today i decided on an alternative strategy: i would try to construct a counterexample.
but i couldn't.
instead, i encountered object after object which were immune to my machinations; that is, examples which satisfy my hypotheses and none of my sufficient (simplifying) conditions ..
.. yet not be a counter-example to my claim.
in other words, no progress and just as much confusion as before.
of course, this doesn't mean i'm right;
it might just mean that i'm no good at imagining pathologies.
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