OS System / ε-Model — Chapter 21 - Atomic Structure from Structural Balance: Empirical Closure from Atoms to Molecules

This work presents a complete, closed empirical analysis of atomic and molecular structure derived from a single invariant structural balance relation.No force laws, field theories, orbital models, probability postulates, or fitted parameters are used. Atomic systems are analyzed using only empirically measured projection-layer quantities (spectral data, ionization energies, characteristic radii and bond lengths) to extract a structural quantity S under a fixed balance condition ε ≈ 0.50. The work demonstrates: Exact cubic structural scaling (S ∝ Z³) in hydrogen-like single-channel atomic systems The breakdown of cubic scaling in neutral multi-channel atoms, revealing discrete structural breakpoints A layered, non-monotonic organization of neutral atoms governed by balance saturation thresholds A bounded structural regime for molecules, distinct from both atomic single-channel and neutral atomic regimes Cross-scale consistency with balance behavior previously observed at planetary and galactic scales Electron count, shell structure, and molecular bonding emerge as consequences of balance closure rather than primitive physical properties. This document is a fixed analytical record.It contains no speculative elements, no adjustable assumptions, and no reinterpretation of quantum mechanics or chemistry.Light is used strictly as a projection tool to reveal structure, never as a causal agent.