arXiv preprints from January 1, 2026 through September 23, 2026 — 21:03:04 EST
Let $R$ be a nonzero associative unital ring, let $G$ be a group, and let $ρ$ be a preorder on $\{1,\ldots,n\}$. A $G$-grading on $ρ$ induces a very good $G$-grading on the structural matrix ring $M_n(ρ,R)$. We show that, for each of the properties trivial, symmetric, epsilon-strong and strong, the grading on $ρ$ has the property if...
The online Ramsey game for graphs $G$ and $H$ is played on the infinite complete graph $K_\mathbb{N}$. In each round, Builder chooses an edge, and Painter colors it red or blue. The online Ramsey number $\tilde{r}(G,H)$ is the smallest integer $t$ for which Builder has a strategy guaranteeing a red copy of $G$ or a blue copy of $H$...
Erdős and Gallai in 1959 proved the seminal result that every $n$-vertex graph with no cycle of length at least $2t+2$ has at most $\frac{2t+1}{2}(n-1)$ edges. We prove the extension that, for every sufficiently large $t$, the same quantity is also the sharp extremal bound for graphs with no $t$ consecutive even cycle lengths,...
We study the moduli of isolated non-normal singularities by introducing the functor $\mathrm{Crimp}_S^d(X)$ of crimpings of $(X \to S)$ corank $d$. This globalizes Ishii's moduli functor of subrings of finite colength. By verifying Artin's criteria, we prove that if $X \to S$ is a separated morphism of finite presentation, then...
Let $\mathbf{C}=\partial E\subset \mathbb{R}^{n+1}$ be a regular area-minimizing hypercone. We first prove that $\mathbf{C}$ is simultaneously strictly stable and strictly minimizing if and only if there exists $c_\mathbf{C}>0$ such that \[ \operatorname{Per}(F;B_R)-\operatorname{Per}(E;B_R) \geq c_\mathbf{C} ...
For every natural number $r\geq 2$, we construct $r^{th}$ powers of bipartite graphs whose chromatic number is quadratic in their clique number, showing that the straightforward quadratic upper bound is best possible. We thereby settle an open problem posed by Chakraborty, Chandran, Jacob and Pillai [J. Graph Theory 112(3) (2026),...
The zero divisor graph $Γ(R)$ of a finite commutative ring $R$ has as vertices the non-zero zero divisors of $R$, with an edge between two elements exactly when their product is zero. We determine the boxicity and threshold dimension of $Γ(R)$ for two classes of finite commutative rings: reduced rings and quotients of principal...
In this article, using the theory of $δ$-geometry, we construct a canonical $z$-isocrystal $(\mathbf{H}_δ(E), \mathfrak{f}^*)$ admitting a Hodge-Pink structure for any abelian Anderson module $E$. The Hodge-Pink structure on $\mathbf{H}_δ(E)$ induces a natural filtration $(\mathbf{H}_δ(E) \supset \mathbf{X}_{\mathrm{prim}}(E) \supset...
We study how sophistication in generative AI (genAI) use varies among the back-office workforce of a large firm. Using proprietary data, we observe 713,564 employee prompts and their corresponding large language model responses from nearly 4,000 back-office employees across 15 functional areas over eight months in 2025. We document...
We study random assignment of indivisible objects among a set of agents with strict preferences and outside options. When agents may rank some objects as unacceptable, we consider different notions of measuring waste of object(s) from an ex-ante perspective. The most natural one is $q$-agent-object-waste whereby both one agent and one...
We study identification of two-way unobserved heterogeneity in the nonparametric panel regression $G_{it}=g(α_i,γ_t)+\varepsilon_{it}$, where identification of the latent types reduces to constructing identified, \emph{injective} proxies for them. To this end we consider the singular value decomposition (SVD) of the bivariate...
How do we define an occupation? By its job title? An accountant at a small trading company keeps the books; at a listed firm the same title demands a certified-accountant licence, and the week goes to the reports that regulators and the board read. Same title, different bar, different work. What defines an occupation is who it lets in...
Which visual choices make a post perform better? A growing literature answers this question with pooled coefficients estimated across many creators, which platforms translate into creative recommendations. We show that these coefficients blend two distinct patterns that can point in opposite directions for the same attribute. The...
We develop a novel method of inference for network-dependent high-dimensional random vectors. Dependence is characterized via a functional dependence measure based on graph distance, allowing the approximation theory to capture the interaction between the decay of dependence and the growth of network neighborhoods. We establish...
This paper develops the Municipal Equitable and Sustainable Well-being Index (MESWI) for all Italian municipalities, extending the 12-domain BES framework to the local level through 49 indicators. Results reveal substantial territorial heterogeneity that regional and provincial statistics may conceal. The North-South divide remains...
Recent work in fair division has focused on either simultaneously satisfying closely related fairness notions or achieving a single notion across the ex-ante and ex-post worlds. We study the compatibility of two fundamentally different fairness notions: envy-freeness and equitability. For indivisible goods-only and chores-only...
This data paper describes an anonymized release derived from controlled behavioral experiments on decision-making under risk (known probabilities) and ambiguous uncertainty (partially specified or unknown probabilities) in Ellsberg-type urn tasks. The release contains 4,486 decision records from 246 adult participant records across...
Quantum algorithms promise advantages beyond classical reach, but running them on error-corrected hardware requires translating Boolean specifications into reversible circuits, and the resources that translation demands determine what is executable. Established methods minimize a Boolean expression and map it to a circuit, assuming...
Rydberg entangling gates driven by a two-photon transition in alkali atoms suffer from an adverse scaling of light-shift-induced errors. Robustness to such detuning errors is known to be impossible to achieve in the design of conventional Rydberg gate protocols, where only one of the qubit states is coupled to the Rydberg state. Here,...
We present a finite element framework to simulate rotating mixing devices using the Mortar Element Method as a domain decomposition strategy. The model is implemented within a matrix-free Navier-Stokes framework which uses a high-order Continuous Galerkin method. The discretized domain is subdivided into rotor and stator parts. An...
We study the formation and interaction of dispersive shock waves (DSWs) in the two-dimensional Toda lattice subject to wedge-type initial conditions, and show that their interaction gives rise to a discrete analog of Mach reflection for dispersive shock waves in discrete systems. The initial jump across each leg of the wedge acts...
We construct Casimir operators of $4D, \,\mathcal{N}=2$ supersymmetry algebra in the harmonic superspace approach, and provide the explicit expressions for them in terms of covariant derivatives in the analytic basis. Specifically, the superisospin operator $C_I$ is expressed in terms of new 'long' harmonic derivatives...
A continuous transition between phases hosting distinct excitations---bosonic magnons versus fermionic spinons---is a long-sought phenomenon in quantum magnetism, analogous to the confinement--deconfinement transition in quantum chromodynamics. We report evidence for such a transition in the triangular-lattice antiferromagnet...
Okuda and Penedones (OP) \cite{Okuda:2010ym} showed the existence of a double scaling limit of four point correlators in ${\cal N}=4$ Supersymmetric Yang Mills (SYM) theory in four spacetime dimensions (4$d$) dual to the flat space limit of tree-level string amplitude in $\mathbb{R}^{1,9}$ with external kinematics in...
Many sub-Neptunes are expected to contain long-lived molten silicate interiors beneath dense H2-rich envelopes. At pressures and temperatures near the atmosphere-interior boundary, MgSiO3 and H2 may become fully miscible, forming a supercritical silicate-hydrogen fluid. Here we use density functional theory molecular dynamics...