Derivation of the Riemann Hypothesis from the Axioms of the Constraint Network: The Inevitable Consequence of Collision-Rebound Symmetry under the Zero-Point Reference Frame

The Riemann Hypothesis asserts that all non-trivial zeros of the Riemann zeta function lie on the critical line σ = 1/2 in the complex plane. This conjecture, proposed over 160 years ago, remains one of the most important unsolved problems in the history of mathematics. This paper presents a mathematical derivation of the conjecture within the axiom system of Constraint Network Dynamics. The Constraint Network Model is defined by three axioms: the ontology of the universe is energy, energy always moves at the speed of light and possesses a direction, encounters result in collision, and the total energy of the entire system is strictly conserved. The direction of energy takes the zero point as an absolute reference—energy directed toward the zero point is defined as positive-direction return to zero, and energy directed toward the zero point from the opposite side is defined as negative-direction return to zero. This paper proves that the trivial zeros of the zeta function correspond to equal-quantity rebounds—the direct output of the rules, producing no new structures. The non-trivial zeros correspond to the accretion judgment in unequal-quantity collisions—the emergent result of the rules, determining the fluctuation of the prime number distribution. The positive-direction and negative-direction return to zero share the same zero point as a reference frame. This zero-point reference frame enforces the statistical symmetry of the accretion success rate in the positive and negative directions, which in turn enforces the symmetry of the prime number distribution fluctuation about σ = 1/2. Therefore, the fact that all non-trivial zeros of the zeta function lie on σ = 1/2 is an inevitable corollary of the axioms of the Constraint Network. This paper does not claim to provide a traditional analytic number-theoretic proof of the Riemann Hypothesis, but rather, starting from physical axioms, explains why the Riemann Hypothesis holds true.