Dino, it is very nice to hear from you again with this interesting question!

1) The Sefas Emes here asks: what is the Halachah if a pauper said "Chatzi Erki Alai"? The question is as follows. The Mishnah above (7b) states that there is no Erchin of less than a Sela. Rashi writes that even a pauper cannot give less than a Sela. However, it is possible to argue that the Mishnah there refers only to a person who said he would give a full Erech. In such a case we say that it cannot be less than a Sela, but if he said he is giving only half his Erech, it may be that he can give half a Sela. The Sefas Emes writes that if he possesses a Sela or more, certainly he must give whatever he has until he reaches half of his Erech, but the question is: what is the Halachah if he does not possess a Sela? Can he give half a Sela?

The Sefas Emes does not decide what the answer to his question is, and he remains with "Tzarich Iyun."

We see clearly that if he possesses a Sela or more, according to the Sefas Emes the concept of Heseg Yad does apply to the pauper who said "Chatzi Erki Alai," and if he is not able to pay more, he pays what he can. The only question of the Sefas Emes is whether there is a Din of Heseg Yad even below a Sela, to enable him to pay half a Sela.

2) The Rogatchover Gaon zt'l writes that when the pauper says "Chatzi Erki Alai" the Din of Heseg Yad does not apply. This is in Tzofnas Pa'ane'ach on the Rambam, Hilchos Erchin 1:16 (near the end). He writes, "Chatzi Erki Alai Yesh Lomar d'Zeh Gam Ken Heveh k'Erech Mefurash she'Kibel Alav Litein ha'Chatzi Mah she'He'erichu Oso v'Im Ken Eino Nidon b'Heseg Yad" -- saying "Chatzi Erki Alai" is like an explicit Erech that he accepted upon himself to give half of what they say his Erech is. "An explicit Erech that he accepted upon himself" seems to mean that it is like a Neder, not like an Erech obligation of the Torah.

3) The Shi'urim of Rav Meshulam David Soloveitchik zt'l here asks whether "Chatzi Erki Alai" works v'Toras Erchin or merely as a Neder. He writes that there is a Nafka Minah concerning Heseg Yad. He points out that since the Mishnah cites this Din together with other Dinim of Erchin, this suggests that it is also a Din of Erchin. The Rambam (Hilchos Erchin 2:2) also cites it together with the Halachos of Erchin which again suggests that it is b'Toras Erchin.

He then asks from the Mishnah on 7b (that we saw above) which states that there is no Erchin of less than a Sela, but if we say that there is such a thing as a Chatzi Erech one can indeed find an Erchin of less than a Sela. Rav Meshulam David concludes that this requires further study.

So we still do not have an answer to your question, Dino!

4) A half is acceptable for many Torah matters as long as atonement is not involved:

I intend, bs'd, to try and continue and defend other aspects of the position of the Sefas Emes that Chatzi Erech is b'Toras Erech, but meanwhile I will just relate to the question of why we do not need a Pasuk or Limud for this.

I think that if we look at Bava Kama 40a, it will help us to understand this. There, the question was asked: "If an ox is owned by two partners and the ox killed a man, how do the partners pay Kofer?" It cannot be that each partner pays half a Kofer, because the Torah says one must pay a complete Kofer, not half a Kofer. Tosfos (DH Kofer) writes that the disqualification of a half applies only to Kofer, because this gives atonement to the owners and one needs a full atonement, while for matters involving monetary compensation, a half payment is acceptable. Therefore, the Gemara in Bava Kama 71b states that if the ox of partners was stolen and then slaughtered or sold, the criminal pays a half of the Arba'ah v'Chamishah payment to each of the partners.

According to this, since Erchin is a gift to the Beis ha'Mikdash and is not an atonement, it should follow that there is nothing wrong with specifying half of one's Erech.

If there is no Pasuk otherwise, we assume that half is acceptable.

5) I will try now to conclude this topic.

Firstly, I should note that there are several Sefarim (in addition to the Rogatchover that I cited above) who disagree with the Sefas Emes and write that Chatzi Erech is b'Toras Neder, and Heseg Yad does not apply to it. These are the Erech Dal, Divrei Meir, Nesivos Yam, Mikdash Yechezkel, and others. The Arichas Ner cites several who discussed this.

According to this opinion, we do not have the question that we have no Pasuk for this new Parshah in the Torah, or that we never find the number 25 in the Torah.

However, we saw above that Rav Meshulam David writes that since the Mishnah and the Rambam cite the Halachah of Chatzi Erech amidst the Halachos of Erchin, this suggests that Chatzi Erech is b'Toras Erech. This is strong support for the Sefas Emes.

We have seen that Tosfos in Bava Kama (40a) writes that when the Torah states a payment, and Kaparah is not involved, half is also an option. According to this, it does not matter that we do not find 25 in the Torah, because we do find 50, and half of 50 is 25.

Yeyasher Kochacha!

Dovid Bloom