MUSE and Bounded Reflection: Mathematical Foundations of the Reflective Light Cone

This monograph develops the mathematical foundation of bounded reflection in the MOBIUS framework. It treats the Reflective Light Cone not as a physical spacetime claim, but as a constrained admissibility region over questions, answers, reframings, and actions in reflective human-AI systems. The core thesis is that a reflective AI system should not ask, answer, guide, or act merely because it can generate the next move. It should move only within a region where evidence, authority, assimilability, reversibility, ecological stability, and curvature impact remain within bounds. The monograph reconstructs the MUSE stack through information-side, meaning-side, and bundle-duality layers; grounds semantic gain through the Semantic Interface Model; integrates half-step guidance, answer entitlement, and operation entitlement; and states finite stability results under explicit Lyapunov and perturbation-budget assumptions. General claims are marked as conjectures or empirical hypotheses, with falsification conditions and local validation evidence separated from proof-level results.