“The paper formulates the covariant hydrodynamics equations as an intersection problem on an infinite dimensional symplectic manifold associated with spacetime.”

“The paper derives sufficient conditions on a compact self adjoint perturbation to guarantee that the perturbed system stays exactly observable.”

“The method effectively suppresses spectral pollution and resolves closely spaced spectral components.”

“Each such variety is irreducible and admits a rational parametrization. The assignment is functorial: algebra quotients correspond to monomial maps among the varieties.”

“Any proper species sampling process can be written, at the prior level, as a finite mixture with a latent truncation variable and reweighted atoms, while preserving its distributional features exactly.”

“The rescaled Hitchin metric converges, in the semiclassical limit, to the hyperkähler metric on the hyperpolygon space.”

“The paper introduces a kernel Cheeger constant that quantifies connectedness relative to kernel localization, yielding a clean stability certificate.”

“The paper presents a class of QSLs formulated in terms of the two-parameter Sharma-Mittal entropy (SME), applicable to finite-dimensional systems evolving under general nonunitary dynamics.”

“The paper derives an exact semidefinite characterization of nonnegative APS and introduces a derivative-based regularizer that promotes smoothly varying APS profiles while preserving transitions of clusters.”

“The paper demonstrates the reconstruction of short-range perturbations from scattering data in a linearized and finite-dimensional setting, along with a stability result.”

“To overcome this limitation, our framework requires only the computation of directional derivatives and a pre-basis for the Hilbert space domain.”

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“The article's focus is on hyperexponential stabilization, suggesting rapid convergence.”