The Riemann Hypothesis, a core unsolved problem in number theory, asserts that all nontrivial zeros of Riemann's zeta function lie on the critical line of the complex plane. This paper proposes an axiomatic theory of RDSUT (symmetric equivalence, derived generation, singularity completion, and closed-loop reduction) based on the E₈ exceptional Lie group. By constructing an 8-dimensional orthogonal embedding of A₂ subsystems to form an E₈ root system, we prove the discrete-continuous duality theorem and rigorously derive the equivalence between the E₈ fundamental scale and the Riemann critical line, ultimately completing a geometric equivalence proof of the Riemann Hypothesis. All conclusions are supported by rigorous mathematical derivations and numerical experiments (30 A₂ subsystems constructing an 180-dimensional truncated E₈ version with constant discretization error and precise fundamental scale of 1/2), forming a complete logical closed loop of "axioms-constructions-theorems-validation-proofs." The construction logic, fundamental scale, and discrete-continuous duality of the truncated version are entirely consistent with the complete E₈ (40 A₂ subsystems, 240 root vectors), demonstrating that the conclusions can be directly generalized to the complete E₈. The innovations of this paper include: (1) Establishing an orthogonal embedding construction method between A₂ subsystems and the E₈ Lie group; (2) Proposing the RDSUT axiomatic system to standardize the geometric structure of E₈; (3) Revealing the geometric origin of the Riemann critical line in E₈; (4) Providing a proof path that combines theoretical rigor with experimental reproducibility.