Is this in your trilogy?

I think so. At the moment I don't remember.

Hello Rabbi.

You were puzzled by the Shakh, who cited the Jerusalem Talmud saying that “her virginity returns.”
I assume your difficulty is with the Jerusalem Talmud, not with the Shakh, right?

The Jerusalem Talmud was troubled by how, once the religious court sanctifies the month, it is determined that her virginity returns until the end of the second Adar.
Here you rejected that by saying: “I have always been puzzled by him, because it is obvious to me that this does not happen. But it has no practical legal implication, because it is clear that we are dealing with the setting of a formal halakhic line.”

I looked at the Rashba in Mishmeret HaBayit (part 3, p. 104 in the Mossad HaRav Kook edition), and I understood from his words that the reason they did not answer as you did—that this is just a “halakhic line”—is one thing: the Sages had the option of setting a halakhic line based on days rather than years. Instead of saying 3 years, they could have said 1,095 days (365×3). If they established it in years, that is a sign that the year is what determines things in the physical world in every case.

And see Yoreh De'ah no. 184, on the Machatzit HaShekel, se'if katan 18, regarding a nursing woman, where “the blood becomes spoiled and turns into milk.” It is explained there similarly, that the Sages intentionally did not say that the process lasts two years, but rather twenty-four months, in order to gain the result that in a leap year the extra month would not be included at all.

I too tend to think that the Sages' determination does not change the virginity in the physical world. I just wanted to explain why the Jerusalem Talmud and the commentators did not think this was a formal line alone (because if you're making a formal line, it makes more sense to do it by days and not by years, as stated).
What do you think?

I'm not sure that's forced in the Jerusalem Talmud. It may assume that even if the line is formal, one must still act according to it precisely (that is the way of Jewish law). And maybe that is also the explanation in Machatzit HaShekel.
The explanation you brought from the Rashba is certainly not necessary. And perhaps in the Rashba too the meaning is as above.
Making a formal line of days is obviously awkward and unreasonable. Should people count 1,095 days? Is that any way to function? It's senseless.

“It may assume that even if the line is formal, one must still act according to it precisely (that is the way of Jewish law).”

I didn't understand: who assumes that? The Shakh?

Certainly not. The Jerusalem Talmud.

I still don't understand.
Do you mean that the Jerusalem Talmud is not trying to describe reality, but to establish Jewish law? Not to make a claim about the world, but to legislate a norm?

That seems very strained to me in its wording: “Rabbi Avun said: ‘I cry out to God Most High, to God who completes for me’ (Psalms 57:3)—a girl of three years and one day, and the religious court decides to intercalate the year, her virginity returns; and if not, her virginity does not return” (Ketubot, ch. 1, halakhah 2).

Why did the Jerusalem Talmud bring the verse?
The commentators there explained that Rabbi Avin interpreted it to mean that the religious court has a metaphysical influence: the court below “calls out to God,” and God in response “completes for him.”
If this is only a normative determination, why was the verse brought?

Maybe the verse is just rhetorical embellishment or an asmachta. I was only raising a possibility.

Even if we assume that this is the intention of the Jerusalem Talmud, it is hard to say that the Rashba understood it that way.
The Ra'ah in Bedek HaBayit was puzzled why menstrual cycles are counted according to the formal calendar dates of the month rather than according to the actual lunar conjunction. And the Rashba answers him:

The author said: “The honor of the Sages they shall inherit, but their questions—this is no question. For certainly the shofar causes it [that is, the shofar blast that proclaims the fixing of the month], for whatever the earthly court does, the heavenly court agrees with them, as it is written: ‘which you shall proclaim them’—‘which you shall proclaim’ them—in their appointed times. And we rely on the fixing of months and intercalation of years in matters involving kareit, such as leavened food on Passover, the slaughtering of the Passover offering, and the affliction of Yom Kippur.
Also with regard to intercourse involving minors, where they said (Niddah 44b): a minor girl of three years and one day—if one of those forbidden sexual relations had intercourse with her, he is exempt and they are not put to death on her account; if she is younger than that, both are exempt. And similarly regarding a minor boy of nine years and one day and thereafter—or younger than that—we do not count days for them, but years, which are built from full and deficient months, and leap years and regular years, according to the enactments of the court.
And so too with bodily developments, as they expounded in the Jerusalem Talmud, Ketubot, on ‘to God who completes for me’: a minor girl of three years and one day who had intercourse—her virginity does not return; but if the court convened and intercalated the year, her virginity returns. This is ‘to God who completes for me.’” End quote.

From his words it is clear that he understood the Jerusalem Talmud in a metaphysical way. At first he speaks about formal determinations, like Passover and Yom Kippur; then he moves to formal determinations like intercourse of an adult with a minor girl or a minor boy with an adult woman; then he adds (at the beginning of section 3), “And so too with bodily developments”—what is added by this? Had he not already been speaking until now about bodily developments? After all, he was discussing the definitions of “minor boy” and “minor girl.”
I think his intent is that until now he was talking about determinations that could be merely formal, and now he is talking about the effect of Jewish law on reality.

The context also seems to point that way. The Ra'ah wants the days of the menstrual cycle to be set according to the conjunction, not according to the formal date of the new month, arguing: “Does the shofar cause it?”! Does the shofar of sanctifying the month cause the cycle? Surely the conjunction causes it. It seems to me that the Rashba could not have rejected his argument on purely formal grounds. It is not plausible that because various laws (mainly connected to counting years) are determined according to the court, the menstrual cycle should also be determined by it. A menstrual cycle is not a matter of date, but of a symptom, so it need not be tied to a particular day; it can be tied to an interval, or to an action such as jumping or eating garlic.
The Ra'ah in Bedek HaBayit understood that the Talmud can be interpreted as counting cycle days according to the conjunction. Why did the Rashba refuse that? It seems to me only for a metaphysical reason.

I'm also uncomfortable with the metaphysical claim, but I think it isn't fair to distort the authors' intention because of that.

I don't see any necessity here at all. Exactly what I said can be said here too.
I’ll only add that even if this is not their intention, it is clear to me that they are mistaken, but I have not been convinced that they are claiming anything different from what I am.