Here is the fragment again:

Such as stacks of tottering books, crumpled paper, empty soda cans, and greasy pizza boxes.

You correctly identified the fragment as an afterthought phrase. Such as, the afterthought transition that begins the phrase, is the clue.

To fix this fragment, you could modify it so that you have the necessary main clause, like this:

Stacks of tottering books, crumpled paper, empty soda cans, and greasy pizza boxes indicated that Marvin was busy with a huge project.

Or you could use Punctuation Rule 7:

Main Clause + , + Afterthought Transition + Ø + Details.

The correction would look like this:

Many things indicated that Marvin was busy with a huge project, such as stacks of tottering books, crumpled paper, empty soda cans, and greasy pizza boxes.

Enjoy that delicious meal!

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