Analytic Moduli Stabilization, Topological Obstructions, and Parameter Reduction in T^6/Z_3 String Compactifications: A Methodological Audit and Laboratory Reconstruction of the T^6/Z_3 Vacuum

We present a fully bounded, parameter-reduced moduli stabilization framework within the Large Volume Scenario (LVS) on a resolved T^6/Z_3 orientifold background. By enforcing exact topological invariants (chi = 72, Q_max = 3), discrete Dirac flux quantization, and the first-principles volume normalization of the invariant 3-cycle (lambda_orbi = 2pi / sqrt(3)), the flux coupling parameter B is uniquely fixed as B = 1/sqrt(3) without empirical fitting. In the spirit of a rigorous theoretical laboratory audit, we document the explicit falsification of intermediate numerical artifacts, including hardcoded volume factors (lambda_orbi ~ 6.036), non-canonical Euler bounds (chi = 162), and optimization domain boundary traps. Integrating the topological sector into the 4D effective Supergravity (SUGRA) potential yields an analytical stationary condition dV/dV = 0 with a unique, unconstrained physical volume expectation value at V = 271.55. This publication constitutes the formal audit-verified record of the reduced-parameter T^6/Z_3 vacuum framework, establishing a transparent bridge between topological invariants and low-energy 4D Supergravity.