The Chronotunnel Toroid: A Dust-Free Closed Timelike Curve Construction with Positive-Energy Shells and Helical Interior Topology

We present the Chronotunnel Toroid, a new closed timelike curve (CTC) construction in pure general relativity requiring no exotic matter, no dust envelope, and no cosmological-scale structures. The base geometry is the Chronotunnel vacuum metric [1]: ds2 = −(dt + a dϕ) 2 + dr2 + α 2 r 2 (dϕ − k dz) 2 + dz2 , a helical spinning cosmic string spacetime with frame-dragging parameter a = 4GJ, conical deficit α = 1 − 4Gµs, and helical pitch k. This metric is exactly Ricci-flat (R ρ σµν = 0) for all r > 0, and admits CTCs for r rc carrying spinning shell matter with positive surface energy density σout > 0. The Z2 identification introduces no new boundary surface and performs no surgery on the manifold: the shell Israel conditions are unaffected by an interior identification. The joint parity constraint k + m ≡ 0 (mod 2) on scalar field modes constitutes a structural intervention in the KRW chronology protection mechanism. The construction is stationary and is the natural dust-free companion to Ori’s 2007 dynamical time-machine [2] and the Ori Z_n helical identification program [3] (formerly called "Mobius-Ori").