It seems to be a difficult and subtle question. So this is one possibly translation.
My answer is "According to the situation"Why don't we use 知った・知っている?
The scrawny black cat comes to know the world is a tough place after a few slaps by the big grumpy cat.
This must be the definition of an entry or a subentry in the dictionary. I would be 100% sure about my judgement if the entry/subentry had been provided as part of the context and background information (Forum Rule #3). Still I am fairly sure that it is the definition for a word that means "come to know one's limits."2. From 小学館漢和辞典：自分の能力の限界を知る
I can understand the 知る in "子を持って知る親の恩".知る
However, I have also noticed that, some of these examples are not completed sentences although there is a 'period' mark. So the first sentence may be uncompleted.2((理解する))懂得;[経緯を経て]理解;[よしあしなどを]识别.
Anyway, if 清楚 is a stative verb, the Chinese translation is wrong. 知る is always an action verb.As for "自分の能力の限界を知る", according to the Chinese translation, it means 自分の能力の限界が分かっている
The examples are full sentences, all but 知る人ぞ知る. This is an adnominal phrase meaning "known to a select number of people."However, I have also noticed that, some of these examples are not complete sentences although there is a 'period' mark. So the first sentence may be uncompleted.
The non-past form 知る is a result of ellipsis. One could write 知った猫だった but the past marker in the main clause obviates the one in the subordinate clause.The author chose 知る because at that time the cat had not finished the process of 知る yet?
Is there a -ing form for 知る?
At the risk of opening a can of worms, here is a discussion about exceptions to the above.知る is always an action verb.
限界を知っている人 is fine too but note that the stative sense can be captured by 知る in a subordinate clause (or at least in an adnominal/relative clause). In fact, -teiru as the sign of imperfective aspect is a modern thing. Many historical expressions still keep 知る in the older tense/aspect system. Some of them are apparently quotes from the classical literature:In addition, 自分の能力の限界を知る人
A man who knows what he could do and couldn't.