Thank you very much. If so, it really is unclear how they saw there a double doubt for stringency (elsewhere it is indeed brought the other way in the name of the Chazon Ish).

By the way, in this kind of case Rabbi Mazuz brought this week in his bulletin a somewhat more complex case, about a woman who was unsure whether she had recited Grace after Meals (he rules that she should not recite it). Based on the above, one could analyze it like this:
A – She recited Grace after Meals
B – She is obligated by Torah law
C – She is obligated rabbinically

Only A: she does not recite
Only B: she recites
Only C: she recites
A and B: she does not recite
A and C: she does not recite
The other combinations are not possible.

And from this it comes out that she does not need to recite it.

I didn't understand this business with Rabbi Mazuz, but never mind.

What's the problem with reciting it twice if she is unsure whether she recited Grace after Meals or not?

As is known, there is a dispute whether women are obligated in Grace after Meals by Torah law or only rabbinically. If a woman is unsure whether she recited it or not, seemingly one should be lenient, because: there is a 50% chance that she did recite it, and even if she did not recite it—perhaps she is obligated only rabbinically, in which case it is a rabbinic-level doubt.

I tried to formulate the above as 3 claims and their truth table.

Avi — a question: if there is a groom and you don't know whether you went to bless him under the wedding canopy, what would you do, Avi?

"And even if she didn't recite it, maybe it's a rabbinic doubt"?
If she didn't recite it, she has to recite it whether that obligation is rabbinic or Torah-level. For your convenience, you can make the opposite double doubt: perhaps she didn't recite it, and even if she did recite it, perhaps the obligation is Torah-level, so this is a Torah-level doubt requiring stringency.

In Rabbi Mazuz's truth table:
It's not clear what "only A" means.
She recited it, but from the outset she had no obligation, neither by Torah law nor rabbinically?

Right, the table is wrong, but the line of reasoning is valid. There is a 50% chance that she recited it. In such a situation, if it were clear that this is Torah-level, she would be stringent because of doubt. Since there is a doubt whether it is Torah-level, we have dropped below 50%, and she does not recite it. You have no way to reverse this, because the doubts for leniency are independent (each one is valid on its own) and therefore they accumulate, whereas the doubts for stringency depend on one another and therefore do not accumulate.

Mainly regarding the first issue above, what they brought from the book Ma'adanei Shlomo. The case needs to be corrected. It was not a case of being unsure whether he counted at night; rather, he definitely forgot to count at night, and only the next day did he count during twilight.

Indeed, in Ma'adanei Shlomo they brought in his name that he cannot continue counting with a blessing because there is also a double doubt for stringency here. But in Halikhot Shlomo they brought in his name that one need not be concerned about this, for a certain reason.

It is clear that it says there explicitly what the sides for stringency are, as Rabbi Michi wrote: to take into account the view of the Ba'al Halakhot Gedolot. But not as it is written here in the name of Rabbi Michi. I simply did not understand the calculation—maybe there is a writing error, with missing words and explanation.

Rather, the explanation is as follows. One side, according to the Ba'al Halakhot Gedolot, is on the assumption that he counted during the day, but daytime counting is not considered counting. A second side for stringency: according to the Ba'al Halakhot Gedolot, even if daytime counting does count as counting, here he did not count during the day but at night, if twilight is considered night. And vice versa. On the other hand, there are also two sides that he should continue counting. First, not according to the Ba'al Halakhot Gedolot, in which case we do not care whether he counted during the day or not. Second, even according to the Ba'al Halakhot Gedolot, perhaps he counted during the day, and perhaps daytime counting is considered counting.

What the questioner asked—whether there is also a double doubt for leniency together with a double doubt for stringency—is obviously like a single evenly balanced doubt. What difference does it make to us that another doubt was added to each side? The law remains like a single doubt requiring stringency, or here, that he should not continue reciting the blessing thereafter.

And to add further: Avi above did not understand what Rabbi Michi answered him. He understood it as though Rabbi Michi held like his own view, against what is explained in Ma'adanei Shlomo. But that is not so; it is exactly the same conclusion. Only there in the book they called it a double doubt for stringency—meaning, not to recite the blessing because of the stringency of a potentially unnecessary blessing. But Rabbi Michi called it a double doubt for leniency—meaning, to be lenient by not continuing to count with a blessing. Take careful note.

After careful analysis, it seems to me that there is no double doubt for stringency here to avoid the blessing. This is based on what many have explained, and as Rabbi Michi explained elsewhere in clarifying the Ba'al Halakhot Gedolot: he too holds that each day is a separate commandment to count on that day. However, there is a condition for the continued fulfillment of the commandment each day—that there be consecutive counting, due to the law of completeness. Therefore, when one misses a day, there is a deficiency in the act of counting from then onward. If so, it seems that an act of counting during the day is enough to complete the matter of continuity, even if there is no fulfillment of the commandment on that day according to the views that daytime counting does not fulfill the commandment. If so, in the case where he counted during the day, there is no need to invoke the law of double doubt at all. Rather, according to the Ba'al Halakhot Gedolot, he certainly can continue counting. And now, in the case where he counted during twilight, we return to a double doubt for leniency, and he can continue counting even according to the Ba'al Halakhot Gedolot, just like the law in a case of doubt whether he counted at night; so too here, it is a doubt whether he counted during the day. Take careful note. That is, the doubt whether daytime counting is effective or not is not included here as a doubt according to the Ba'al Halakhot Gedolot. For even if it is not a commandment-counting, it is still a factual act of counting for the sake of maintaining consecutive counting. Consider this carefully.