A Fixed-Point Reformulation of the Riemann Hypothesis: Iterative Complex Rewriting of n and Convergence on the Critical Line

Version 5.0 — Complete argument with conditional conclusion. We propose a new reformulation of the Riemann Hypothesis based on the iterative complex rewriting of n in the zeta function. The following results are established: (1) the complex rewriting lemma n^(s_n) = n; (2) transformation of zeta(s) with phase factorisation; (3) F(s)·F(1-s) = 1 via Euler's reflection formula; (4) |F(s)| = 1 iff sigma = 1/2; (5) general derivative relation zeta^(k)(s0) = F(s0)·(-1)^k·zeta^(k)(1-s0) for all orders k, verified numerically at 30 decimal places for k=1,2,3. Conditional on the verification of Step 4 of the main theorem — that the ratio of k-th derivatives equals |F(s0)| without circular reasoning — the Riemann Hypothesis is therefore true. Independent verification by the mathematical community is invited. ORCID: 0009-0007-4590-9874