So far all the "classic" ciabatta recipes I have found propose using small amounts of instant yeast.
But I'm pretty sure that ciabatta predates invention of instant yeast so why not use sourdough instead?
It work pretty well for me except the poolish doesn't get bubbly overnight in the fridge (6 degree Celsius) but if I keep it for like 3 days it looks like gluten gets over-fermented. On the other hand, if I add more sourdough to the poolish it probably will get too contaminated with over fermented whole wheat and rye (I use it to feed my sourdough). So is it the reason?