I don't think it is eggs - my feeling is that it is trying to send out air roots for whatever reason. I've got a few dwarf tomatoes that send out a mass of very short roots - not sure why - as a test, see if you can scrape any of that off gently. If not, it may be that the stem split - pressure, bending - and it is essentially trying to guarantee its future by re rooting.
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Craig
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