Holographic Correspondence: From Particle-Scale Hierarchy to Cosmological Parameters

We propose a phenomenological framework in which the finite Bekenstein–Hawking entropy of the cosmological horizon implies a holographic correspondence between the electron scale and the large-scale structure of the Universe. The central relation, $r_e^3 = (2/ \pi ) R_H \ell_{Pl}^2$ , follows from identifying the classical electron radius with the three-dimensional sector of a finite configurational basis defined by the horizon entropy.Building on this correspondence and a small number of explicitly stated structural postulates, the framework yields numerical predictions for the Hubble constant $H_0$, the fine-structure constant alpha, and the cosmological density fractions $\Omega_b$, $\Omega_{DM}$, $\Omega_m$, without introducing adjustable free parameters beyond the postulates themselves. A projection-balance condition among six configurational sectors gives $\alpha^{-1} = 136.3564$ and so on (0.5% from the CODATA 2022 value) and $\Omega_m = 0.31512$ (0.06% from Planck-2018). The same construction predicts an ultralight bosonic dark-matter candidate with mass $2.7 *10^{-14}$ eV /c^2 and Compton wavelength is similar to $4.6 *10^4$ km, offering a concrete, falsifiable target for astrophysical and laboratory searches for wave-like dark matter. The framework also reproduces the Eddington–Dirac large-number relations.This is a phenomenological/exploratory work: several of the structural postulates (the projection-balance normalization, the density-fraction weighting rule) are motivated by geometric analogy rather than derived from an underlying dynamical theory, and are stated explicitly as such. The manuscript is offered as a candidate framework for further scrutiny, refinement, or falsification, not as a completed theory.