Parametric Doubling Centered-Cylinder All-Radius Theorem — Restricted Research Preservation Record

Restricted preservation record documenting an exact mathematical research development for a centered-cylinder binary and parametric doubling family. The deposit contains the theorem-development chain, corrected sign-aware dual formulation, primal construction, exact symbolic verification material, provenance information, explicit claim boundaries, and cryptographic integrity hashes.

The preserved result concerns the declared centered-cylinder model only. It is not presented as a solution of unrestricted Gröchenig Problem 2.4, and no worldwide novelty or priority claim is made at this stage. External release of the mathematical contents remains withheld pending further verification and publication decisions.