How do we know that mold on bread is a decomposer

Most mold on bread is harmless.  Some molds are poisonous though and can make you very ill.

This might help also :
Although mold can grow on many types of foods, mold on bread is common because bread provides a very desirable source of nutrients for mold.  It’s often kept in a warm area of your home – a cupboard or breadbox rather than the refrigerator.  It’s moist.  And mold likes the ingredients in bread.