  This paper is a Response to Professor J.H.H. Perk's recent Comment
(arXiv:1209.0731v1). We point out that the singularities of the reduced free
energy {\beta}f, the free energy per site f and the free energy F of the 3D
Ising model differ at {\beta} = 0. The rigorous proof presented in the Perk's
Comment is only for the analyticity of the reduced free energy {\beta}f, which
loses its definition at {\beta} = 0. Therefore, all of his objections lose the
mathematical basis, which are thoroughly disproved. This means that the series
expansions cannot serve as a standard for judging the correctness of the exact
solution of the 3D Ising model. Furthermore, we note that there have been no
comments on the topology-based approach developed by Zhang for the exact
solution of the 3D Ising model. A Rejoinder to Professor J.H.H. Perk's open
letter in arXiv:1209.0731v2 is added. We show that the analyticity in {\beta}
of both the hard-core and Ising models is proved for {\beta} > 0, not for
{\beta} = 0. Furthermore, the free energy per site f and the reduced free
energy {\beta}f lose their definitions at {\beta} = 0, and thus either of them
could have two different forms for high-temperature series expansions at/below
infinite temperature. Three independent Virasoro algebras for 3D conformal
field theory can be written within the 3+1 dimensional space (i.e., 3-sphere)
with weight factors.
