Can the auxiliary verb Vteみる along with Vteいる i.e. Vteみている make the imperfect verb into a perfect verb

Question

I just got a hang of Vteいる form, and was studying Vteみる and I wanted to ask whether, the Vteみる form causes the imperfect verb to become perfect (for that purposes).

Background of the concept ている:

Before going into the details let me clear that I am saying those verbs to be imperfect which can have a continuous state with Vteいる form, e.g. 食べている 、見ている、歩いている etc. These verbs take the continuous form after the Vteいる because they are imperfect in a sense, and can be continued.

Further, I am classifying those verbs (both transitive and intransitive) to be perfect, which take perfect tense, when Vteいる is used example 行っている (he has gone.. somewhere and is still there)、死んでいる　（has died) 、送っている (have send) etc. These verbs take the the perfect tense form.

As per my inference (please correct me if I am wrong or lagging), the reasoning is that, once these verbs are performed (once) or partly are performed, they are complete and cannot be further performed (in continuation of that action, as they are complete in one moment i.e. instantly, e.g. once the person is dead, he achieves the stage of death and cannot further, perform the action of death in continuation, as the moment that thing acted he died or achieved the goal of the verb (instantly)). In other words, they are punctual verbs (for those who already have studied this topic).

てみる and imperfect verb:

While I was studying てみる, I inferred that (not sure if I am correct, please correct me if I am wrong), this form is was showing more or less the punctual characteristic i.e. the moment the person has (even partly completed) done that action for the first time then the action is complete. Now if we apply it to the the stage of "trying". This stage occurs only when the person has actually performs the main action. Further, the person can do the action (of trying) only at the time the main action is performed. That is to say, that once the main action is performed then only the stage of "try" will exist and end as well i.e. it will be instantaneously be completed. (like the punctual verb 試す). In other words, the stage of "trying" will never exist as the action will be instantaneously be performed once it is tried.

For explaining it further, I will use an example; 

So, if I use this auxiliary (i.e. てみる) with 食べて and if we look at the action closely, the stage of try will only exist when the person has, put the food in his mouth (not before that). Now, once he has put the food in the mouth in that moment itself the action of trying will be complete (as he has tried it) i.e. it will be punctual because he cannot perform "to try eat(to see how it is like) " again in a series i.e. continuation, as he has already achieved the state of trying and he knows how it is (though the action eat can still continue). (like the verb 試す (to try) has perfect form with ている)

Following are my question, after considering the above-mentioned reasoning:

1. Can てみる take ている and form Vてみてみる e.g. 食べてみている and in other verbs as well.
2. Can てみる make the imperfect verb like other punctual verbs?
3. If question number 2 is affirmative, whether, the form 食べてみている will be present perfect i.e. I have eaten it (and have seen what it is like)?
4. If question 2 is in negative, will てみている for a verb meaning trying to see what it is like e.g. 食べてみている i will eat or I eat (for trying to see what is like)?

Following are the resources that, I referred to get that understanding of ている:

https://japanese.stackexchange.com/questions/3122/when-is-v%E3%81%A6%E3%81%84%E3%82%8B-the-continuation-of-action-and-when-is-it-the-continuation-of-state


https://www.quora.com/How-do-I-distinguish-the-different-meanings-of-the-teiru-%E3%81%A6%E3%81%84%E3%82%8B-form-in-Japanese-e-g-%E4%BB%8A%E5%AF%9D%E3%81%A6%E3%81%84%E3%82%8B-%E4%BB%8A%E9%96%8B%E3%81%84%E3%81%A6%E3%81%84%E3%82%8B

https://www.mamori.com/Sugita2009.pdf

https://www.researchgate.net/profile/Yasuhiro_Shirai2/publication/227647906_The_Acquisition_of_Tense-Aspect_Marking_in_Japanese_as_a_Second_Language/links/5a750d1b45851541ce56673b/The-Acquisition-of-Tense-Aspect-Marking-in-Japanese-as-a-Second-Language.pdf?origin=publication_detail

Answer 1

the reasoning is that, once these verbs are performed (once) or partly are performed, they are complete and cannot be further performed

This is awesome inference... You thought there are 2 types of verbs at least, one is quite performable/redoable and the other is not, right?

One thing, we also use 食べている、見ている、歩いている as a perfect form(and not continuous) depending on the context. For example, 「私は以前あのレストランで食べている」 meaning 'I have ever eaten it at that restaurant.'

Similary, we also use 行っている、 送っている as imperfect form(and continuous) depending on the context. For example 「今コンビニに行っています！」 "Now I'm going to a convenience store!", 「今ファイル送っています！」 "Now I'm sending the file!"

I would suggest that you think every verb has multiple meaning in Vている form basically.

However, your classification could be helpful to detect which meaning sounds natural under the least context. Japanese native sometimes refrain from using Vている form to avoid meaning confusion. We use 「食べたことがある」 rather than 「食べている」 to simply tell 'I have ever eaten it.' because 食べている sounds more 'be eating'. That's probably because of the difference between 'Type 1: action/event verbs ' and 'Type 2: change-in-state verbs' as explained here https://japanese.stackexchange.com/a/3140/38911. Although some verbs are very subtle to be classified like 送る.

While I was studying てみる, ..., this form is was showing more or less the punctual characteristic

This is very interesting for me. As you said, once we try something, it's completed (it has un-redoable feature). But in my sense, "てみる" has also certain period of time. In examples like 食べてみる(try eating) and はたらいてみる(try working), 'trying' phase will be kept until the subject get something on the experience.

Can てみる take ている and form Vてみてみる e.g. 食べてみている and in other verbs as well.

Surely yes!!

In this case, I think Vてみている got more common to lead the continuous meaning.
For example, 「納豆を食べてみている」 is much easier to interpret as "I started to try eating Natto." than "I have ever tried Natto."

Thus, along with the guideline https://japanese.stackexchange.com/a/3140/38911, "試す" and "試みる" may be classified Type 1.

Can てみる make the imperfect verb like other punctual verbs?

question number 2 is affirmative, whether, the form 食べてみている will be present perfect i.e. I have eaten it (and have seen what it is like)?

If question 2 is in negative, will てみている for a verb meaning trying to see what it is like e.g. 食べてみている i will eat or I eat (for trying to see what is like)?

As I explained above, '食べてみている' surely has a meaning of '食べてみているところ' or '食べてみている最中' (In the middle of trying phase).

Moreover, 「納豆を食べてみる。」「納豆を食べてみようと思う。」 can be translated as "Let me try Natto." and "I'll try to eat Natto." These are examples using "てみる" alone. There is no perfect meaning.

Lastly, てみた (past tense of てみる) certainly has a perfect meaning like '納豆を食べてみましたか？' means "Have you tried Natto?"

I'm sorry if I missed something important of your question!!