The Non-Locality of Extendability: An Impossibility Theorem for Bounded Information Systems, with Applications to Generative Sequential Systems

Forward-case specialization of the Projection Insufficiency Theorem (PIT) for generative sequential systems. Introduces the Non-Observability of Extendability (NEO) theorem and the explicit adversarial divergence-kernel construction — the arithmetic-witness machinery on which the remainder of the program's policy-level impossibility arguments build. Abstract Generative sequential systems — language models, planning agents, and reinforcement learning policies — construct trajectories step by step. At each step, an action is selected based on locally available information, under the implicit assumption that locally valid choices can be assembled into globally valid outcomes. In environments governed by non-local…