Before I speak on the veridicality (eh?) of the POTV, I am writing up a summary that I want the OP to approve. Please tell me if this summary suffices.
"The point towards which ‛Allāmah Tabātabā’ī draws attention is that the proposition “There is a reality,” and the proposition “Sophistry is void,” have eternal necessity. That is, the modality of these propositions is not attributive, conditional, or essential necessity. Acceptance of this claim, like acceptance of reality, needs mere drawing of one’s attention (tanbīh). In other words, just as the entertainment of the concept of reality is sufficient to acknowledge its truth, the conception of the notion of eternal necessity of reality is sufficient for accepting its validity. A human being cannot accept sophistry in any situation or condition, since situations and conditions are realities, which attest to the invalidity of sophistry, which is the negation of reality."
Something exists.
"Should reality be annihilated in a specific condition—in a beginning, or an end, or in any particular supposition—then only two situations are conceivable. The first is that its annihilation is not real, and an equivocal or false claim has been made that reality is annihilated. In this case, reality is preserved and it has not been annihilated. The second is that its annihilation is true; that is, reality has really been annihilated. In this supposition, again, the affirmation of the basic reality is acknowledged, since the supposition asserts that reality has really been destroyed; therefore, as a real phenomenon, the destruction of reality reflects the real presence of reality. Therefore, the falsehood of sophistry and veridicality of reality is well secured in every perceivable supposition; and a single instance of reality’s destruction is inconceivable."
If the statement "something is real" is claimed to be false, the claim is either true or false. If false, then the statement "something is real" still stands. If "true," the existence of the claimant negates the claim; the claimant exists, and therefore something is real.
"A proposition, which negates reality, is a proposition, that neither its veridicality can be related in any supposition, nor its falsehood could ever be doubted. That is, its utterance always presupposes its own falsity. On the other side of the spectrum, it is impossible to doubt the meaning of the proposition, which affirms reality, because dismissing it as meaningless or doubting its meaning entails the affirmation of reality."
Any claim that nothing is real is undoubtedly false.
"If, like a finite being, reality lacked eternal necessity and its necessity were conditional, say, with the continuance of its existence (al‑dharūra al‑dhātiyya), sophism would have had veridicality in the realm of reality’s destruction. Nevertheless, the veridicality of sophistry is a reality, which has its own specific nafs al-amr."
If the existence of at least something was conditional, it would be possible for nothing to exist. We have shown that this is not possible.
The realm of sophistry’s veridicality is not the abode of the narrator’s existence, in which case its veridicality would pertain to the reality of the narrator. Rather, its realm of truth is that very supposition, which the proposition reflects. When, in a given supposition, reality is negated, real negation of philosophy and real affirmation of sophistry is a reality that has been narrated. Thus, reality is still manifested in the context of its very negation. For this reason, reality cannot be denied in any supposition; and the primary and self-evident proposition (al-qadhiyya al-awwaliyya al-badīhiyya), which holds its truth, has eternal necessity.
The narrator is not not real (is real). That something is real is not falsifiable.
Since the truth of the propositions, which relate reality of finite and conditional beings, is subject to certain conditions, and it is only within certain boundaries that they are true, beyond which they are false, finite and conditional beings cannot be the extension (misdāq) of the reality that has eternal necessity.
Finite beings only exist within certain boundaries, outside of which they don't exist. For the statement "something is real" to always be true, something other than finite beings must exist.
Given that the aggregate of finite beings is not another entity, which has something additional to its parts, it does not have any reality at all. Similarly, their universals (jāmi‛) do not have any external reality either, and they are notions that exist in the mind by the mental mode of existence (al-wujūd al-dhehnī) in such a way that if the mind did not to exist, the universals would not even have found the mental existence. Therefore, reality, the eternally necessary existence of which is axiomatic and primary, is other than the finite beings, their totality, and their universals, as the first have finite realities, the second has no reality, and the third has a limited mental reality.
The aggregate (the entirety) of anything is essentially the sum of its parts and nothing more. Aggregates of finite beings can be said to not exist. For the statement "something must exist" to be true, something other than finite things or aggregates must exist.
"Therefore, the first ontological proposition, which the human being cannot not know, is the affirmation of the basic reality, and its modality is eternal necessity. And since, as just explained, finite entities, such as the heavens, the earth, the cosmos, and so forth, cannot be the extension of this proposition, its extension is only an Absolute Reality—Who is above the restrictions of conditions, is present with all of the finite realities, and no absence or termination is perceivable with respect to Him."
The statement "something exists" must always be true. Something must exist that cannot cease to exist.
The text then continues and talks about the proof, but it has nothing of import to offer to the overall argument.
OP says that this argument, the POTV, and a few attribute tracings prove the existence of something that is "necessary, eternal, self-subsisting, independent, primary, absolute/infinite, unrestricted, unique, one-and-only, omnipresent, immaterial, formless, ineffable, uncaused, doesn't have any rivals." He then beckons readers to focus and not spew crap.
"The point towards which ‛Allāmah Tabātabā’ī draws attention is that the proposition “There is a reality,” and the proposition “Sophistry is void,” have eternal necessity. That is, the modality of these propositions is not attributive, conditional, or essential necessity. Acceptance of this claim, like acceptance of reality, needs mere drawing of one’s attention (tanbīh). In other words, just as the entertainment of the concept of reality is sufficient to acknowledge its truth, the conception of the notion of eternal necessity of reality is sufficient for accepting its validity. A human being cannot accept sophistry in any situation or condition, since situations and conditions are realities, which attest to the invalidity of sophistry, which is the negation of reality."
Something exists.
"Should reality be annihilated in a specific condition—in a beginning, or an end, or in any particular supposition—then only two situations are conceivable. The first is that its annihilation is not real, and an equivocal or false claim has been made that reality is annihilated. In this case, reality is preserved and it has not been annihilated. The second is that its annihilation is true; that is, reality has really been annihilated. In this supposition, again, the affirmation of the basic reality is acknowledged, since the supposition asserts that reality has really been destroyed; therefore, as a real phenomenon, the destruction of reality reflects the real presence of reality. Therefore, the falsehood of sophistry and veridicality of reality is well secured in every perceivable supposition; and a single instance of reality’s destruction is inconceivable."
If the statement "something is real" is claimed to be false, the claim is either true or false. If false, then the statement "something is real" still stands. If "true," the existence of the claimant negates the claim; the claimant exists, and therefore something is real.
"A proposition, which negates reality, is a proposition, that neither its veridicality can be related in any supposition, nor its falsehood could ever be doubted. That is, its utterance always presupposes its own falsity. On the other side of the spectrum, it is impossible to doubt the meaning of the proposition, which affirms reality, because dismissing it as meaningless or doubting its meaning entails the affirmation of reality."
Any claim that nothing is real is undoubtedly false.
"If, like a finite being, reality lacked eternal necessity and its necessity were conditional, say, with the continuance of its existence (al‑dharūra al‑dhātiyya), sophism would have had veridicality in the realm of reality’s destruction. Nevertheless, the veridicality of sophistry is a reality, which has its own specific nafs al-amr."
If the existence of at least something was conditional, it would be possible for nothing to exist. We have shown that this is not possible.
The realm of sophistry’s veridicality is not the abode of the narrator’s existence, in which case its veridicality would pertain to the reality of the narrator. Rather, its realm of truth is that very supposition, which the proposition reflects. When, in a given supposition, reality is negated, real negation of philosophy and real affirmation of sophistry is a reality that has been narrated. Thus, reality is still manifested in the context of its very negation. For this reason, reality cannot be denied in any supposition; and the primary and self-evident proposition (al-qadhiyya al-awwaliyya al-badīhiyya), which holds its truth, has eternal necessity.
The narrator is not not real (is real). That something is real is not falsifiable.
Since the truth of the propositions, which relate reality of finite and conditional beings, is subject to certain conditions, and it is only within certain boundaries that they are true, beyond which they are false, finite and conditional beings cannot be the extension (misdāq) of the reality that has eternal necessity.
Finite beings only exist within certain boundaries, outside of which they don't exist. For the statement "something is real" to always be true, something other than finite beings must exist.
Given that the aggregate of finite beings is not another entity, which has something additional to its parts, it does not have any reality at all. Similarly, their universals (jāmi‛) do not have any external reality either, and they are notions that exist in the mind by the mental mode of existence (al-wujūd al-dhehnī) in such a way that if the mind did not to exist, the universals would not even have found the mental existence. Therefore, reality, the eternally necessary existence of which is axiomatic and primary, is other than the finite beings, their totality, and their universals, as the first have finite realities, the second has no reality, and the third has a limited mental reality.
The aggregate (the entirety) of anything is essentially the sum of its parts and nothing more. Aggregates of finite beings can be said to not exist. For the statement "something must exist" to be true, something other than finite things or aggregates must exist.
"Therefore, the first ontological proposition, which the human being cannot not know, is the affirmation of the basic reality, and its modality is eternal necessity. And since, as just explained, finite entities, such as the heavens, the earth, the cosmos, and so forth, cannot be the extension of this proposition, its extension is only an Absolute Reality—Who is above the restrictions of conditions, is present with all of the finite realities, and no absence or termination is perceivable with respect to Him."
The statement "something exists" must always be true. Something must exist that cannot cease to exist.
The text then continues and talks about the proof, but it has nothing of import to offer to the overall argument.
OP says that this argument, the POTV, and a few attribute tracings prove the existence of something that is "necessary, eternal, self-subsisting, independent, primary, absolute/infinite, unrestricted, unique, one-and-only, omnipresent, immaterial, formless, ineffable, uncaused, doesn't have any rivals." He then beckons readers to focus and not spew crap.
