# Reproduction package: Power-Weighted Lifts

## One-command executable verification available here

```bat
python verify_sympy.py
```

Expected terminal result begins with:

```json
{"status":"PASS"}
```

The command creates `certificate_sympy.json` using exact rational arithmetic.

## Independent implementations

```bat
sage verify_sage.py
maple -q verify_maple.mpl
```

These are intentionally separate implementations rather than wrappers around the SymPy script.

## Claims checked

- 27 exact Jacobian checks on `1 <= k <= 6`, `k < d <= 8`.
- 10 exact instances of the uniform odd-parameter collision.
- Fully expanded `(k,d)=(2,3)` map.
- Exact determinant `-2/3` for that map.
- Exact distinctness of its two rational source points.
- Exact common image `(0,9/64,1)`.

The arbitrary-parameter results are proved in `paper.md`; finite grids are regression tests, not the proof.