The authority of the sages

But how can one establish the authority of the sages from one verse to another when this is their own interpretation of the verse and they have preserved my verse. It is possible to establish the authority of factor x from factor z, but not for that factor to be the source of its own authority?

Easily. Just like the legislator determines its own powers. With us it's even easier, because they only interpret and don't determine.

Yes, but I can interpret it differently and in any case not understand it the way they interpreted the verse (and you kept my watch), and then I will not be subject to their obligation.

That's right. You can also not accept your commitment to the Torah or the laws of the state.

I'm asking seriously, so why should I accept their authority if it's not really necessary?

And I answer seriously, because there is no legal/normative system without a body that is authorized to interpret, update, and legislate.

Noam, Michael has a certain bug in understanding the concept of authority. He doesn't feel the arbitrariness of the recursion in defining authority. He repeated it over and over again and doesn't grasp the difference between "it has to be this way and that way" and "it has to be that way and that way". The ideal/desire becomes the necessity. Someone wrote to him here that because he is hungry, there must be a sandwich in the next room, as in your question, the source of authority is because there must be authority. Many have tried and succeeded in cracking this bug in Michael's thinking.

How good that Michael is still alive and we can ask him. We are blessed.