“”

“The paper establishes a complete classification for fermionic symmetry protected topological phases (FSPT) with purely discrete internal symmetries, which determines the crystalline case via the crystalline equivalence principle.”

“The paper derives bilinear tau forms of the canonically quantized Painlevé equations, relating them to those previously obtained from the $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations.”

“The paper develops an approximate Stein's Unbiased Risk Estimator (SURE) for the average mean squared error and establishes asymptotic optimality and regret bounds for a class of machine learning-assisted linear shrinkage estimators.”

“The paper shows that the homeomorphism problem for compact topological n-manifolds is Borel equivalent to equality on natural numbers, while the homeomorphism problem for noncompact topological 2-manifolds is of maximal complexity.”

“The paper derives fundamental estimation limits for a wide-band near-field sensing systems employing orthogonal frequency-division multiplexing signaling over a coherent processing interval.”

“The paper establishes a correspondence between solutions of the Liouville equation and the Weierstrass representations of spacelike and timelike minimal surfaces.”

“The paper shows that commutative Frobenius pseudomonoids in the bicategory of spans are in correspondence with 2-Segal cosymmetric sets.”

“The paper derives an exact identity for overdamped Langevin dynamics that equates the total EP rate to the mutual-information rate.”

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

“The regularized local markers eliminate the obstructive boundary irregularities successfully, and give rise to the desired global topological invariants such as the Chern number consistently when integrated over all the lattice sites.”

“For heavy scalar masses between 500 GeV and 1 TeV, we find that Br($H\to hh$)/ Br($H\to ZZ)\approx 9.5.”

“The paper introduces computational deficiency ($δ_{\text{poly}}$) and the class LeCam-P (Decision-Robust Polynomial Time).”

“The paper demonstrates a continuum of collisions between hydrodynamic modes at complex wavevector for dispersion relations with a branch point at the origin.”

“The paper establishes sharp two-sided heat kernel estimates for these Markov processes.”

“The paper establishes the consistency of the QMLE and derives its asymptotic distribution, and proposes a bias-corrected estimator.”

“The paper describes the structure of the twisted Jacquet module π_{N,ψ} of π with respect to N and a non-degenerate character ψ of N.”

“For any Feller's Brownian motion that is not purely driven by jumps at the boundary, we construct a sequence of boundary random walks whose appropriately rescaled processes converge weakly to the given Feller's Brownian motion.”

“The paper establishes continuity of the operators and the unique strong solvability of the corresponding nonlocal parabolic equations in $L_p$ spaces.”

“The paper provides a necessary and sufficient condition for the incenter of a given n-simplex with k-rational vertices to be k-rational.”

“The paper establishes error bounds for the reconstructed solution and the source term without requiring classical source conditions, and derives an expected convergence rate for the source error in a weaker topology.”

“The resulting acceptor layer achieves a striking Δn response time as short as 9 fs, approaching a single optical cycle, and is further tunable to sub-cycle timescales.”

“The paper identifies the obstruction to the existence of the Prequantum Groupoid as the non-additivity of the integration of the prequantum form on the space of loops.”

“For every irrational ω with β(ω) < L, where L > 0 denotes the Lyapunov exponent, and every non-resonant phase θ, we prove Anderson localization, i.e. pure point spectrum with exponentially decaying eigenfunctions.”

“Solutions are attracted toward the unique invariant probability measure at polynomial rates of arbitrary order.”

“Convolution defines a matrix transform that preserves positivity.”

“The paper finds a partial extension of Poincaré duality theorem to hypersurfaces obtained by non-primitive Viro's combinatorial patchworking.”

“The paper proves that any ancient, asymptotically cylindrical flow is non-collapsed, convex, rotationally symmetric, and belongs to one of three canonical families: ancient ovals, the bowl soliton, or the flying wing translating solitons.”

“The paper establishes TEDPara and YTSegPara as the first benchmarks for the paragraph segmentation task in the speech domain.”

“The paper establishes the existence of weak steady solutions and provides a necessary and sufficient condition for nontrivial translational or rotational motion.”

“The paper proves that the 'chordality condition' is also sufficient.”

“Sub-ensemble correlations are determined by the covariance operator, inducing a natural geometry in which statistical independence corresponds to orthogonality of the measurement functionals.”

“The Schwarzschild exterior maximizes the event horizon formation time $ΔT_{\text{eh}}=\frac{19}{6}m$ among all asymptotically flat, static, spherically-symmetric black holes with the same ADM mass $m$ that satisfy the weak energy condition.”

“The paper establishes factorization results that clarify the relationship between a minimal isometric dilation and an arbitrary isometric dilation of a contraction.”

“The paper derives the polynomial rate of decay of ruin probabilities in insurance portfolios where insolvency is driven by a single extreme claim.”

“The paper identifies the tangent map with the dual HKR map and proves liftability along square-zero extensions to be a derived invariant.”

“Backpropagation arises as the differential of a KL projection map on a delta-lifted factorization.”

“The paper proves the existence of an optimal closed-loop policy for the original MFTG when the state spaces are at most countable and the action spaces are general Polish spaces.”

“The paper constructs a general class of unique solutions to certain matrix equations and derives several equivalent properties of W-weighted DMP and MPD inverses.”

“The paper gives a new algorithm that terminates in a single iteration to construct all possible sign idempotent sign patterns.”

“The paper demonstrates that a previously proposed condition for consistency does not hold and provides new characterizations and conditions.”

“The key ingredient of our proof is the Cauchy-Schwarz inequality from probability theory.”

“For all \( n \geq \exp\exp(30.5) \), \( \mathrm{PD}_n \) is graphic.”

“The paper proves that the unreduced singular instanton homology has 2-torsion for any null-homologous fibered knot (except for a specific case) and provides a formula for calculating it.”

“If a reflexive sheaf $\mathcal{E}$ on a log terminal Kähler-Einstein variety $(X,ω)$ is slope stable with respect to a singular Kähler-Einstein metric $ω$, then $\mathcal{E}$ admits an $ω$-admissible Hermitian-Yang-Mills metric.”

“The paper establishes congruences modulo p^3 and p^4 for sums of the form ∑(2k+1)^(2a+1)ε^k T_k(b,c)^4 / d^(2k).”

“The paper explains how the hierarchical hull of a pair of points in any colorable hierarchically hyperbolic space is quasi-isometric to a finite CAT(0) cube complex of bounded dimension.”

“HY-MT1.5-1.8B demonstrates remarkable parameter efficiency, comprehensively outperforming significantly larger open-source baselines and mainstream commercial APIs.”

“The paper concludes the existence of a biregular morphism between the corresponding de Rham complex structures.”

“FHDR outperforms the best-known algorithms by at least an order of magnitude in execution time and up to several orders of magnitude in terms of the number of interactions required, establishing a new state of the art for scalable interactive regret minimization.”