SpectralisTM: Predictive Engine of Atomic Properties

Atomic number Z is an assigned integer index that tracks the ordering of the measured K-edge frequencies, ν_max, which define the internal spectral coordinate. However, Z advances by a fixed increment (ΔZ = 1), while the spectral intervals increase non-uniformly (Δν_max = a + bν_max, Z > 54). As Δν_max increases, progression along the spectral coordinate seems to accelerate relative to the uniformly spaced Z index. This apparent acceleration can be mistaken for a high-Z physical effect. Adding the accumulated coordinate mismatch to the empirical spectral predictions reconstructs the full Carlson–Nestor Dirac–Fock sequence with a median absolute percentage error of 0.0422% and an RMSE of 0.185 keV.^(1,2,3)

Z = 3–200 denotes the spectral extrapolation range; it does not imply that distinct elements exist throughout this range. The Spectral Framework describes the spectral contraction of periodic differentiation with increasing spectral scale by the empirical relation Δp ∝ ν_max^−1.19 (R² = 0.9995). As ν_max increases, the spectral branches that distinguish chemical groups become increasingly compressed and approach quasi-degeneracy, so the spectral structures defining distinct chemical and physical elemental identities progressively lose resolution. The well-known lanthanide contraction is a manifestation of this broader spectral contraction. At sufficiently high spectral scale, distinct elemental identity may therefore no longer be physically meaningful within the framework. The Radiation Limit Hypothesis extends this observed trend: if the scaling law persists asymptotically, periodic branches converge until internal spectral hierarchy and periodic distinguishability disappear, approaching a single-scale spectral regime rather than distinguishable atomic structures.⁽⁴⁾