Aperiodic Invariants in Atomic and Cosmological Spectra: Evidence for the Reflexionsmanifest

This paper investigates whether aperiodic invariants appear consistently in both atomic spectra and cosmological gravitational-wave spectra, providing empirical evidence for the Reflexionsmanifest.

Using the hydrogen atom as a paradigmatic mesoholon, we show that its electronic spectral series (Lyman, Balmer, Paschen, etc.) exhibit a hyperbolic, aperiodic-yet-invariant law: level spacings are neither random nor periodic, but governed by relational structures. These microscopic invariants are then compared with macroscopic invariants in the stochastic gravitational-wave background, predicted by the AEI/BLH framework, which displays analogous shifts, drifts, and asymmetries.

Statistical tests (Pearson, Spearman correlations >0.97; KL and Jensen–Shannon divergences ≈ 0.004) confirm a strong structural equivalence. Both micro- and macro-systems instantiate the same reflexive syntax: universality emerging not from strict periodicity, but from the balance of local perturbation and global recurrence.

We conclude that this convergence constitutes first empirical evidence for the Reflexionsmanifest as a unifying grammar of physical law, bridging quantum and cosmological scales.

Keywords: Aperiodicity, Invariants, Reflexionsmanifest, Hydrogen Spectra, Gravitational Waves, Holonic Universe, Reflexive Syntax