The Talmud in tractate Yevamos (pg. 63b) says, "[Moshiach] Ben David won't arrive until all the souls are depleted from the body."
Rashi (the most important Talmudic commentator of all times) explains this very cryptic passage. "Body," says Rashi, "is the name of a partition that separates the Sechina (Divine presence) from the angels, which serves as the warehouse for all the souls that were created during the six days of creation, and that are destined to be given to bodies that will subsequently be created."
The above Talmudic passage teaches us that all the souls must assume bodily forms on earth before Moshiach can come. Even though unborn babies all possess divine souls (neshoma, since the unborn learn the entire Torah - oral, written, and esoteric - from an angel while in the mother's womb), the entire spiritual/soul complex that includes nefesh, ruach, and neshoma [basic vitality, spirit, and divine soul] all come together in the body momentarily before the baby is born (full references provided in the original post).
When a baby is born with a 'new' soul (yes, there is recycling also), that soul leaves the heavenly "Body", that is (in Rabbi Brody's words) "the heavenly warehouse for unborn souls. Until Guf [body] is empty, Moshiach is delayed in arriving."
I heard it said from a friend in Israel that one of the mekubalim (master kabbalists) announced, right before Shavuos (the holiday that just passed) that this task completed, the heavenly warehouse of new unborn souls is now empty, and simultaneously reports came out that the silver watch of the Geulah struck 12:00.
I'll attempt to get the name of the mekubal (kabbalist) and source. (If you can't quote with a source, it's just a rumor.)
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