1Cademy - Four-Module Factorization of Canonical and Recursive Agent Scaffolds

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Four-Module Factorization of Canonical and Recursive Agent Scaffolds

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 ( $F_{\text{route}}$ ).

Updated 2026-10-02

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