Required portable control:
  python3 -I -B reproducibility/check_outer_focal_product.py
Dependencies: Python standard library only.
The checker is byte-identical to the accepted originating script.
It verifies nine polynomial identities, an exact primitive N8 geometry
fixture and repeated-triangle product arithmetic. Its historical
triangle-certificate path is a provenance string, not a runtime import.
It does not execute the general elliptic-function proof or rerun that
earlier triangle reflection certificate. The manuscript supplies the
triangle's reflection and caustic-tangency proof explicitly.

Optional numerical diagnostic:
  python3 -B reproducibility/check_direct_geometry.py
Optional dependency: mpmath==1.3.0.
The retained actual originating output describes 39 families at four
phases each and 85 decimal digits. This is a floating-point regression,
not an exact certificate. The package harness does not execute it.

The source-provenance manifests record the archival project layout.
No third-party PDF, HTML or page image is included in the ZIP.
