The entire government of the universe is ordered under the four letters of the Four-Letter Name.
Adam Kadmon — Primordial Man — is the first ordered emanation: the Tree of the Four-Letter Name, the original Likeness of Man, the central tree under which all other worlds are garments.
Op. 30 closed the Tzimtzum unit by establishing the cosmic-temporal architecture. Op. 31 opens the next unit by naming the first ordered emanation — Adam Kadmon — that fills the contracted space the Tzimtzum opened. The chapter introduces the term that becomes the structural template of everything that follows.
The Tetragrammaton (the Four-Letter Name) is the four-letter Name yod-heh-vav-heh. Its four letters map onto the cosmic structure with great precision. Yod corresponds to Chochmah; the upper heh to Binah; the vav to the six middle Sefirot (Chesed through Yesod, Zeir Anpin (Z"A)'s six Directions); the lower heh to Malchut. The four letters also map onto the four expansions (AV (gematria 72), SaG (gematria 63), MaH (gematria 45), BaN (gematria 52), Op. 22) and onto the five primary Partzufim of Atzilut (Atik Yomin = the apex; Arich Anpin = the yod; Abba/Imma = the upper heh; Z"A = the vav; Nukva = the lower heh).
Adam Kadmon is this entire structure — not as one component among others, but as the integrated form under which everything else is organised. There are worlds without number in Lurianic literature (Etz Chayim Derushey Igulim VeYosher 12:1; Tikkuney Zohar 57; Zohar Pinchas 257b), each with its own Tree, its own Sefirot, its own Partzufim. Adam Kadmon is the one order under which all of these are garments. The other worlds operate; Adam Kadmon governs.
The Tikkuney Zohar 57:94b passage Klach cites is structural: the Name does not change in any place in its four letters. The four-letter pattern of the Four-Letter Name is constant through every operational variation in the cosmos. Adam Kadmon's structural identity — the four-letter mapping — does not vary as the cosmos descends through its successive levels. The same Tree, the same letters, the same integrated Likeness of Man.