Geometric Sparsity Principle: A Structural Framework for Functional Rarity

This paper introduces the Geometric Sparsity Principle (GSP), a structural framework explaining how layered constraints induce admissibility contraction and geometric sparsity in high-dimensional state spaces. The framework proposes that functional rarity can arise directly from state-space geometry, prior to optimization, adaptation, or search processes. This paper constitutes Foundation 0 (F0) of the broader Ho Minh Framework. Earlier works explored downstream manifestations such as structural drift, structural asymmetry, optimization failure, and collapse dynamics. Here, a deeper upstream structural origin is proposed through the Geometric Sparsity Principle.