Cosmological Stabilization of Quantum Gravity: Spectral Realization of the Yang-Mills-Einstein System

This paper carries the Spectral Realization program past the Standard Model through three nodes: gravity, the QFT slice compared with itself; cosmology, that slice compared with gravity; and chemistry, cosmology compared with itself. At each node the laxator induces a cell measuring a state's residual off the gauge-fixed sector.

At the gravity node the classifier is Einstein--Cartan and the promotion datum is the tetrad. Transgression is taken to be the spectral action. Its heat-kernel expansion returns the Einstein--Hilbert term, the negative Higgs mass term the electroweak node left open, and Einstein's equations, with vacuum, Weyl and contorsion terms whose content cosmology returns. The node supplies the master equation, the Lorentz-level retract and, conjecturally, a Majorana neutrino mass.

At the cosmology node the cell compares pass count with proper time, failing by the lapse deviation. Horizons compactify Euclidean time with period $2\pi/\kappa$, fixing the finite inverse temperature. The spectrum, the change in expansion and the shear of the holographic boundary, carries the dark sector in a fluid model. Counting fixes the volume element, so the cosmological constant becomes an integration constant whose fluctuations set its magnitude. Cosmology thereby stabilizes quantum gravity.

At the chemistry node the obstruction is the symmetric group of identical fermions, and its sign character is the Pauli principle. Hartree--Fock is the lift, and the correlation energy the residual. Newton's and Boltzmann's constants and the Planck-to-electroweak ratio are universal ratios. The sign character is the Lorentz node's $\mathbb{Z}/2$, so matter is stable because fermions are spinors.