I really feel that paper is an underrepresented mechanic in puzzles, so this puzzle explores the numerous sides of this topic. It’s (nearly) all lovingly handmade, so please excuse any errors.

1. Orikami

2. Transformation

https://imgur.com/a/S4stWDA

3. Twists and Flips
   

4. The Main Proof of FACT

https://imgur.com/a/4wAuquk

5. Cubed

META:

Your last reply ought to be a single phrase that describes this puzzle.

(This is my first metapuzzle so constructive criticisms are welcome!)

Hint 1: Still no progress? Perhaps you do not know the place to start out. Here’s rating of the difficulties of the puzzles from best to hardest:

1, 4, 3, 2, 5