What is the ruling on my fasting while there is blood stuck between my teeth, but it does not mix with the saliva nor does it come out as a hemorrhage?

Unchanged saliva, when swallowed, does not affect the validity of the fast. What is seen between the teeth after flossing, if it does not disappear with mouthwash, is not blood; rather, it may be a change in gum color that will fade over time.