CONSTRUCTING TURING COMPLETE EULER FLOWS IN DIMENSION 3

The uploaded paper proves the exact statement in question. It constructs (i) a C∞ area-preserving disk diffeomorphism, equal to the identity near the boundary, that is Turing complete (Theorem 6.2), and (ii) realizes it as a global disk-like section/return map of a Reeb flow on S^3, then uses the contact–Beltrami correspondence to obtain a stationary Euler flow whose metric equals the round metric outside a solid torus (Theorem 7.1). This directly resolves the problem and supplies the model’s missing ingredient (C). See Theorem 6.2 and Theorem 7.1 in the paper, as well as the contact/Beltrami and realization mechanisms (Theorems 3.2 and 4.1) that mirror the model’s Steps 1–4, including the “round outside a torus” metric claim . The model declares the result “likely open as of cutoff” and leaves the solution conditional on (C), but the paper provides (C) and completes the construction.