Leynstrinsic Field Theory: Paper 5 - Quantum State Structure and Hilbert Space Obstruction in Leynstrinsic Field Theory

This paper presents a quantum structural analysis within Leynstrinsic Field Theory, introducing the Leyn Global State Obstruction, whereby gravitational horizons prevent the factorization of the global Hilbert space into independent subsystems. The result implies that globally defined quantum states may not exist in such systems and must instead be described through connectivity-dependent structures. This provides a framework for understanding non-factorizable quantum systems in gravitational contexts and contributes to ongoing efforts in quantum gravity and the foundations of spacetime physics.