Combine all ingredients with stick blender. Slowly add more liquid while blending until the result is the consistency of ketchup.
Cover and store in a warm (65-85F) place for 1-4 weeks. Ketchup will bubble and get more sour as it ages. Remove to refrigerator when the ketchup is tart enough to be delicious.
Notes
You'll some kind of culture to inoculate this. You can use pickle juice or sauerkraut juice or something else that you've fermented. You can even use a small amount of whey strained out of some fresh yogurt.