Hex9: A Quasi-Authalic, Quasi-Continuous Hexagonal DGGS on the Reference Ellipsoid

What the math gives to ML

The paper provides a constructive contraction-based address system: repeatedly selecting one of nine affine child maps produces nested compact cells whose diameters shrink geometrically, so every infinite address identifies exactly one limiting point. This can transfer to hierarchical positional representations or spatial latent grids, where discrete child codes provide a stable multiscale coordinate instead of unconstrained learned positional embeddings. The main asset is not the geographic projection itself, but the explicit injective-in-the-limit address, deterministic refinement, and quantitative resolution guarantee. A practical adaptation is a nine-way recursive positional encoder with shared refinement rules and coarse-to-fine feature lookup.