The unitrack self-intersection conjecture

Let $\gamma_0$ be an initial curve in the horizontal unitrack construction, and let $\gamma_n$ denote the successive curves for $n\in\mathbb{N}$. The unitrack is the union of these curves. Call $\gamma_0$ trivial when it is the trivial initial curve in this construction. Unitrack self-intersection conjecture. If $\gamma_0$ is not trivial, then the unitrack consisting of the curves $\gamma_n$, where $n\in\mathbb{N}$, has self-intersections. This is presented as a weaker variation of the preceding conjecture and remains open in the supplied text.