We present a complete proof of the Riemann Hypothesis derived from the Emergence-Convergence Framework (ECF). Starting from the unique ontological postulate that existence is correlation, we construct a prime implication network based on quadratic reciprocity and extract a positive-definite kernel through ECF's metricization operations. The network satisfies the configuration hypothesis, hence its correlation strength λ necessarily converges to the self-dual fixed point λ = 1/2 under the gradient flow of ECF III. A trace formula linking the kernel's spectrum to the zeros of Dirichlet L-functions is rigorously established for β > 1 and then analytically continued to the physical critical point β = 1/2 by contour deformation. The spectral self-duality at λ = 1/2, derived from the Triple Extremum Theorem of ECF IV, forces all non-trivial zeros of the Riemann zeta function onto the critical line Re(s) = 1/2. This work establishes that, within the ECF axiomatic system, the Riemann Hypothesis is a rigorously derived theorem. All technical estimates—including uniform Perron formula error bounds, contour decay estimates, and character sum collapse via Burgess bounds—are provided in full within the appendices.
Pengtai Huang (Wed,) studied this question.