Idea 1: {{idea1}}
Idea 2: {{idea2}}
Idea 3: {{idea3}}
Idea 4: {{idea4}}
Idea 5: {{idea5}}

Propose {{N}} hypotheses that would be appropriate given the ideas. Provide short commentary for each of your decisions. Do not talk about topics related to the simplicity or complexity of the expressions. I want ideas that are unique and interesting enough to amaze the world's best mathematicians. End with a JSON list that enumerates the proposed hypotheses following this format:
```json
["hyp1",
 "hyp2",
 ...
 "hyp{{N}}"
]
```