How do you know when a cartridge has broken in?

It seems very gradual to me...it happened during my first week of listening. But you'll definitely notice. The sound becomes less "stiff," soundstaging improves, etc. I'm no analog expert, I'm actually just getting into it, but those are my observations.

I understand the theory of what occurs but in real-world experience, how exactly do you know?

Aurally, it sounds smoother and more extended on either end of its fr. It probably tracks slightly better as the suspension softens a bit.

Is the effect subtle, transitional or abrupt? Is stylus wear part of the break-in process? Is there more value on the resale market for a cartridge that is broken in or is it just considered used and possibly abused?

The effect is gradual -- but perceptible. Stylus wear: strictly speaking, no. More value -- no.

it should sound fine from to get-go

The amount of time also depends on the particular cartridge, as some cartridges take longer than the 20-50 hours you state. Koetsu is certainly one of those that take at least a hundred hours or so to break in. Both my Koestu's, the Black and the Rosewood Signature, while doing the majority of breaking in during the first 50 hours, continued to change their sonic characteristics up to at least a hundred hours (and possibly even after that, but I was too happily listening to notice at that point!).

The affects of the breaking in on the Koetsus was pretty obvious, as both the treble response and to a lesser extent, the bass response, became more fully extended. Also, a less obvious improvement, (a refinement actually), was to the soundstaging and imaging.

And to answer you questions, the break in is very gradual, (not abrupt), stylus wear is not a part of it (the suspension is actually what is being broken in), and no, the resale market value (like virtually everything in this world), goes down the more you use it.

My two cents worth.

Then how do the cartridge break in tracks of the Cardas Sweep record speed up the break in process. I do not believe the suspension break in is accelerated. But then, I have not really been clear what these tracks do and how they work.

My experience breaking in quite a few cartridges is very similar to Kurt tank's, and I echo what he said.

The break-in tracks on the Cardas LP have greater amplitudes and a more varied mix of frequencies and phase relationships than most music. They work the elastomers in a suspension more completely and vigorously than playing music for the same length of time.

That said, I don't use the break-in tracks unless a cartridge is unlistenably unpleasant. If the sound is tolerable (or better) then I listen to music and enjoy the changes. Hearing what happens and thinking about why it's doing so is educational and part of the fun, and I'd rather listen to music, even "imperfect" music, than test tones.