Golden Cut-and-Project Adapter

Abstract

The existing golden Minkowski lattice instantiates the generic cut-and-project carrier without changing its model sets.

Theorem 1.1 (The generic and existing golden model sets coincide).

$$\mathrm{modelSet}(\mathrm{goldenScheme}(),W)={\mathrm{modelSet}}_{\mathrm{golden}}(W)$$

Proof. Machine-checked in Lean as D5/S3/Fourier/GoldenCutProjectSchemeAdapter.goldenScheme_modelSet_eq (✓ std3). ∎

Source. Repository-derived.

Commentary.

The lattice carrier is the existing range of the two real golden embeddings.

Injectivity of physical projection follows from injectivity of the distinguished real embedding on GoldenInt.

Unfolding a lattice-range witness identifies the generic internal-window selection with the repository’s established modelSet predicate. The existing object therefore becomes the consumer of the shared cut-and-project API.

References

• Truth anchor: D5/S3/Fourier/GoldenCutProjectSchemeAdapter.goldenScheme_modelSet_eq
• Dependency: D5/S1/Scale/MinkowskiModelSet
• Dependency: D5/S3/Fourier/CutProjectScheme