$\mathcal{H}$olographic $\mathcal{N}$aturalness and Information See-Saw Mechanism for Neutrinos

Abstract: The microscopic origin of the de Sitter entropy remains a central puzzle in quantum gravity related to the cosmological constant problem. Within $\mathcal{H}$olographic $\mathcal{N}$aturalness, we propose this entropy is carried by light, coherent degrees of freedom - "hairons" - emerging as moduli of gravitational instantons on orbifolds. From the Euclidean de Sitter instanton ($S^4$), we construct a new class of orbifold gravitational instantons, $S^4/\mathbb{Z}_N$, where $N$ corresponds to the de Sitter entropy. The moduli space dimension scales linearly with $N$, and we identify these moduli with hairon fields. A $\mathbb{Z}N$ symmetry from Wilson loops ensures mode distinguishability, yielding the correct entropy. Hairons acquire a mass of the order of the Hubble scale with negligible interactions, suggesting the de Sitter vacuum is a Bose-Einstein condensate of these excitations. We then unify the neutrino mass generation with the cosmological constant via gravitational topology. The small neutrino mass emerges naturally without new physics beyond the Standard Model. The gravitational Chern-Simons structure and anomaly force a topological Higgs mechanism, leading to neutrino condensation via $S^4/\mathbb{Z}_N$ instantons. The topological degrees $N \sim M\text{P}^2/Λ\sim 10^{120}$ provide both a holographic entropy counting and a $1/N$ information see-saw mechanism for neutrino masses. Predictions: (i) neutrino superfluid condensation forming Cooper pairs below meV as cold dark matter; (ii) resolution of the strong CP problem via a QCD composite axion; (iii) time-varying neutrino masses tracking th dark energy evolution; (iv) signatures in astroparticle physics, ultra-high-energy cosmic rays and high magnetic field experiments.