Tznius = Torah?
I only said, categorically, that it does not exist in the Gemara. I also said I had my doubts about the GRA making that wholesale equation of tznius keneged kulam, as well.
Anyway, as I believe in checking what sources say rather than speculating on them as possibilities, I did crack open the Wizard of Oz's tome (we got it from a neighbor who thought it was not for her) to the pages that Chaim told me was missing from the text available online.On p. 36, Falk begins a section C. entitled "What Torah Does for men, tznius does for women." 1.Tznius is an antidote to theyetzer horah. On p. 37, he says, "a woman, whose function is to establish and manage a home and family, does not have Torah learning to counteract her yetzer horah." He goes on to claim the power of tznius is such that "when kept properly is all encompassing. It gives so much kedusha and strength to the woman that she is capable of outwitting the yetzer horah and withstanding its relentless pressure. "
On p. 37 he refers to the GRA and quotes the same close to the letter to his mother that Chaim quoted above, "My dear mother, I know that you do not require my mussar, for I am aware that you ara a tzanua." It is Falk's own huge leap of logic that brings him to conclude from that phrase alone, " He was convinced, that just as being steeped in Torah enables a man to combat his 'lower self', so too, being steeped in tznius enables a woman to be victorious in the same way."
It is proven, thus, that the GRA never said what people say he did, and that people confuse what Falk argues for with what the GRA actually said.
He does have a bit more to hang his hat on when quoting the Chazon Ish, but that relies on a secondary source: Falk p.42: "It is appropriate in this context to quote from the life story of Rebbetzin Karelitz a.h. the mother of Hagaon Harav Nissim Karelitz shlita ('Silence is Thy Praise' p. 106)"'How much the Chazon Ish valued the modesty of a Jewish woman as perhaps best evident in the response he once gave when asked, 'What can a young lady do to match the merit of young man's learning?'
"'Let her work on her tznius!' he answered."
Even that, though, does not exactly equate the effectiveness of tznius with that of Torah but merely suggests it as something women could occupy themselves with. I wonder a bit at this, though, because Chazal clearly said that women earn Olam Haba through the Torah learning of their husbands and sons -- not through their tznius. Perhaps this was a suggestion for a woman who was unmarried and childless.