Tzachtzachos

Tzachtzachos is the primary root of the Sefiros as they "exist" in Atik Yomin or in Akudim. At this level, the Sefiros are not in three lines (right, left, and center), nor even in two (right and left), but are included in one point: in Atik in a way of "leis smola b'hai atika" (there is no left in this Atik), and in Akudim in a way of "akudim b'kli echad" (bound in one vessel).

Source of the Concept

The source of the concept "Tzachtzachos" is from the Braisos of the Geonim (Rav Hai Gaon and Rav Chamai Gaon) brought in the Pardes by the Ramak. The author of the Pardes was asked there about the language of the Braisa of Rav Hai Gaon, how is it possible that the 13 attributes of mercy are thirteen (since in Sefer Yetzira it states that the Sefiros are "ten and not nine, ten and not eleven")? He explains that the 13 attributes are three head of heads (in Kesser) called Ohr Kadmon, Ohr Metzuchtzach, and Ohr Tzach, together with the ten Sefiros of Atzilus that were drawn and emanated from them.

In Chassidus

Ohr Kadmon, Tzach, and Metzuchtzach are the three highest levels in the inner dimension of Kesser (in Atik) (higher than Kesser-Chochma-Bina of Atik), and they are the first three attributes of the 13 attributes of mercy, which are the roots of the ten hidden Sefiros (also called "three head of heads").

This level (called "Taanug Hashem" and "Noam Hashem" and "Tzachtzachos") is what is called in other places RADLA (Reisha D'Lo Isyada), as written in Eitz Chaim near the end of Shaar Atik.

Additional Explanations

It should be noted that in various places in Chassidus, the concept of the three lights "Kadmon, Tzach, and Metzuchtzach" is explained in many additional ways. Both in levels below Atik (in Atzilus, in Arich Anpin, in Chochma Stimaa, and in lower levels within Atik itself (Kesser-Chochma-Bina of Atik)), and in levels above it (in Adam Kadmon and in the Ohr Ein Sof before the Tzimtzum).

Tzachtzachos and the Sukkah Schach

The Zohar brings that the Ushpizin who come to the Sukkah recite verses. Avraham, Yitzchak, Yaakov, and Dovid each say a different verse, and the rest of the tzaddikim all say the verse "And Hashem will guide you always and satisfy your soul in Tzachtzachos."

Two explanations are given for this:

1. The "Tzachtzachos" that "the rest of the tzaddikim" say refers to "the intensity of the light that the vessel cannot contain, causing the light to break through." This explains the previous verse that Yaakov says ("Then your light shall break forth like the dawn," which speaks of the strengthening of the light that can break through the concealment of Tzimtzum, namely – the Kav).
2. The "Tzachtzachos" is the shade of the Sukkah. Shade in general represents makif (encompassing light), and the shade of the Sukkah specifically represents the ten Sefiros of Atik called "ten hidden Sefiros."

The Vowel Point Kamatz

Kamatz is an acronym for "Kadmon Tzach Metzuchtzach," and the explanation is:

Regarding Moshe Rabbeinu, it says that he saw Hashem "in a vision and not in riddles" – the Alef of "mareh" (vision) is vowelized with a segol. In contrast, in a regular "mareh" (mirror, in which one looks to see oneself), the Alef is vowelized with a kamatz. From here we learn that Moshe saw Hashem through an "aspaklaria hame'irah" (illuminating lens, like binoculars or a magnifying glass, through which things appear larger or closer than in reality), but other prophets see Hashem only through an "aspaklaria she'einah me'irah" (non-illuminating mirror, meaning they see only His image and not directly Him).

This means that today it is impossible (except for the few tzaddikim who are on the level of Moshe Rabbeinu) to see these three elevated levels (Kadmon, Tzach, and Metzuchtzach) except through an aspaklaria she'einah me'irah, and only in the future will the inner dimension of Atik be revealed to all.