Entropy Chains Driven by Geometric Phases in Riemann Zeta Zeros

We demonstrate a causal chain of entropy-driven structure emerging from geometric phase deviations τn in the nontrivial zeros ρn =1/2 + iγn of the Riemann zeta function. By defining structural amplitude ϕ(n), entropy H(n), and the structure ratio K(n), we uncover a robust derivative chain τn →ϕ(n) →H(n) →K(n) →κ(n) with remarkable statistical coherence. We further validate the reverse reconstruction of ϕ(n) from target K(n), suggesting a stable, geo- metric entropy attractor. Additionally, transfer entropy analysis reveals significant information flow from τn to ϕ(n), highlighting the dynamic nature of the causal chain.