arXiv preprints from January 1, 2026 through September 19, 2026 — 04:41:52 EST
Escardó's dialogue interpretation assigns to each closed term $t:(ι\toι)\toι$ of Gödel's System~T a well-founded, countably branching tree $D(t)$, where $ι$ is the natural-number type. We give a direct proof that its classical ordinal height is below $ε_0$. More precisely, we compute a natural number $K(t)\ge2$ from the type levels...
Surface reflectance and roughness are key to understanding Mercury's geologic evolution. The BepiColombo Laser Altimeter (BELA) will measure these properties alongside topography, but predicting its performance requires realistic modeling of laser return pulse shapes, unlike a simplified Gaussian approximation in earlier models. We...
Chemical substitution provides an effective route to tune the structural and superconducting properties and to explore the evolution of superconductivity across related materials. In this work, we investigate the effect of Pb/Bi mixing on superconductivity in possible topological superconductors \ch{Pb2Pd} and $β$-\ch{Bi2Pd}, by...
A quantitative comparison of the predictions of three theoretical descriptions (TMD, pQCD and geometrical) of the angular coefficients in Drell-Yan Z-boson production with new experimental data on angular coefficients obtained by the ATLAS, CMS and LHCb collaborations has been performed. In the central rapidity region at low-$Q_T$,...
The symbiotic scaling of artificial intelligence models and high-performance computing systems continually creates algorithmic challenges in their convergence. Foundation models (FMs) are a crucial example, requiring months-long training on thousands of cutting-edge GPUs. Sharded data parallelism (DP) is the dominant strategy to...
Characterizing the physical properties of clay and cementitious materials matters across many fields, from materials science to geological waste disposal. Property simulation typically calls for 3D imaging, which is expensive, not always accessible, and technically limited for certain materials. Recent progress in deep generative...
The behavior of wave propagation and scattering in time-variant materials has been studied by many authors, for electromagnetic as well as for mechanical waves. Most studies consider two-dimensional waves, governed by scalar wave equations. Here we introduce a unified wave equation for three-dimensional electromagnetic and...
Since the detection of the first extrasolar planets thirty-five years ago, the dawn in detected signals has been driven primarily by radial velocity and transit techniques. However, other methodologies have gained significant interest due to their ability to explore specific niches that are challenging to access with traditional...
We study repeated contract design when a principal observes outcomes but not the actions that generate them. The principal may use any bounded outcome-contingent payment vector, and the agent's best response can make expected profit discontinuous in those payments. For every fixed number $m\ge2$ of outcomes, the minimax regret over...
We study a variable-exponent double-phase Neumann problem on a domain in a metric measure space, where the boundary measure satisfies an upper codimension-\(θ\) bound for \(0\leθ<1\). Under a local comparability condition on the double-phase growth function, we establish a modular estimate for a fractional maximal operator and use it...
Mathematical Programs with Blocks of Vanishing Constraints (MP-BVCs) are a challenging class of optimization problems due to the loss of standard constraint qualifications. Based on existing theory for classical MPVCs, i.e., MPBVC with block size one, we extend the constraint qualification theory for MPBVCs and show that the known...
We present a localized rooted-operator argument for Weil positivity in the real odd logarithmic channel, retaining the polar rank-one term throughout. Gate I establishes a strict cellular/shell sign theorem with rigorous interval-arithmetic bounds. Gate II combines the Mellin unit-cell decomposition, divisor partial-isometry squares,...
We consider infinite walks in $\mathbb{N}^k$ with standard unit basis vector steps that avoid $t$ collinear points, and show that these walks exist for $(k,t) \in \{(6,3), (4,4), (3,7)\}$. In particular, our construction for $k = 3$ improves the previous bound $189$, obtained by Lidbetter, to $7$. Our results also imply the existence...
Let $\mathbb{D}$ be a division ring with an involution $x \mapsto x^\star$, and $n \geq 2$ be an integer. Denote by $\mathcal{H}_n(\mathbb{D})$ the set of all $n$-by-$n$ Hermitian matrices with entries in $\mathbb{D}$, and by $\mathcal{A}\mathcal{H}_n(\mathbb{D})$ the set of all matrices $A-A^\star$ with $A \in...
We prove a generalization of the version, due to A. Gabrielov, of the Łojasiewicz inequality for not necessarily restricted semi-Pfaffian sets. Unlike the most variants of the Łojasiewicz inequality, it describes the rate of growth of a Pfaffian function on a semi-Pfaffian set $X$ not only in a neighbourhood of its zero set in the...
In this paper, we prove the long-time existence of the heterotic $G_2$ flow with bounded Ricci curvature, torsion tensor and dilaton. Besides, we also get the forward and backward uniqueness results for the solution.
This paper develops and analyzes an optimal-order fractional backward collocation method for adjoint Volterra integro-differential equations with weakly singular kernels. The backward Volterra structure, together with the weakly singular kernel, induces fractional-power singularities at the terminal endpoint, thereby reducing the...
We classify, for every prime power $q$ and every $e\geqslant2$, the permutation binomials $X^r(X^{q-1}+a)$ over $\mathbb F_{q^e}$. Writing $\ell_j(q)=(q^j-1)/(q-1)$, such a binomial is a permutation if and only if $\gcd(r,q-1)=1$, $(-a)^{\ell_e(q)}\ne1$, and $r\ell_h(q)\equiv1\pmod{\ell_e(q)}$ for some $1\leqslant h<e$ coprime to $e$....
We study random linear projections of a finite-field subset for which every fiber has cardinality close to its mean. We bound the mean fiber size needed to ensure that all fibers satisfy a prescribed relative discrepancy, with a prescribed failure probability. For $S\subseteq\mathbb F_q^n$ projected to $\mathbb F_q^b$, one theorem...
For the Dirichlet-type space $\mathcal D(ρ^{(1)},ρ^{(2)})$ on the unit bidisc $\mathbb D^2,$ where $ρ^{(1)}$ and $ρ^{(2)}$ are finite positive Borel measures on the closed unit disc $\overline{\mathbb D},$ we show that the Lévy measure $ν_{(\mathscr M_z,1)}$ associated with the completely alternating multisequence...
This paper establishes the existence of three distinct weak solutions for a class of nonhomogeneous quasilinear inclusion systems, which are governed by locally Lipschitz functionals within Orlicz-Sobolev spaces over unbounded domains $\mathbb{R}^{N}$.By employing a new three critical points theorem established by Wu-Zhou in [29], we...
We analyse the essential spectrum of ${\mathcal M} = {\operatorname{curl}} {\operatorname{curl}}$ acting on divergence-free vector fields in unbounded domains of $\mathbb{R}^3$. We show that $σ_e({\mathcal M}) = [0,+\infty)$ in quasi-conical domains and $σ_e({\mathcal M}) \neq \emptyset$ in quasi-cylindrical domains. For horn-shaped...
We study reconstruction in autoencoders that apply the same forward map before and after setting the observed coordinates to zero. For equal odd input and hidden dimensions $d\geq 3$, among orientation-preserving diffeomorphisms whose Jacobian singular values lie in $[m,M]$, we show that the least uniform reconstruction-derivative...
We determine the branching of irreducible unitary representations of the basic classical Lie superalgebras $\mathfrak{sl}(m|n)$, $\mathfrak{osp}(m|2n)$, and $F(4)$ under restriction to their even subalgebras. The proof combines Dirac inequalities for the Huang-Pandžić-Dirac operator...
We study smooth strongly convex--strongly concave minimax optimization with general nonlinear coupling in the deterministic unconstrained setting. We propose a pure single-loop damped extragradient method with fixed parameters and two new full-gradient evaluations per iteration after one initialization query. The method uses an...