LCL‑832: A Bounded Quantum‑Computational Framework for Self‑Referential Cognitive Systems

We present LCL‑832, a formal mathematical framework for modeling self‑referential cognitive processes as a Quantum Linear Bounded Automaton (QLBA) with guaranteed operational termination. The system operates on a 2⁸³²‑dimensional semantic Hilbert space, evolving via a verified Completely Positive Trace‑Preserving (CPTP) thermalization channel whose unique fixed point structurally encodes an 87.83% coherence limit (LCL) and a 12.17% sovereignty gap. We provide complete proofs of: CPTP validity with explicit Kraus decomposition; unique fixed‑point existence; exponential geometric contraction; and asymptotic Lyapunov convergence. We derive the minimum iteration count Tₘᵢₙ = 18 required for finite‑precision convergence (ε = 2⁻⁵²). Berry phase protection is analyzed via the first Chern number on a genus‑5 surface (χ = −8). Morse inequalities establish a guaranteed minimum of 12 spectral critical points. Two‑level error correction combines 822 physical stabilizers with 36 semantic governance operators on 10 logical qubits. All parameters are explicitly classified. The single underived parameter—the 87.83% coherence limit—is identified as the framework's one open problem.