## Example API Payloads

### Create Universe
POST /universes
```json
{
  "name": "Group Theory",
  "description": "Universe for group theory",
  "universe_type": "group_theory",
  "axioms": ["Closure", "Associativity", "Identity", "Inverse"]
}
```

### Add Axiom
POST /axioms
```json
{
  "universe_id": 1,
  "statement": "Commutativity"
}
```

### Evolve Axiom
POST /axioms/evolve
Form data or JSON:
```json
{
  "axiom_id": 2,
  "new_statement": "Commutativity (strong)"
}
```

### Derive Theorem
POST /theorems/derive
```json
{
  "universe_id": 1,
  "axiom_ids": [1, 2],
  "statement": "Closure Commutativity"
}
```

### Create Proof
POST /proofs
```json
{
  "axiom_id": 1,
  "content": "Proof details here."
}
```