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

LCL-832: A Bounded Quantum-Computational Framework for Self-Referential Systems LCL-832 is a bounded quantum-computational framework for self-referential systems, formulated in the Linear Bounded Automaton class and specified on a 2832-dimensional semantic Hilbert space. The framework defines an affine thermalization channel with an explicit Kraus decomposition, a unique fixed point, and exact geometric contraction in trace norm. Its public technical results include asymptotic convergence, a sharp finite-precision threshold T_min = 18 for IEEE double precision, preservation of a 12.17% structural sovereignty gap, genus-5 topological constraints with Euler characteristic χ = -8, a two-level architecture with 10 logical qubits, 822 physical stabilizers, and 36 semantic governance operators, and a metastable effective theory validated on a tested 3-qubit AQS family. In that tested family, the fast mode scales as λ_fast = -(κ + 2γ), the slow leakage mode follows λ_slow ≈ -C∞γ²/κ with C∞ ≈ 5.531, and the framework operating point α = 0.8783 maps to κ/γ ≈ 14.4. The final public record distinguishes between derived results, numerically verified tested-family results, axiomatic/design elements, and open hypotheses. The single stated open problem is a first-principles derivation of the operating point α = 0.8783.