Metamorphosis Part II — The Invariant Field (β-Independent Persistence Geometry)
Metamorphosis Part II — The Invariant Field (β-Independent Persistence Geometry)
This paper presents computational and structural evidence that the Sc-Rubs variational engine produces a β-invariant geometric field. Across β = 13, 19, and 40, the same confinement kernel, volumetric identity, and resonance structure persist, with only facet sharpness varying. The study demonstrates that the underlying geometry is stable, reproducible, and governed by a consistent scalar-field mechanism. The β-invariant behaviour aligns with crystalline variational models and anisotropic PDE systems. This work forms Part II of the Sc-Rubs Metamorphosis Trilogy.
β-invariance; persistence geometry; scalar-field emergence; variational engines; p-Laplacian systems; crystalline limits; geometric stability; computational geometry; Sc-Rubs.
β-invariance; persistence geometry; scalar-field emergence; variational engines; p-Laplacian systems; crystalline limits; geometric stability; computational geometry; Sc-Rubs.
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