A common non-perturbative quantization structure in black holes, atomic physics and Regge trajectories

Motivated by a semiclassical mass-quantization relation previously proposed for extremal primordial black holes, we investigate whether its algebraic structure admits formal counterparts in atomic physics and in the description of hadronic Regge trajectories. In the electromagnetic case, the corresponding algebraic relation is shown to be compatible with the conventional Bohr construction; the discrete atomic spectrum itself, however, follows from the usual Bohr angular-momentum quantization condition and is not independently derived from the proposed correspondence. An analogous formal construction is then considered for strong interactions using Abelian color projections. It leads to an expression for the inverse Regge slope, S = 1/α′, in terms of an energy scale and the strong coupling. The phenomenological inverse Regge slope is used as an input, and crossings with the two-loop running QCD coupling are studied as a qualitative self-consistency test rather than as a prediction of the Regge slope. The sensitivity of these crossings to the relevant parameters and color projections is examined, and the limitations of the perturbative treatment at low energy are explicitly discussed. Representative meson and baryon spectra are also compared with the standard linear Regge form, illustrating both the phenomenological scale of the inverse slope and the role of the nonzero Regge intercept, which is not determined by the present construction. The results therefore point to a common formal algebraic pattern across the gravitational, atomic, and strong-interaction cases, without establishing a dynamical equivalence or a universal physical quantization mechanism among the three systems.