arXiv preprints from January 1, 2026 through July 28, 2026 — 07:22:31 EST
We establish a non-ergodic version of the Host-Kra-Ziegler structure theorem for measure-preserving $\mathbb{Z}^d$-actions. Our argument reduces the non-ergodic case to the ergodic theorem (for $d\ge 2$ due to Candela and Szegedy) via a measurable selection procedure. We also establish a non-ergodic vertical nilcharacter version of...
Formation of a rapidly spinning, strongly magnetized neutron star (NS) may occur in various classes of core-collapse events. If the NS injects an amount of energy comparable to the explosion energy of the accompanying supernova (SN) before the SN ejecta becomes transparent, the nascent NS wind bubble can overtake the outer ejecta and...
Banderier, Marchal, and Wallner considered Young tableaux with walls, which are similar to standard Young tableaux, except that local decreases are allowed at some walls. In this work, we prove a conjecture of Fuchs and Yu concerning the enumeration of two classes of three-row Young tableaux with walls. Combining with the work by...
This work investigates binary hypothesis testing between $H_0\sim P_0$ and $H_1\sim P_1$ in the finite-sample regime under asymmetric error constraints. By employing the ``reverse" Rényi divergence, we derive novel non-asymptotic bounds on the Type II error probability which naturally establish a strong converse result. Furthermore,...
In this article, we propose a novel discretization method based on numerical integration for discretizing continuous systems, termed the $αβ$-approximation or Scalable Bilinear Transformation (SBT). In contrast to existing methods, the proposed method consists of two factors, i.e., shape factor ($α$) and time factor ($β$). Depending...
We consider cylindrical algebraic decompositions (CADs) as a tool for representing semi-algebraic subsets of $\mathbb{R}^n$. In this framework, a CAD $\mathscr{C}$ is adapted to a given set $S$ if $S$ is a union of cells of $\mathscr{C}$. Different algorithms computing an adapted CAD may produce different outputs, usually with...
Rubin's generalized Minkowski--Funk transforms $M_t^α$ on the sphere $\mathbb{S}^n$ give rise, for irrational radii $t=\cos(βπ)$, to a small denominator problem governed by the asymptotic behavior of their spectral multipliers. We show that for Lebesgue-almost every $β$ the corresponding two-sine small divisor inequality has...
For an associative algebra $A$ over a field of characteristic zero, let $P_n(A)$ and $P_n^z(A)$ denote the spaces of multilinear polynomials of degree $n$ modulo the polynomial identities and the central polynomials of $A$, respectively. We also write $Δ_n(A)$ for the space of multilinear central polynomials of degree $n$ modulo the...
To trigger precipitation, water droplets in warm clouds need to attain a sufficient size. Theoretical estimates based on condensation and gravitational collisions alone fail to explain the observed timescales for the onset of precipitation for a range of droplet sizes. This suggests the involvement of collisional growth mediated by...
One of the major advantages of $\infty$-category theory over classical $1$-category theory is its robust and homotopically meaningful framework for taking (co)limits of diagrams of $\infty$-categories. However, it is both subtle and crucial to specify which variant of the $\infty$-category of $\infty$-categories is being used when...
Web pages form a cornerstone of available data for daily human consumption and with the rise of LLM-based search and learning systems a treasure trove of valuable data. The scale of this data and its unstructured format still continue to grow requiring ever more robust automated extraction and retrieval mechanisms. Existing work,...
We propose to discuss the modular flavor model and the stabilization of single modulus field in the Jordan frame supergravity with non-minimal scalar-curvature coupling of the form $Φ(τ,\barτ)R$. Modular invariance, positivity of the scale factor and positive definiteness of the Kahler metric constrain stringently the form of the...
Digital advertising platforms and publishers sell ad inventory that conveys targeting information, such as demographic, contextual, or behavioral audience segments, to advertisers. While revealing this information improves ad relevance, it can reduce competition and lower auction revenues. To resolve this trade-off, this paper...
We perform for the first time a full study of spin correlations in inclusive WZ production at the LHC with leptonic decays in the presence of NLO QCD corrections and of effects from a dimension-six operator in the SMEFT modifying the electroweak triple-gauge coupling. We carry out the complete quantum-state tomography of the di-boson...
Modern LLM-based recommenders can generate compelling ranked lists, but they struggle to reliably satisfy governance constraints such as minimum long-tail exposure or diversity requirements. We present PCN-Rec, a proof-carrying negotiation pipeline that separates natural-language reasoning from deterministic enforcement. A base...
Let $ρ$ be an $n$-dimensional representation of $\mathcal{G}_{\mathbb{Q}_p}$ over $\overline{\mathbb{F}_p}$. When $ρ$ is generic and a good conjugate, the article "Conjectures and results on modular representations of $\mathrm{GL}_n(K)$ for a $p$-adic field $K$", by Breuil-Herzig-Hu-Morra-Schraen, introduces the notion of...
The investigation of small-scale energy release in the Sun's atmosphere is important in understanding how the corona is heated. Previous work has been able to study small EUV and SXR brightenings outside of active regions (i.e. the quiet Sun), but with HXRs this has mostly focused on active region transients/microflares due to the...
Sweepstakes reproduction may be generated by chance matching of reproduction with favorable environmental conditions. Gene genealogies generated by sweepstakes reproduction are in the domain of attraction of multiple-merger coalescents where a random number of lineages merges at such times. We consider population genetic models of...
Multimodal Large Language Models (MLLMs) are making significant progress in multimodal reasoning. Early approaches focus on pure text-based reasoning. More recent studies have incorporated multimodal information into the reasoning steps; however, they often follow a single task-specific reasoning pattern, which limits their...
Modern understanding of symmetry in quantum field theory includes both invertible and non-invertible operations. Motivated by this, we extend Nielsen's geometric approach to quantum circuit complexity to incorporate non-invertible gates. These arise naturally from fusion of topological defects and allow transitions between...
We extend Nielsen's formulation of quantum circuit complexity to include intrinsically non-invertible operations. Such gates arise from fusion with topological defect operators and remove a basic limitation of symmetry-based circuits: the inability to change superselection sectors, or in two-dimensional CFTs, conformal families. We...
The energy transition challenges operational tasks based on simulations and optimisation. These computations need to be fast and flexible as the grid is ever-expanding, and renewables' uncertainty requires a flexible operational environment. Learned approximations, proxies or surrogates -- we refer to them as Neural Solvers -- excel...
We employ the MIT bag model with density-dependent bag constant for the equation of state (EOS) to estimate the gravitational mass and Keplerian frequency of rapidly rotating strange quark stars (SQS). In a companion paper we discuss the structural parameters of such rotating stars under the influence of strong magnetic fields. We use...
We explore a situation in which the target domain is accessible, but real-time data annotation is not feasible. Instead, we would like to construct an alternative training set from a large-scale data server so that a competitive model can be obtained. For this problem, because the target domain usually exhibits distinct modes (i.e.,...
Spatiotemporal vector retrieval has emerged as a critical paradigm in modern information retrieval, enabling efficient access to massive, heterogeneous data that evolve over both time and space. However, existing spatiotemporal retrieval methods are often extensions of conventional vector search systems that rely on external filters...