THE CHEMICAL BOND AS A SPARSE INVARIANT STRUCTURE

Schilling, Ding, and Matito (Nature Communications, 2026) demonstrate that classical
chemical bonding patterns emerge strictly from Maximally Entangled Atomic Orbitals (MEAOs).
We prove that their information-theoretic procedure is mathematically isomorphic to orthogonal projection onto a lower-dimensional persistent sparse invariant manifold. This establishes the Representation Boundary Principle across both quantum chemistry and hydrodynamics: continuous unitary representations must be replaced by discrete topological projections to recover physically interpretable persistent structures Ψ. The Deterministic Spectral Manifold (DSM-861) provides one arithmetically rigid realization of such a projection space, unifying the mathematical treatment of macroscopic fluid singularities and subatomic chemical bonds