Uniform Non-Vanishing of Ramanujan's Mock Theta Functions at Odd Roots of Unity

This paper proves a uniform non-vanishing theorem for Ramanujan’s mock theta functions at all primitive odd roots of unity. Using only Appell-Lerch collapse and cyclotomic independence, the author shows that the radial limits of all order-3, order-5, and order-7 mock theta functions are finite and nonzero at these points. The argument avoids case-by-case analysis and heavy modular machinery, consolidating scattered results into a single, elementary proof. Numerical checks confirm the non-vanishing behavior across small odd moduli. The result has implications for cyclotomic persistence, entropy floors in odd-cycle lattices, and coherence stability in quantum and cosmological systems.