yesterday i printed out some research notes i wrote in february ..

.. all 24 pages of them, just to prove one lemma. [1]

ye gods; the ideas still make intuitive sense, but the proofs are painfully technical .. much more so than i recall. [2]

they're not even a complete set of notes! for the lemma to have a complete proof, i'll have to read another set of 5 pages of notes for a sub-lemma, as well as a short 3-page section of an old preprint of mine ..

no wonder why i couldn't convince myself to work hard in april. after that and then that trip to spain in march, i had little to no energy left.

anyway, it's time to write up the result(s) ..

.. because what currently exists are the **notes**, not a preprint. there's a lot of exposition and simplification before i have anything remotely readable!

[1] *at this point maybe i should promote it to "theorem" status. (before i thought it was .. well, obvious, and the proof would be short.)*

[2] *one series of estimates involved 4-5 indices. i was comparing intervals at different dyadic scales, as well as the same scale, which explains two indices .. but the intervals aren't nested in one another, which requires two more indices. lastly, these estimates were "fibrewise," so an additional fifth index kept track of which fibre was which.*

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