THE CHEMICAL BOND AS A PERSISTENT SPARSE INVARIANT STRUCTURE

Michael I Aksman

Published Jun 2, 2026• 0 citations

Abstract

Schilling, Ding, and Matito (Nature Communications, 2026) demonstrate that classical chemical bonding patterns emerge from Maximally Entangled Atomic Orbitals (MEAOs).We prove that their construction is mathematically equivalent to orthogonal projection onto a lower-dimensional persistent sparse invariant manifold. This establishes the Representation Boundary Principle: continuous unitary representations must be replaced by discrete topological projections to recover physically interpretable persistent structures Ψ. We unify this with the Bethe Ansatz and Thermodynamic Bethe Ansatz (TBA), the limitations of unitary quantum machine learning in fluids (Itani & Sreenivasan, 2025), and the Deterministic Spectral Manifold (DSM-861). The chemical bond, like vortonic structures in hydrodynamics, is a Persistent Sparse Invariant Structure extracted from dense continuous states.DSM-861 provides an arithmetically rigid realization of the required projection operator.

DOI: 10.5281/zenodo.20512482

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