Latent Geometry and the Emergence of Lorentzian Time in Matrix Quantum Mechanics

Abstract

We introduce \emph{latent geometry} in BFSS/BMN models. Before an emergent geometry evaporates at the geometric transition, large-$d$ Gaussianization encodes its information in the exceptional $N=2$ sector selected by the baby fuzzy sphere, a single active spin-$1/2$ Pauli block. Dimensional reduction, finite-$N$ Gaussianization and exact Molien--Weyl projection transport this encoding to mass-deformed BFSS$_2$. At $N=2$, the same stable BFSS$_2$ oscillator admits inequivalent unitary $\mathbf{H}^2_\theta=\mathbf{EAdS}^2_\theta$ and $\mathbf{dS}^2_\theta$ decodings, realizing spacetime transmutation and the emergence of Lorentzian time.