A Constructive Proof Program for the Riemann Hypothesis/黎曼猜想构造性证明纲领

This paper presents a constructive proof program for the Riemann Hypothesis (RH) within the NCDFT (Non-Commutative Discrete Fourier Transform) framework. The core logic is a Double-Locking Mechanism: First Lock (Necessity): Via Carleman's criterion, we prove that only when the parameter \alpha=1/2 is the Jacobi operator J_\alpha essentially self-adjoint, forcing its spectrum onto the critical line \Re(s)=1/2; Second Lock (Sufficiency): Via functorial fidelity (Weil explicit formula), only \alpha=1/2 yields zero arithmetic-spectral distance (d_{\text{spec}}=0), ensuring the operator spectrum coincides exactly with the Riemann \zeta zeros.The key discovery is the intrinsic weight function w_\alpha(x) and its topological singularity: for \alpha \neq 1/2, the measure has non-compact support (recurrence coefficients a_n \sim \sqrt{n}), yielding sublinear Carleman sums (non-self-adjoint); for \alpha = 1/2, the measure compactifies (a_n \to \text{const}), yielding linear growth and essential self-adjointness. This geometric-spectral phase transition is intrinsic, requiring no external regularization.We establish a seven-fold inequality system (constructive with computable error bounds) and provide numerical validation via FFT (100% match for the first 30 zeros), confirming the explicit formula-spectrum correspondence. Physical Closure version:https://doi.org/10.5281/zenodo.18670983