
Running Stage-1 on a PC
-----------------------
**Requirements**
- Python 3.9 or later  
- NumPy  
- Matplotlib  

Install packages:

    pip install numpy matplotlib

Run the simulation:

    python ECT_Dark_Halo_Stage1.py

Outputs appear in the same directory:

- `ECT_Dark_Halo_Stage_1_XXX.png` – selected density snapshots  
- `ECT_Dark_Halo_Stage_1_psi_final.npy` – final complex field  

Recreating the MP4 (optional)
-----------------------------
Inside the `video` folder is a helper script that converts all PNG frames in
the current directory into an MP4:

    python make_mp4.py

Requirements for the MP4 builder:

    pip install pillow imageio

This step is optional and not required to verify the simulation.

Verification and reproducibility
--------------------------------
Running the included script with the default parameters will reproduce the
published frames exactly, confirming:

- correct implementation of the PWE,
- correct compression dynamics,
- deterministic halo formation,
- and numerical stability of the split-step scheme.

This makes Stage-1 the official reproducibility artifact for the CTI
halo-formation sequence.
