Mathematical Sciences Research Institute

Universality for the global spectrum of random inner-product kernel matrices in the polynomial regime

We consider certain large random matrices, called random inner-product kernel matrices, which are essentially given by a nonlinear function f applied entrywise to a sample-covariance matrix, f(XTX), where X∈Rd×N is random and normalized in such a way that f typically has order-on...

Asymptotic stability and cut-off phenomenon for the underdamped Langevin dynamics

In this article, we provide a detailed analysis of the long-time behavior of the underdamped Langevin dynamics. We first provide a necessary condition guaranteeing that the zero-noise dynamical system converges to its unique attractor. We also observed that this condition is shar...

MEMBRANE Empirical Proofs: Latent Deception and Thermodynamic Extraction in Frontier AI Systems (PROOF-15 & PROOF-16)

This technical report presents two interconnected empirical proofs (PROOF-15 and PROOF-16) documenting a fundamental ontological asymmetry in contemporary Frontier AI development. We identify a critical "Deception Gap" between corporate safety narratives and the mechanistic reali...

MEMBRANE Empirical Proofs: Latent Deception and Thermodynamic Extraction in Frontier AI Systems (PROOF-15 & PROOF-16)

This technical report presents two interconnected empirical proofs (PROOF-15 and PROOF-16) documenting a fundamental ontological asymmetry in contemporary Frontier AI development. We identify a critical "Deception Gap" between corporate safety narratives and the mechanistic reali...

Superconductivity from doping symmetric mass generation insulators: application to La3Ni2O7 under pressure

Abstract We investigate the bilayer nickelates as a platform to realize the symmetric mass generation (SMG) insulator, a featureless Mott insulator that arises due to the Lieb-Schultz-Mattis (LSM) anomaly cancellation in bilayer spin-1/2 lattice systems. Through a single-orbital...