GAM3ARCH is a cognitive framework for ethical engagement, player resonance, and sustainable retention in interactive environments. The architecture models the dynamics between cognitive load, intrinsic motivation, and the horizon of meaning. It introduces WeakBridges as a structural mechanism driving cognitive burnout (incidence ≈0.42) and defines Resonance as a measurable state of balanced, ethical engagement. The framework formalizes design principles for sustainable participation and provides the theoretical foundation for applied methodologies like SpineForge. Keywords: cognitive engagement, player resonance, burnout modeling, ethical design, game analytics, agent-based simulation, motivation dynamics.
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