“The L-PT phase transition point is typically a critical exceptional point, where multiple collective excitation modes with zero excitation spectrum coalesce.”

“The paper obtains mean-field analogues of momentum distribution formulas for electron gas in high density and metallic density limits, and applies to a general class of singular potentials.”

“The prosumer community can achieve gains from trade up to 40% relative to the grid-only benchmark.”

“The paper provides quantitative estimates on propagation of chaos for the deterministic case, showing an improved convergence rate.”

“The article is based on DFT+DMFT calculations, a computational method.”

“Threshold rules produce a distinct non-mean-field universality class with β≈0.75 and a systematic failure of MF-DP dynamical scaling. We show that thresholding acts as a relevant perturbation to DP.”

“The model is consistent with the quasi-criticality hypothesis in that it displays regions of maximal dynamical susceptibility and maximal mutual information predicated on the strength of the external stimuli.”

“Skill drift imposes an intrinsic ceiling on long-run accuracy (the ``Red Queen'' effect).”

“Gaussian spatial correlations reshape roughness increments, eliminate asymmetric multi-site traps, and thereby recover mean-field diffusion.”

“The article uses mean-field theory on a tree structure.”

“The article's focus is on Quantum Mean-Fields Spin Systems in a Random External Field.”

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