Ultimately it is your choice. I'd toss it. Slimy viscous brine is usually a sign of unacceptable bacteria activity - one reason why we skim it regularly throughout the process - due to unnecessary exposure to air.

Dave

I'd toss it as well. It's too bad after the time you've invested in that kraut, but i wouldn't be comfortable eating it.

If in fact the pH of brine is 3 , even 3.8 I would not worry about it. To further assure that no bad bacteria /spore can survive in that kind of acidic environment, I will add a Tbs of vinegar to a quart of kraut and refrigerate it.

your decision.
Seysonn

Is it slimy all the way down the container? Does the 'slime' rinse off after digging down a few inches? I would not "sample" the top 2-3 inches but I'd rinse and sample the kraut down below.

Thanks for everyone's responses!
Follow-up: I refrigerated the kraut for a few days while I was deciding what to do. I then decided to compost it but when I took it out of the refrigerator and started to spoon it out into the compost container, the slime was gone. The brine looked, smelled and tasted like my normal kraut, so I put it back in the refrigerator. I have since read that the cabbage core contains sucrose, which can produce a slimy characteristic to the brine due to dextran formation (see p.4 of the pdf link, upper right column). Maybe I shredded the cabbage a little too close to the core? Or maybe just the kraut being up out of the brine contributed. Upshot is...we've been eating it, it tastes great and no untoward effects...aside from the usual natural consequences of ingesting cabbage. :)

Here is a link that might be useful: NCSU fermentation article