Are Corn Cereal Solids Gluten Free?

Maybe. If corn is the only questionable ingredient, it's probably safe to call gluten-free (unless it has been processed and combined with modified food starch or something like that... In which case such an alteration would also be listed within the ingredients).
For gluten-free diets you'll need to stay away from wheat, rye, barley and possibly oats.
Short answer: You're likely safe with corn, HOWEVER, most cereals are not gluten-free due to other added stabilizers, ingredients and flavorings. Specific corn cereals are available at health food stores which are gluten-free. Corn Chex are also now gluten free, as are Rice Chex and the Strawberry, Chocolate, Cinnamon and Honey Nut flavors of Chex brand.