Thanks for the reference; I’ll look into it.

That is not what I meant by my third possibility.
What I wanted to say is that apparently the later authorities understood that if the liability is due to the very fact that his property caused damage, then when there is doubt whether he guarded it properly (that is, doubt whether the damage happened due to an accident beyond his control) or was negligent, we say he is liable because we have a certain basis for liability and only a doubtful basis for exemption.
But one could also say that the accident is not a reason that exempts him from liability; rather, it is a reason that negates the liability from the outset. In other words, if there was an accident beyond his control, then there is no liability at all from the outset. It is not that if there was an accident then there was liability, but now there is an exemption. Rather, as I wrote, when there is an accident, the basis for liability never even takes effect. (Maybe something like “superseded” versus “deferred.”) And based on this, one could say that when there is doubt whether he guarded it properly, then he is exempt even if the basis for liability is that his property caused damage, because we have doubt about the very basis of the liability—whether it applies or not.

An accident, by definition, is not a reason that neutralizes liability; it is an exemption.

From the inquiry whether what creates liability is the act of his property or his negligence, they derive several practical differences.
But really, in almost all of them, it seems to me there is room to question them. For example:
If he was negligent, then declared it ownerless, and afterward it gored, Rabbi Shimon Shkop writes that if what creates the liability is the act of his property, then now it is no longer his property and therefore he is exempt.
Or, if a competent guardian was negligent and afterward the owner lost his sanity, and then it gored—if what creates liability is his property, then here he is exempt because at the time of the damage he was not legally liable.

But really, it seems obvious to me to say that although what creates liability is the act of his property, that already begins from the moment of negligence. In other words, the damaging act of his property already begins from the moment of negligence!
A practical difference for this would be: what is the law when my ox enters the property of the injured party and starts breaking all his vessels—first vessel A, then vessel B, then vessel C, and so on—and I declare it ownerless between vessel A and vessel B. Would anyone imagine that the owner is exempt from paying for B and C? Surely, once the damage process has already begun, you are liable, and once you were negligent you already became responsible and liable.

Is what I’m saying correct or not?

That is definitely possible. I have written more than once that this inquiry has almost no practical ramifications. And even the classic practical difference in the dispute between the Penei Yehoshua and the Chazon Ish about the burden of proof is not really a practical difference either (at least in one direction).

One could also say in the other direction that although the act creating the liability is his property, still the burden of proof is on the injured party, because the damager is believed when he says that he guarded it properly, since an ox is presumed to be under guard. So he is not introducing a new claim here; on the contrary, it is the injured party who is introducing a new claim—that the damager did not guard it properly—and therefore he must bring proof.
Do you agree?

We do not say that an ox is presumed to be under guard. That is not plausible. If it caused damage, then apparently it was not guarded (as the Chazon Ish wrote). Only regarding an innocuous ox is there an opinion that oxen are generally presumed guarded, and even there it is not because of the owner’s guarding but because the ox itself is not considered damaging.

In lecture 4 of Talmudic conceptual thinking, you mentioned that Rabbi David Povarsky tried to prove that negligence in guarding is the cause that obligates the damager to pay, in the following way:
According to the one who says that the prohibition against causing damage is learned from the fact that there is an obligation of monetary payment, then certainly negligence is what creates the liability. Otherwise, if it were just the fact that it was his property, why should there be any prohibition because my property caused damage? Rather, clearly negligence is what creates the liability, and therefore there is both a prohibition and an obligation to guard my property well.

And then he rejected that proof, in your wording, in this way:
One should distinguish between the prohibition and the obligation to pay: the first belongs to criminal law and the second to civil law. Meaning, true, you violated a prohibition, but I am not coming to sue you for that; I am coming to sue you because you are responsible for the fact that your property caused damage, and based on that you owe me money.

I understand the proof on its own, and I understand the rejection on its own. What I do not understand is the connection between them. After all, the proof itself was based precisely on the assumption that from the existence of a prohibition we learn that there is an obligation to pay. So you cannot then separate the two. If I assume that I learn the prohibition from the obligation to pay, that means the obligation to pay is the result of the fact that I violated a prohibition—that the prohibition I violated causes me to be obligated to pay. And then it really does come out according to the negligence side. Meaning: the prohibition I violated (= I was negligent in guarding) caused me to become obligated to pay.

The prohibition is not learned from the obligation to pay. Only the Levush and the She’iltot apparently understood it that way. According to their approach, there is room for Rabbi Povarsky’s proof (and that is why I mentioned them), but Rabbi Povarsky did not tie his proof specifically to them; he stated it more generally. Beyond that, I rejected the proof in another way as well.