Symbolic Moonshine Part II: Modular Injections and Composite Resonance in Symbolic Fields

This paper extends the symbolic cognition framework developed in Symbolic Moonshine Part I, investigating how modular forms influence symbolic memory dynamics in KN-modulated fields. We introduce modular injections based on the j(τ)-function, mock theta series, and composite symbolic loops incorporating Leech lattice structures. Through simulation, we demonstrate that: Mock theta sequences induce volatility and symbolic instability. The j(τ) modular loop creates a structured, resilient symbolic field. Composite injections (j(τ) + Leech) generate high-stability attractors. Even under phase drift and decay, j(τ) structures retain symbolic coherence. These results further support the hypothesis that Moonshine symmetries—including those of the Monster group and its modular connections—can function as stabilizers in symbolic AI systems. The findings lay groundwork for future unification with gravity, Standard Model symmetries, and memory formation in artificial cognition.