arXiv preprints from January 1, 2026 through September 10, 2026 — 04:16:41 EST
We study the relation between linear stability of generated linear series on smooth curves and slope stability of their associated syzygy bundles. Motivated by conjectures of Mistretta and Stoppino, we establish new cases in which linear stability implies slope stability, focusing first on generated linear series over general curves...
Though the sharp $L^{2}$-Caffarelli--Kohn--Nirenberg (CKN) inequalities have been extensively studied in the entire Euclidean spaces, the corresponding problem on domains whose boundary contains the origin remains largely unexplored. We investigate the sharp $L^{2}$-CKN inequalities on half-spaces and orthants $\mathbb R^{n}_{k,+}$ by...
Previously we have explicitly characterized by certain linear inequalities the ${\mathfrak{k}}$-highest weight tableaux in the quantum Littlewood-Richardson (LR) rule produced by $1$-$0$-slack recording tableaux. Using the composition of promotion operators to defining the Naito-Suzuki-Watanabe bijection between...
We consider the Euclidean distance geometry problem (EDG): given a subset of the pairwise distances of an unknown cloud of $n$ points in $\mathbb{R}^\ell$, recover the point cloud up to rigid motions. When $n$ is large, a popular practical approach is to minimize a nonconvex quartic, known as the squared-stress or s-stress, over point...
The $Λ$-distribution of a compact matrix group is an invariant in algebraic probability theory that was recently introduced to study zero distributions of function field $L$-functions. It is encoded by the $σ$-moment generating function, a generalization of the Molien series of classical invariant theory. In this work, we compute the...
We study the quantum drift-diffusion, or Derrida-Lebowitz-Speer-Spohn (DLSS), equation for a nonnegative density $\varrho$ on a bounded convex domain with Neumann boundary conditions, in the square-root variable $u=\sqrt\varrho$. We show that the DLSS operator, defined and monotone on smooth strictly positive functions, admits a...
The aim of the present paper is to develop a spectral perturbation theory from a higher perspective. More precisely, we consider a one-parameter family of varying bilinear forms, each of them defined on a (possibly) different Hilbert space. Assuming the stability of the corresponding spectra, our first main result establishes a...
Long-horizon robot manipulation chains many contact-rich skills into one multi-stage task. Vision-language-action (VLA) models increasingly master the individual skills, yet the chain still fails: errors compound beyond the policy's ability to correct, and one subtask silently constrains the next. A promising recipe freezes the VLA...
The development of safe and beneficial AI requires that systems can learn and act in accordance with human preferences. However, explicitly specifying these preferences by hand is often infeasible. Inverse reinforcement learning (IRL) addresses this challenge by inferring preferences, represented as reward functions, from expert...
This paper investigates an increasingly important topic in generative modeling: pixel-space diffusion models. Although numerous studies have explored this topic, most focus on small-scale or class-conditional settings. Consequently, a practical recipe for training pixel-space models that rival or exceed well-established latent-space...
Entrepreneurs increasingly use end-user generative AI technologies such as ChatGPT for high-stakes documents like loan applications and business plans, where AI-generated errors---a wrong price, a fabricated product---can affect loan or funding outcomes. Current approaches to supporting evaluation of AI-generated text assume a single...
Long-horizon robot manipulation requires a robot to both execute individual skills reliably and sequence them coherently over extended tasks. Most hierarchical vision-language-action (VLA) models make each such decision with a single forward pass, leaving no mechanism to allocate additional computation to difficult or consequential...
The current best bounds on the matrix multiplication exponent $ω$ are obtained through a refinement of the laser method called combination loss analysis (Duan et al., 2022; Williams et al., 2024; Alman et al., 2025). In this note, we address the optimization problem at the core of this approach and propose several improvements. First,...
For $q> p$, let $T(n,q,p)$ be the minimum number of translates of the cube \(\{0,1,\dots,p-1\}^n\) required to cover the $n$-dimensional torus $(\mathbb{Z}/q\mathbb{Z})^n$. We show that for each $q$ there exists a constant $1\le Λ_q \le 2$ such that $T(n,q,2)=(Λ_q + o(1))(q/2)^n$.
Let $X_H$ denote the number of copies of a fixed graph $H$ in $G_{n, p}$. Gilmer and Kopparty conjectured that $X_H$ satisfies a local central limit theorem (LCLT) provided that $H$ is connected, $p \gg n^{-1/m(H)}$, and $n^2 (1-p) \gg 1$, where $m(H)$ is the maximum density. Following the work of Berkowitz, Sah and Sawhney...
This paper captures and extends some of the core results from the tech memo "A New Semantics for Belief Revision in Simplicial Complexes". As such, we set out to explore the implementation of action models in the setting of simplicial semantics for modal logic. Such an idea is not entirely new to the literature, showing up in both "A...
The only Einstein metrics currently known on complex projective spaces are homogeneous: the Fubini-Study metric, arising via the Hopf fibration; and, in odd complex dimensions, Ziller's metric, obtained as a canonical variation along the twistor fibration over the quaternionic projective space. In 1965, Berger proved that the...
For any convex body $\mathcal{K}\subset\mathbb{R}^{n}$ containing a unit ball, the spectral gap of Hit-and-Run is $Ω(1/(n^2 C_{\mathsf{PI}}))$, where $C_{\mathsf{PI}}$ is the Poincaré constant of the uniform distribution $π$ over $\mathcal{K}$. This implies that Hit-and-Run converges to a distribution within $χ^2$-divergence...
There are several non-equivalent notions of infinitesimal symmetry in the literature of second order linear differential equations: Lie point symmetries, vertical (gauge) symmetries, operator symmetries, infinitesimal contact symmetries, and Lie--Bäcklund operators. We construct an explicit correspondence among the first three, We...
We propose a three-terminal thermal amplifier based on a Sierpiski-gasket Aharonov-Bohm interferometer, where the third (base) terminal is realized as a floating Buttiker probe that acts as an engineered dissipative reservoir, exchanging energy with the conductor while carrying no net charge current. Using the nonequilibrium Green's...
We introduce Automatic Symbolic Regression (AutoSR), a fully automated system that instantiates Research-Space Symbolic Regression by searching persistent scientific investigations rather than isolated equations. Finite, noisy data often yield numerically competitive expressions that imply very different behavior outside the observed...
A fundamental open question in hadron spectroscopy is whether the radial excitation ladder of quarkonia truncates at a finite level---a possibility that would challenge the conventional quark-antiquark bound-state picture and offer decisive clues to the nonperturbative strong interaction. Taking advantage of the newly observed...
Colloidal gels are frequently modeled as monodisperse particle networks, although practical formulations commonly contain particles with multiple characteristic sizes. Here, we use large-scale, hydrodynamically resolved simulations of colloidal depletion gels to isolate the effects of particle size and local packing in bimodal systems...
High-fidelity finite-element simulations can provide accurate numerical predictions for side-branch resonators, but large simulation datasets are expensive to generate and purely data-driven surrogates may become unreliable when simulation-labelled data are scarce. This study develops an analytical-prior learning framework that reuses...
Offline evaluation is a major gateway before online evaluation of ranking models in A/B testing. Standard offline metrics measure predictive accuracy, but are only a surrogate for downstream utility: a model can improve them while redistributing impressions across objective buckets in ways that degrade downstream utility. No offline...