AV (gematria 72) is Arich Anpin, the root of AV, SaG (gematria 63), MaH (gematria 45) and BaN (gematria 52) — Abba and Imma, Zeir and Nukva.*
AV (the highest expansion of the Four-Letter Name) is Arich Anpin. The four expansions map to the five primary Partzufim. Atika Kadisha (the Holy Ancient One) and the Name of Atika are distinguished.
Op. 55 makes one of the most consequential identifications in Klach: AV is Arich Anpin. The four expansions of the Four-Letter Name (introduced at Op. 22) are now mapped onto the five Partzufim of Atzilut. The chapter also distinguishes Atika Kadisha from the Name of Atika — vocabulary that becomes load-bearing in the second half of the book.
AV is the highest expansion (gematria 72), produced by spelling the Four-Letter Name with yods in a specific pattern. Klach identifies AV with Arich Anpin — the operational root of all Atzilut. The other expansions follow in mapping: SaG corresponds to Abba and Imma (the parental pair); MaH corresponds to Zeir Anpin (Z"A); BaN corresponds to Nukva.
Klach also unfolds the four pathways to 72 — the arithmetic by which each expansion produces operational counts. AV simple (the basic count, 72). SaG +10+kolel (63 + 10 + 1 = 74, near 72 with adjustment). MaH +simple-the Four-Letter Name+kolel (45 + 26 + 1 = 72). BaN via ribu'a (the squaring of the Four-Letter Name yields 72 by another arithmetic). The four pathways are how the cosmic government's arithmetic produces the same operational total at each level.
The Atika Kadisha (Holy Ancient One) / Name of Atika distinction operates at a higher cosmic level. Atika Kadisha is the highest concealed root — the Atik aspect that connects upward toward Eyn Sof. The Name of Atika is the operational identity by which Atik manifests downward. Both are aspects of Atik Yomin (Op. 74); the distinction Op. 55 plants becomes structurally important in the Concealed Government unit (Op. 78–84) and the Unknown Head unit (Op. 85–89).
Op. 74 will introduce Atik as a Partzuf formally. Op. 90 will name A"A as the root of all Atzilut Partzufim. The four-expansions-to-five-Partzufim mapping operates throughout the rest of the book.