Namely this definition of 澄ます:

よけいなことを考えないで、その事一つに注意・意識を集中する。

(under 3, http://dictionary.goo.ne.jp/leaf/jn2/131116/m0u/%E3%81%9D%E3%81%AE/).

This seems to be used like ある, e.g. あること ("a certain thing"), not like "that thing"　そのこと, since the noun which その describes isn't referenced anywhere else. Can this be the case?

Checking definitions of 其の 1 to 4 here http://dictionary.goo.ne.jp/leaf/jn2/131116/m0u/%E3%81%9D%E3%81%AE/, none of them seem to fit.

So what does 其の in the 澄ます definition mean here?

Namely this definition of 澄ます:

よけいなことを考えないで、その事一つに注意・意識を集中する。

(under 3, http://dictionary.goo.ne.jp/leaf/jn2/119957/m0u/).

This seems to be used like ある, e.g. あること ("a certain thing"), not like "that thing"　そのこと, since the noun which その describes isn't referenced anywhere else. Can this be the case?

Checking definitions of 其の 1 to 4 here http://dictionary.goo.ne.jp/leaf/jn2/131116/m0u/%E3%81%9D%E3%81%AE/, none of them seem to fit.

So what does 其の in the 澄ます definition mean here?

Namely this definition of 澄ます: よけいなことを考えないで、その事一つに注意・意識を集中する。　 (under 3, http://dictionary.goo.ne.jp/leaf/jn2/131116/m0u/%E3%81%9D%E3%81%AE/).

This seems to be used like ある, e.g. あること ("a certain thing"), not like "that thing"　そのこと, since the noun which その describes isn't referenced anywhere else. Can this be the case?

Checking definitions of 其の 1 to 4 here http://dictionary.goo.ne.jp/leaf/jn2/131116/m0u/%E3%81%9D%E3%81%AE/, none of them seem to fit.

So what does 其の in the 澄ます definition mean here?

Namely this definition of 澄ます:

よけいなことを考えないで、その事一つに注意・意識を集中する。

(under 3, http://dictionary.goo.ne.jp/leaf/jn2/131116/m0u/%E3%81%9D%E3%81%AE/).

This seems to be used like ある, e.g. あること ("a certain thing"), not like "that thing"　そのこと, since the noun which その describes isn't referenced anywhere else. Can this be the case?

Checking definitions of 其の 1 to 4 here http://dictionary.goo.ne.jp/leaf/jn2/131116/m0u/%E3%81%9D%E3%81%AE/, none of them seem to fit.

So what does 其の in the 澄ます definition mean here?