Written Torah and more.

Thanks.
Regarding G: What about the Beit Din? In the public sphere, it is difficult to say that there is no authority left today, and the last authority is the Talmudic sages. And besides that, why are only the Talmudic sages a source of authority? Why is the way in which the words of the Rishonim, customs, etc., are treated today as a source of authority - and thus the prevailing halakhic path has not made these a source of authority as well, according to our current acceptance?
Forgive me for answering before I read the above article, unfortunately I do not have time for that right now.

I don't know what the public level is. From a halachic perspective, everyone agrees that there is no authority after the Talmud. This is the case in the Rishonim and the Achriim, and even in the Ram”a in the Shul (which the Sanhedrin chief, P”d 6’ 6), which we refer to as the Rishonim is a substantive and not a formal authority (search for these definitions here on the site).
We did not accept the Rishonim and not even the Shul as a condition of accepting the Talmud. There is no dispute about them, and they do. We accepted that they have weight, and indeed it is necessary and appropriate to give them weight.

On the public level – I mean, for example, conversion. Its validity from the Torah in our day is due to the fact that it is a duty of the Torah to follow it. It is difficult to say that every person who converts and believes that he understands and converts is said to have his conversion valid because of the above. Simply put, there is a public convention – for formal authority even in our day that only a court that is accepted by the public is the one that converts and only it has the above validity. According to this, it follows that there is a convention regarding formal authority even in our day – in matters related to the rule and not to the individual in his home.

In general, I think this convention also exists in matters of gittin and divorce. Although in the days of the sages, the matter was certainly simpler, it was because of the clear familiarity between the people and the limited possibilities of falsification that were possible for their rights. But in our day, with the various developments – if there is no institution to manage this business, any sensible person understands that a completely chaotic situation can arise in these matters. Of course, there are disputes about the institution itself and its boundaries, but apart from occasional Feiglinists who claim that for matters of sanctification, we can “Google it” or all sorts of irresponsible statements like that, there seems to be a widespread consensus that it needs to be managed somehow. If I am being honest, then even in our own day, it must be said that there are formal authorities in areas that can affect the entire public. And just as the public’s acceptance of the words of the Talmud and the words of the sages creates formal authority in the interpretive realm of the Torah, even for a person’s private halakhic life, so this acceptance creates formal authority in ruling in certain areas related to the entire public as mentioned above.

There is no way to determine who is subject to the law of missionary service. This is an explanation, and therefore I do not specifically link Zaat to a religious institution. Just as every bi”d in any field is three people who sit and discuss, I do not see what is different in conversion. There is a difference in explanation, but not in the law itself. And of course, in conversion and sanctification, there is no agreement on an authorized institution. You are perhaps talking about what is appropriate and not about what is available. No one doubts the conversion or sanctification of a private, obscure bi”d in Mea Shearim that does not recognize the state and the rabbinate, and they do not recognize it.

In my understanding, it is difficult to determine when the law of the mission applies because it is difficult to determine to whom the public consent applies – but do you agree with the hanging of one on the other? That the conversion of a convert in our time depends on the public acceptance of the court – and only this is what gives validity to this conversion from the Torah (after all, conversion was dependent on ordination, in contrast to the court of Mammon, for example, which could rule on certain matters according to the direction of the Torah) and therefore there is indeed a source of formal authority even at this time. This acceptance as formal authority certainly does not exist only with the rabbinical institution, the courts of the haredi communities are also agreed upon by it, therefore even the “dark” court in Mea Shearim falls under it, such is the prevailing perception among the majority who are faithful to the law.

The issue will be with figures who do not act with the consent of a significant religious community, even if they are within Orthodox Judaism, of course it is impossible to prove this, but at least there is concern about this for these conversions.

Besides, if we say that there is no formal authority, what would lead us to cancel, for example, the conversion of a reformist lawyer if it is done in a way that is halakhically acceptable. In my opinion, it is far from saying that this has any validity.

You're trying to square the circle. There are no clear criteria, but that doesn't mean there's no right or wrong. If in my opinion the Reformers are not worthy of being judged, then there's no reason and no conversion. If someone thinks that way about me, then my conversion won't be conversion in their eyes either. A mess? Right. But there's no other way out. In your opinion, there are no criteria either. So what's the discussion about?

As I understand it, if the validity of the conversion is due to public consent and acceptance, then if any court does not have such consent, then his conversion is not valid even if in my opinion it is very worthy. Because there is no objective truth in this, but rather subjective acceptance by the public. Indeed, there is no clear criterion for defining public acceptance, but there are extreme situations that clearly involve the consent of a minority and not the consent of the whole.

But it is true that even if you do not think so, there is no question of a reform court being invalid on its own part, as you wrote.