# Evidence: Optimize with Optax

Copy this template into your own portfolio and fill it after running your modified exercise.

## Evidence required

Save the analytic first update, manual/Optax equivalence, retained/reset momentum comparison, continuation replay and double-subtraction repair. Include the zero-gradient momentum step and explain why retained state still moves the parameter.

- Command: `python3 phases/04-optimization/04-optimize-with-optax/code/main.py`
- Working directory: repository root
- Python / JAX / NumPy versions: 
- Hardware and device: 
- My prediction before running: 
- My change to the exercise: 
- Exit code and meaningful output: 
- Why the result supports or contradicts my prediction: 
- Checkpoint result: 
- Artifact link or saved filename: 
- Portfolio status: saved in local workspace