The numerical value of "Joseph" [in Hebrew, "Yosef"] is 6 times that of the name Havayah.
"Yosef" is spelled: yud-vav-samech-pei = 10 + 6 + 60 + 80 = 156.
6 x 26 (the numerical value of Havayah) = 156.
The significance of these [six names Havayah] is as follows: We have explained in numerous contexts, including that of the commandment of circumcision in our discussion of parashat Lech Lecha, at length, that even though the five states of chesed spread throughout the body of Zeir Anpin, from chesed to yesod, nonetheless, the radiance of all the five states of chesed is absorbed in yesod; the five states of gevura descend into yesod as well.
The content of all the midot coalesces in yesod, where it is prepared to be transferred to expression in malchut.
Still, even though all five states of chesed and all five states of gevura descend [into yesod], their main states are the three revealed states of chesed, i.e. those present in tiferet, netzach, and hod, as is known.
The three revealed states of gevura are sweetened by the three revealed states of chesed….
As we have mentioned previously, yesod of Imma extends until the upper third of tiferet of Zeir Anpin, meaning that the drive of the intellect to express itself is present in the midot produced by the intellect as far as the intellectual aspect of tiferet. From that point on, the midot "take over", and the dominant consciousness is that of pure midot, with the intellectual rationale for the midot present only in the background.
The three [revealed] states of gevura are sweetened by the three [revealed] states of chesed there [i.e. in yesod].
True, all five states of gevura are given to the feminine [partzuf, Nukva,] i.e. into her daat, as is known. And so too, all the five states of chesed are transferred to the feminine [partzuf] during the coupling [of Zeir Anpin and Nukva], as a drop of "male water" [i.e. seed]. Nonetheless, since [the lower three states] are revealed lights, [only] their source and radiance remains in yesod.
Though all five states of chesed and gevura that make up the sub-sefirot of chesed-gevura-tiferet-netzach-hod of Zeir Anpin pass through its yesod, what remains in it is the lower midot, i.e. the summation of chesed and gevura in tiferet and the orientation of the midot outward in netzach and hod.
Joseph… personified yesod….
These [states] are the three names Havayah of the [revealed] states of chesed and [those of] the three [revealed] states of gevura. [These six names Havayah] are the numerical equivalent of "Joseph".
Joseph, as is known, personified yesod.
With this knowledge, you can understand why yesod is called "the second arbitrator", for the said reason, namely, that in it the three [revealed] states of chesed are intertwined with the three [revealed] states of gevura, which are thereby sweetened.
The first "arbitrator" is tiferet, which reconciles chesed and gevura. Here, yesod reconciles the states of chesed and gevura above it.
With this you can also understand why this sefira is called "yesod". The reason is that this sefira tends to the left, this being the mystical meaning of "the live end", referring to yesod tending toward Isaac, which is the left axis.
The name "Isaac", in Hebrew, "Yitzchak" (spelled yud-tzadik-chet-kuf) can be rearranged to spell "the live end" ("keitz chai", kuf-tzadik chet-yud). The midot are also known as the six "ends" or "extremities", inasmuch as they define the six directions of three-dimensional space. Yesod is the "alive" "end", for it undergoes change (growth and shrinkage), thus exhibiting the properties of life.
The numerical value of the three states of gevura that remain in it, which are three names Havayah, is 78. Together with 1 for each of them, this sums to 81, the numerical value of "yesod" with the kolel.
3 x 26 = 78.
"Yesod" is spelled: yud-samech-vav-dalet = 10 + 60 + 6 + 4 = 80
The seven names…are called 'seven pearls'….
Another reason [this sefira] is called "yesod" is the following. What is written in the Zohar (II:92a, in Raya Mehemna) about the verse, "Remember the Shabbat day" (Ex. 20:8), concerning the seven names, is well-known. They are called "seven pearls", and the Shabbat is called "Y-ah Ado-nai".
These seven names are associated with the seven blessings of the Shabbat Standing Prayer (see third installment of parashat Tetzaveh), and that the fourth blessing of the Shabbat Standing Prayer, which is the only one that refers specifically to the Shabbat, is associated with the name Y-ah Ado-nai.
It is also known that the Shabbat is associated with yesod, which is called "the Seventh".
Normally, we associate the Shabbat with malchut, the seventh midah. However, in the context of Zeir Anpin, malchut is not truly a separate sefira, but is called "the crown of the yesod", associated physically with the glans of the male reproductive organ. Malchut comes into its own only as the full partzuf of Nukva. Thus, the "seventh" of the midot within Zeir Anpin - and therefore, the Shabbat as well - can still be considered to be part of yesod.
Therefore, the numerical value of "yesod" is the same as that of the names Y-ah Ado-nai.
"Yesod" = 80, as above.
"Y-ah Ado-nai" is spelled: yud-hei alef-dalet-nun-yud = (10 + 5) + (1 + 4 + 50 + 10) = 15 + 65 = 80.
These two names correspond to the two aspects with [yesod]: yesod [itself] and its "crown". Yesod itself is called "Y-ah", and its "crown" is called "Ado-nai".
Furthermore, the yesod of Leah and the yesod of Rachel are [signified by] two final mem's, the combined numerical value of which is also that of yesod.
Leah and Rachel are the two partzufim of Nukva, as we know. The female yesod, the womb, is indicated by a final, closed mem, which depicts a closed, empty space that will be filled by the male seed. The numerical value of mem is 40, so the 2 yesod's of Leah and Rachel equal together 80, the numerical value of "yesod".
This indicates that yesod couples with the two yesod's of Rachel and Leah.
[Adapted by Moshe Yakov Wisnefsky from Shaar HaPesukim, parashat Lech Lecha]