QVM-10G Ω v13.1: A Semantically Correct Tensor-Network Quantum Virtual Machine with Formal Routing Invariant Preservation

QVM-10G Ω v13.1 introduces a formal semantic routing invariant for tensor-network quantum simulation under nearest-neighbor constraints. This work proves that routed non-local controlled operations preserve exact logical operator identity through permutation-aware logical tracking and dual-operator CNOT selection, guaranteeing: P_R^ U_phys P_R ≡ CX(q_c, q_t) The system eliminates silent control-target inversion failures commonly produced by naive SWAP-based routing in Matrix Product State (MPS) simulators. Empirical validation across Bell, GHZ, QFT, Clifford, deep-circuit, and ablation benchmarks demonstrates fidelity preservation of 1.000000 under semantic routing, compared to catastrophic fidelity collapse as low as 0.500000 under naive routing. The implementation operates under strict bounded-memory execution (10 GB ceiling) with formal correctness treated as a first-class invariant rather than an implementation detail.