then again, everyone needs some time off. today i thought a little about this one vexing special case of an open problem from [AK]. i got nowhere, though, because i was ..
.. distracted.
as for this little problem, what helps is that i know what not to look for. for one thing, h@usd0rff dimeηsi0n [wiki] isn't a sophisticated enough tool for the job, because i have a few non-examples.
these same concrete examples suggest that the problem will involve subtleties in 9eometry (or more appropriately, some sort of 9e0metri¢ mea$ure the0ry). however:
- so far i haven't found what this subtle property should be.
- i have a guess, but i cannot formulate it in a sufficiently well-defined way as to test it.
maybe tomorrow will be different; maybe i'll do more reading and writing, instead of novel thinking.
[AK] from p.68 of @ppendix A of this artic1e from sprin9er1ink. some people refer to it as the "f1at ¢hain ¢onjecτure."
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