Analyticity of the giant-component fraction away from the critical point

Let $\rho(c)$ denote the giant-component fraction as a function of the scaling parameter $c$, and let $c_0$ be the critical value. Theorem5(i) establishes analyticity under condition (t5a). Analyticity conjecture. Theorem5(i) holds without condition (t5a): $\rho(c)$ is always analytic except at $c_0$. This is proposed as an extension of Theorem~5(i); the supplied text gives no resolution status.