From your articles it sounds like this is not merely an ancient conception. You base the conceptual analysis on it, as well as modern fields of knowledge such as mathematics, logic, and more. I have no interest in pinning down Plato's own view, but rather in clarifying the conception that there are non-physical entities, and that there are interactions between physical entities and those metaphysical ones.
It seemed to me that this is a cornerstone in your thought, and therefore I asked for guidance toward further expansion and clarification.
As for the individual Form: Kabbalah claims that a tallit to which tzitzit were attached has become holy in some sense. If the tallit is matter, how can one even discuss its holiness? How is this different from saying that the water is wise or that the fire is arrogant? Therefore it seems that the view is that there is an abstract entity behind each material particular, and regarding it we can claim that it is not holy or holy or undergoes a change of becoming sanctified [and without the assumption that there is an individual Form, we would not be able to speak about sanctifying a specific piece of matter, only about sanctifying matter in general].
And I would ask—if in your opinion my line of thought is mistaken, I would be glad if you would spell out the error.

The discussion of Forms is ancient philosophy. It is true that I make modern use of it. The mathematicians, most of whom are Platonists, are not really engaged with the meaning of this Platonism.

I did not understand what this has to do with Forms. If one says that the tallit became holy, or that some object is holy (the ten degrees of holiness are in the Mishnah, not a Hasidic idea), that means that the material object is holy. I see no reason in the world to assume that there is some Form above it in order to explain such claims. And even if you understand holiness as an ontic state of the thing, that means that a halot of holiness rests upon the object. What does that have to do with the concepts of Forms?

Rests upon? In the article on halot too you used the term "lie upon." What does that mean? How can I explain to myself an interaction between metaphysical entities and matter?
[Of course the ten degrees of holiness are in the Mishnah, but the necessity of understanding this as an ontic state stems from Hasidic or kabbalistic ideas.]

First of all, there is interaction between spirit and matter, and I do not see why there should not be interaction between matter and a halot. Second, where do you see interaction? Holiness is a property of the material body and not in interaction with it. And third, the question whether holiness is ontic or not is unrelated to Hasidism and unrelated to Kabbalah. The simple view in the Talmudic passages and among the medieval authorities (Rishonim) is that this is an ontic reality.
In any case, I do not see any connection to the question of Forms.