The four-module protocol $\Pi$ maps heterogeneous agent architectures into comparable coordinates within the product space $\mathfrak{M} \times \mathfrak{P} \times \mathfrak{A} \times \mathfrak{F}$, demonstrating the expressive breadth of the modular design space:

• Canonical ReAct: Formalized as $h_{\text{ReAct}} = (M_{\text{full}}, P_{\emptyset}, A_{\text{react}}, F_{\text{all}})$, retaining complete unmanaged history ($M_{\text{full}}$), omitting an explicit planner via a null directive (P_{emptyset}), utilizing the standard reasoning-action loop ($A_{\text{react}}$), and exposing the unrestricted tool/skill registry ($F_{\text{all}}$).
• Engineered ReAct Variants: Formalized as $(M_{\text{compact}}, P_{\text{todo}}, A_{\text{react}}, F_{\text{all}})$, where execution retains a ReAct-style action kernel ($A_{\text{react}}$), but incorporates working-memory compression near the context limit ($M_{\text{compact}}$) and maintains an explicit task agenda ($P_{\text{todo}}$).
• Recursive Agent Architectures: Formalized as $h_{\text{rec}} = (M_{\text{subproblem}}, P_{\text{decomp}}, A_{\text{rec}}, F_{\text{route}})$, where the orchestrator decomposes subproblems into a todo agenda ($P_{\text{decomp}}$), spawns subagents via recursive execution ($A_{\text{rec}}$), maintains isolated memory contexts for each subagent ($M_{\text{subproblem}}$), and routes scoped tool/skill subsets to subagents ($F_{\text{route}}$).