Non-Singular Quantum Remnants, Holographic KMS Screens, and the Resolution of the Hawking Information Paradox within Stochastic Non-Commutative Quantum Geometry

This paper presents a formal, non-perturbative resolution to the Hawking information paradox and formulates the structural topology of Planckian black hole remnants within the framework of stochastic non-commutative quantum geometry. By marrying the discrete area-volume spectral gaps of loop quantum gravity (LQG) with the operational formalism of Connes’ spectral action, we replace the classical gravitational singularity with a stable, non-singular quantum core governed by a regularized Gauss-Nicolini potential. The event horizon is modeled not as a smooth mathematical continuous boundary, but as a holographic Kubo-Martin-Schwinger (KMS) screening layer acting on von Neumann algebras of type III₁. We demonstrate that the partial trace operation over unobservable Planckian degrees of freedom dynamically generates macroscopic thermodynamic time and open-system Lindbladian dissipation while strictly preserving underlying microscopic quantum unitarity (Tr(ρ) = 1). Definitive "here-and-now" numerical verification pipelines and strict falsification criteria for quantum optomechanical and astrophysical channels are explicitly detailed.