In Section \[sec-initial\], we prove that our assumptions are not vacuous; i.e., we show that the open subset of initial data satisfying the Closeness Assumptions is not empty.

We clarify the relationship between Kähler geometries and the \[${\mathcal}S^2\tilde\times{\mathcal}S^2$\]-warped Berger geometries in Section \[SingularityModel\]. Also in that section, we provide some background information about the blowdown soliton.

In the remainder of this paper, we prove a sequence of Lemmata and Corollaries that combine to establish the following result:

There exists a nonempty open set of non-Kähler metrics on ${\mathcal}S^2\tilde\times{\mathcal}S^2$ (contained in the \[${\mathcal}S^2\tilde\times{\mathcal}S^2$\]-warped Berger class, and satisfying the Closeness Assumptions) such that any Ricci flow solution originating from this set has the following properties:

1.  Inequalities (a)–(d) in the Closeness Assumptions are preserved by the flow.

2.  The solution develops a Type-I singularity at $T<\infty$, with $|{\mathcal}S^2_-(T)|=0$.

3.  Every blow-up sequence $\big({\mathcal}S^2\tilde\times{\mathcal}S^2,G_k(t),p\big)$ with $p\in{\mathcal}S^2_-$ subconverges to a Kähler singularity model that is the blowdown shrinking soliton $({\mathcal}L^2_{-1},h)$.

The set-up {#sec:evolve}
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Topology and geometry
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In [@IKS14], we study “warped Berger” metrics which take the form $$\label{metric-standard}
 G = {{\mathrm}{d}s}{\otimes}{{\mathrm}{d}s}+\Big\{f^2\,\omega^1{\otimes}\omega^1
       + g^2\big(\omega^2{\otimes}\omega^2
       + \omega^3{\otimes}\omega^3\big)\Big\}$$ on $[s_-,s_+]\times{\mathrm}{SU}(2)$, where $\{ \omega^1, \omega^2, \omega^3\}$ constitutes a one-form basis for ${\mathrm}{SU}(2)$, where $s(x,t)$ denotes arclength 