Abstract. Holographic aspects of 2D Fresnel type memory patterns with 3D couplings and mutual diffractions are considered. Encoding topological charges and spin, the nonlinear interaction potentials are assigned to a shared holographic memory phase space with limited information storage density. Neutral intermediate structures arise in the overlap region. The neutralizing process is regarded as a generator of anti-charge around the topological monopole singularity and maps Coulomb/Kepler to oscillator potentials. The overlap pattern projects a quasiparticle into the orthogonal holographic extra dimension while providing for a massless and stereographic coupling (Gudermannian function). Basic interactions are: local strong between overlapping topological charges, weak by neutral intermediate quasiparticle overlap patterns, topological charge stereographic long-range interaction in 2D, and a weak long-range higher-dimensional interaction. It is conjectured that the mediating neutral patterns responsible for interaction and energy shifts behave like neutrons, neutrinos, photons, and quasiparticles in 2D crystals (graphene). A cluster of Z=4 partially overlapping topological charge memory patterns could explain the exceptional stability of Beryllium with 5 neutrons. Forcing special phase conditions this principle could act as a prototype for holographic energy releases/drives.

Abstract. Curvature-Invariant de Sitter spin currents mediating between spaces of different constant curvature are assigned to special holographic twistorial/gyro angular density patterns on low-dimensional AdS/dS surfaces. The corresponding curvature-invariant geodetic impedance and matching condition for spin currents are given by a conformal Gudermannian mapping between surfaces of different constant curvatures by the AdS/CFT correspondence. The corresponding geodetic extra rotations and frequency/phase shifts leading to characteristic holographic memory precession patterns on the Poincaré disc are quantified in Euler angular dynamics and related to the functional equation of the Riemann zeta function.