --- evolution layer};
\node[layer, fill=green!8] (L4) at (0,2.4) {AnimaWorks --- cognitive layer};
\node[layer, fill=yellow!8](L3) at (0,1.6) {AsyncThink --- thinking layer};
\node[layer, fill=orange!8](L2) at (0,0.8) {Ralph\,/\,DeerFlow\,/\,Swarms --- orchestration layer};
\node[layer, fill=red!8]   (L1) at (0,0.0) {Operon --- structural layer};
\end{tikzpicture}
\end{center}

Every adapter produces an \texttt{ExternalTopology}---a framework-agnostic
intermediate representation carrying a source tag, a pattern name, agent
specifications, directed communication edges, and arbitrary metadata. The
analysis pipeline is source-agnostic: \texttt{analyze\_external\_topology()}
consumes any \texttt{ExternalTopology} and applies three of the four epistemic
bounds---error amplification, sequential penalty, and tool density---plus a
topology-mismatch flag to produce topology advice, structural warnings, and
a composite risk score. (Parallel acceleration is computed by the epistemic
layer but not included in the adapter risk score.) Adding a new orchestration target therefore requires
writing a single parse function---no changes to the analysis code.

Four TLA+ specifications verify safety invariants that are difficult to test
exhaustively at the unit level: \emph{TemplateExchangeProtocol} (provenance and
trust monotonicity), \emph{DevelopmentalGating} (irreversible stage transitions
and capability constraints), \emph{ConvergenceDetection} (intervention-count
convergence or HALT), and \emph{EvolutionGating} (monotonic score safety for
A-Evolve's evolutionary loop). Together, these cover the critical safety
boundaries of the convergence stack.

For the complete treatment---including adapter implementation details, template
exchange protocols, memory bridge semantics, TLA+ specification listings, and all
107 worked examples---see the standalone convergence companion
paper.\footnote{\url{https://coredipper.github.io/operon/convergence/}}

A live evaluation harness (Example~107) measures quality, latency, and token
cost across Gemini~API, Claude~CLI, and Codex~CLI providers. Guided
multi-stage pipelines show a consistent $+6.2\%$ quality improvement over
unguided configurations; single-agent CLI execution shows no effect,
confirming that structural guidance helps when there is topology to guide.

\paragraph{Meta-evolution (Phase~C8).}
The meta-harness extends the convergence stack to \emph{evolving} organism
configurations---modes, models, and intervention thresholds---rather than
just running them. A \texttt{FilesystemOptimizer} protocol (distinct from
C7's prompt-level \texttt{EvolutionaryOptimizer}) drives an
\texttt{EvolutionLoop} that maps candidate configs to \texttt{Genome}
objects, evaluates via \texttt{LiveEvaluator}, and persists full execution
traces to a candidate-first filesystem store.

The key scientific finding: Operon's biological abstractions generalize to
the meta-level. The \texttt{Genome} mapping is lossless (${\sim}5$ lines of
flattening logic). The \texttt{EpiplexityMonitor} generalizes across scales
via a pluggable \texttt{DistanceProvider}---\texttt{ConfigHammingDistance}
triggers STAGNANT/EXPLORING transitions identically to embedding cosine
distance. \texttt{DesignProblem} wrapping of evolution steps is natural.
Boundaries: \texttt{feedback\_fixed\_point} does not fit (evolution is not
convergent iteration), and \texttt{TrustRegistry} is overkill for two
proposer strategies.

An Ao~et~al.~\cite{ao2026delegation} test of exogenous signals shows that
rich filesystem context (configs $+$ trace metadata) yields a $3\times$
improvement over compressed history for the LLM proposer ($0.49$ vs
$0.15$), but config-space evolution does not strongly benefit from LLM
reasoning over blind tournament mutation ($0.49$ vs $0.44$). Phase~B
(topology mutations with DAG execution) improved tournament ($0.60$) but
degraded the LLM proposer ($0.36$), confirming that biological abstractions
generalize as \emph{code structure} but not as \emph{optimization
algorithms}. The structural guarantee features---immune systems, epiplexity,
developmental gating---remain the core value proposition.
de~los~Riscos~et~al.~\cite{delosriscos2026categorical} provide a
category-theoretic framework (\textsc{ArchAgents}) that formalizes
Operon's architecture: objects are organisms, morphisms are compilers,
agents are configured instances. A detailed treatment of the C8 findings
appears in the companion meta-evolution paper.
