Tootfinder

On Complex Dimensions and Heat Content of Self-Similar Fractals
William E. Hoffer, Michel L. Lapidus
https://arxiv.org/abs/2508.09512 https://arxiv.org/pdf…

On Complex Dimensions and Heat Content of Self-Similar Fractals
Complex fractal dimensions, defined as poles of appropriate fractal zeta functions, describe the geometric oscillations in fractal sets. In this work, we show that the same possible complex dimensions in the geometric setting also govern the asymptotics of the heat content on self-similar fractals. We consider the Dirichlet problem for the heat equation on bounded open regions whose boundaries are self-similar fractals. The class of self-similar domains we consider allow for non-disjoint over…

On Casimir effect in Yang-Mills theories in three and four dimensions
Dimitra Karabali, Antonina Maj, V. P. Nair
https://arxiv.org/abs/2509.10301 https://a…

On Casimir effect in Yang-Mills theories in three and four dimensions
We calculate the Casimir energy for the configuration of two parallel plates coupled to nonabelian gauge fields with a Yang-Mills action. We consider both 2+1 and 3+1 dimensions in the manifestly gauge-invariant formalism we have pursued over the last several years which allows us to factor out the gauge degrees of freedom. A boundary action in the functional integral, equivalent to the insertion of operators representing the plates, is used to enforce the required boundary conditions for the g…

Tightening the mixed integer linear formulation for the piecewise linear approximation in general dimensions
Quentin Ploussard, Xiang Li, Matija Pavi\v{c}evi\'c
https://arxiv.org/abs/2508.09395

Tightening the mixed integer linear formulation for the piecewise linear approximation in general dimensions
This paper addresses the problem of tightening the mixed-integer linear programming (MILP) formulation for continuous piecewise linear (CPWL) approximations of data sets in arbitrary dimensions. The MILP formulation leverages the difference-of-convex (DC) representation of CPWL functions. We introduce the concept of well-behaved CPWL interpolations and demonstrate that any CPWL interpolation of a data set has a well-behaved version. This result is critical to tighten the MILP problem. We presen…

On $\mathrm{BV}^{\mathbb{A}}$-Minimisers in two Dimensions
Ferdinand Eitler, Peter Lewintan
https://arxiv.org/abs/2508.10508 https://arxiv.org/pdf/2508.105…

On $\mathrm{BV}^{\mathbb{A}}$-Minimisers in two Dimensions
We investigate into the regularity of $\mathrm{BV}^{\mathbb{A}}$-minimisers for $\mathbb{C}$-elliptic differential operators $\mathbb{A}$ in $2$ dimensions. Our studies strongly rely on the special structure of such differential operators. The gradient integrability is established for the sharp ellipticity range known from the (symmetric) gradient case.

An Anthropic report details how Claude usage varies by country and US states, finding 36% use it for coding, 77% of enterprise use is for automation, and more (Anthropic)
https://www.anthropic.com/research/anthropic-economic-index-september-2025-report

Anthropic Economic Index report: Uneven geographic and enterprise AI adoption
To study such patterns of early AI adoption, we extend the Anthropic Economic Index along two important dimensions, introducing a geographic analysis of Claude.ai conversations and a first-of-its-kind examination of enterprise API use. We show how Claude usage has evolved over time, how adoption patterns differ across regions, and—for the first time—how firms are deploying frontier AI to solve business problems.

1 O(1) asymptotics for loop percolation in five and higher dimensions
Quirin Vogel
https://arxiv.org/abs/2508.09291 https://arxiv.org/pdf/2508.09291…

1+O(1) asymptotics for loop percolation in five and higher dimensions
We calculate the one-arm probability and the two-point function for loop percolation in dimensions five and higher on the lattice up to first order. This answers a question posed by Y. Chang and A. Sapozhnikov in Probability Theory and Related Fields (2016).

Spectropolarimetric Inversion in Four Dimensions with Deep Learning (SPIn4D): II. A Physics-Informed Machine Learning Method for 3D Solar Photosphere Reconstruction
Kai E. Yang, Xudong Sun, Lucas A. Tarr, Jiayi Liu, Peter Sadowski, S. Curt Dodds, Matthias Rempel, Sarah A. Jaeggli, Thomas A. Schad, Ian Cunnyngham, Yannik Glaser, Linnea Wolniewicz
https://…

Spectropolarimetric Inversion in Four Dimensions with Deep Learning (SPIn4D): II. A Physics-Informed Machine Learning Method for 3D Solar Photosphere Reconstruction
Inferring the three-dimensional (3D) solar atmospheric structures from observations is a critical task for advancing our understanding of the magnetic fields and electric currents that drive solar activity. In this work, we introduce a novel, Physics-Informed Machine Learning method to reconstruct the 3D structure of the lower solar atmosphere based on the output of optical depth sampled spectropolarimetric inversions, wherein both the fully disambiguated vector magnetic fields and the geometri…

Information Retention in Iterative Random Projection of Convex Bodies to Lower Dimensions
Nazanin Mirhosseini
https://arxiv.org/abs/2508.10218 https://arxi…

Information Retention in Iterative Random Projection of Convex Bodies to Lower Dimensions
In this paper, we consider a bounded convex body $K_0 \subset \mathbb{R}^{n}$ subjected to two successive random orthogonal projections onto $\mathbb{R}^{n-1}$ and $\mathbb{R}^{n-2}$, respectively. First, we project $K_0$ orthogonally onto $U_{1}^{\perp}$, the orthogonal complement of $\mbox{\boldmath $U$}_1$, where $\mbox{\boldmath $U$}_1$ is uniformly distributed on the unit sphere $S^{n-1}$. This yields a random convex body $K_1 = \mathrm{Proj}_{{U_1}^{\perp}}(K_0) \subset \mathbb{R}^{n-1}$.…

QM2-branes and the Swampland Distance Conjecture in nine dimensions
Mar\'ia Pilar Garc\'ia del Moral, Camilo las Heras, Alvaro Restuccia
https://arxiv.org/abs/2509.09967

QM2-branes and the Swampland Distance Conjecture in nine dimensions
We discuss the relationship between the Swampland program and QM2-branes, which are supersymmetric M2-branes with discrete spectrum. The worldvolume description of these M2-branes is well-known. The global description is given in terms of twisted torus bundles with monodromy in $\mathrm{SL}(2,\mathbb{Z})$. In particular, we show that the towers of states that ensure the Swampland Distance Conjecture for type II maximal supergravity in nine dimensions are directly related to QM2-branes with triv…

Loop functions of sunset graphs in 2 1 space-time dimensions
N. Kaiser
https://arxiv.org/abs/2510.08704 https://arxiv.org/pdf/2510.08704

Loop functions of sunset graphs in 2+1 space-time dimensions
In these notes the relativistic $n$-body phase-phase is calculated iteratively in $2+1$ space-time dimensions for all $n$. The obtained result shows a simple power-law behavior $α_n (μ-M)^{n-2}/μ$ with a dependence only on the total mass $M=m_1+\dots + m_n$. As a consequence of this feature, the $(n-1)$-loop integrals $J_n(-q^2)$ associated to sunset graphs with $n$ internal lines can be expressed through of elementary (arctangent and logarithmic) functions, modulo polynomial terms in $q^2$ …

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Virtual Agent Economies
Nenad Tomasev, Matija Franklin, Joel Z. Leibo, Julian Jacobs, William A. Cunningham, Iason Gabriel, Simon Osindero
https://arxiv.org/abs/2509.10147 https…

Virtual Agent Economies
The rapid adoption of autonomous AI agents is giving rise to a new economic layer where agents transact and coordinate at scales and speeds beyond direct human oversight. We propose the "sandbox economy" as a framework for analyzing this emergent system, characterizing it along two key dimensions: its origins (emergent vs. intentional) and its degree of separateness from the established human economy (permeable vs. impermeable). Our current trajectory points toward a spontaneous emergence of a …

Adversarial Attacks Leverage Interference Between Features in Superposition
Edward Stevinson, Lucas Prieto, Melih Barsbey, Tolga Birdal
https://arxiv.org/abs/2510.11709 https://…

Adversarial Attacks Leverage Interference Between Features in Superposition
Fundamental questions remain about when and why adversarial examples arise in neural networks, with competing views characterising them either as artifacts of the irregularities in the decision landscape or as products of sensitivity to non-robust input features. In this paper, we instead argue that adversarial vulnerability can stem from efficient information encoding in neural networks. Specifically, we show how superposition - where networks represent more features than they have dimensions …

Benchmark of stylistic variation in LLM-generated texts
Ji\v{r}\'i Mili\v{c}ka, Anna Marklov\'a, V\'aclav Cvr\v{c}ek
https://arxiv.org/abs/2509.10179 https://…

Benchmark of stylistic variation in LLM-generated texts
This study investigates the register variation in texts written by humans and comparable texts produced by large language models (LLMs). Biber's multidimensional analysis (MDA) is applied to a sample of human-written texts and AI-created texts generated to be their counterparts to find the dimensions of variation in which LLMs differ most significantly and most systematically from humans. As textual material, a new LLM-generated corpus AI-Brown is used, which is comparable to BE-21 (a Brown fam…

Lower-depth local encoding circuits for the surface code
Jahan Claes
https://arxiv.org/abs/2509.09779 https://arxiv.org/pdf/2509.09779

Lower-depth local encoding circuits for the surface code
The surface code is the most studied error-correcting code thanks to its high threshold, simple decoding, and locality in two dimensions (2D). A key component of any code is its encoding circuit, which maps an unencoded state to the corresponding encoded state. The best previous surface code encoding circuit compatible with 2D local connectivity requires depth $2d$ to encode distance-$d$ surface codes. This paper presents depth $d$ encoding circuits for the rotated surface code. Our circuit is …

On Thompson Sampling and Bilateral Uncertainty in Additive Bayesian Optimization
Nathan Wycoff
https://arxiv.org/abs/2510.11792 https://arxiv.org/pdf/2510.…

On Thompson Sampling and Bilateral Uncertainty in Additive Bayesian Optimization
In Bayesian Optimization (BO), additive assumptions can mitigate the twin difficulties of modeling and searching a complex function in high dimension. However, common acquisition functions, like the Additive Lower Confidence Bound, ignore pairwise covariances between dimensions, which we'll call \textit{bilateral uncertainty} (BU), imposing a second layer of approximations. While theoretical results indicate that asymptotically not much is lost in doing so, little is known about the practical e…

A classification algorithm for reflexive simplices
Marco Ghirlanda
https://arxiv.org/abs/2510.09131 https://arxiv.org/pdf/2510.09131

A classification algorithm for reflexive simplices
We present a general classification algorithm for reflexive simplices, which allows us to determine all reflexive simplices in dimensions five and six. In terms of algebraic geometry this means that we classify the Gorenstein fake weighted projective spaces in dimensions five and six. As a byproduct of our methods, we obtain explicit formulae for the Picard group and the Gorenstein index of any fake weighted projective space.

Revisiting Trust in the Era of Generative AI: Factorial Structure and Latent Profiles
Haocan Sun, Weizi Liu, Di Wu, Guoming Yu, Mike Yao
https://arxiv.org/abs/2510.10199 https:/…

Revisiting Trust in the Era of Generative AI: Factorial Structure and Latent Profiles
Trust is one of the most important factors shaping whether and how people adopt and rely on artificial intelligence (AI). Yet most existing studies measure trust in terms of functionality, focusing on whether a system is reliable, accurate, or easy to use, while giving less attention to the social and emotional dimensions that are increasingly relevant for today's generative AI (GenAI) systems. These systems do not just process information; they converse, respond, and collaborate with users, bl…

The Chevalley--Weil formula for finite group actions on higher dimensional compact complex manifolds
Wenfei Liu, Renjie Lyu
https://arxiv.org/abs/2510.10430 https://

The Chevalley--Weil formula for finite group actions on higher dimensional compact complex manifolds
Building on the Atiyah--Singer holomorphic Lefschetz fixed-point theorem, we define ramification modules associated to the fixed loci of a finite group acting on a compact complex manifold. This allows us to generalize the Chevalley--Weil formula for compact Riemann surfaces to higher dimensions. More precisely, let $G$ be a finite group acting on a compact complex manifold $X$, and let $\mathcal{E}$ be a $G$-equivariant locally free sheaf on $X$. Then, in the representation ring $R(G)_\mathbb{…

Characterizing Web Search in The Age of Generative AI
Elisabeth Kirsten, Jost Grosse Perdekamp, Mihir Upadhyay, Krishna P. Gummadi, Muhammad Bilal Zafar
https://arxiv.org/abs/2510.11560

Characterizing Web Search in The Age of Generative AI
The advent of LLMs has given rise to a new type of web search: Generative search, where LLMs retrieve web pages related to a query and generate a single, coherent text as a response. This output modality stands in stark contrast to traditional web search, where results are returned as a ranked list of independent web pages. In this paper, we ask: Along what dimensions do generative search outputs differ from traditional web search? We compare Google, a traditional web search engine, with four g…

Counting Martingales for Measure and Dimension in Complexity Classes
John M. Hitchcock, Adewale Sekoni, Hadi Shafei
https://arxiv.org/abs/2508.07619 https://

Counting Martingales for Measure and Dimension in Complexity Classes
This paper makes two primary contributions. First, we introduce the concept of counting martingales and use it to define counting measures, counting dimensions, and counting strong dimensions. Second, we apply these new tools to strengthen previous circuit lower bounds. Resource-bounded measure and dimension have traditionally focused on deterministic time and space bounds. We use counting complexity classes to develop resource-bounded counting measures and dimensions. Counting martingales ar…

VCB Bench: An Evaluation Benchmark for Audio-Grounded Large Language Model Conversational Agents
Jiliang Hu, Wenfu Wang, Zuchao Li, Chenxing Li, Yiyang Zhao, Hanzhao Li, Liqiang Zhang, Meng Yu, Dong Yu
https://arxiv.org/abs/2510.11098

VCB Bench: An Evaluation Benchmark for Audio-Grounded Large Language Model Conversational Agents
Recent advances in large audio language models (LALMs) have greatly enhanced multimodal conversational systems. However, existing benchmarks remain limited -- they are mainly English-centric, rely on synthetic speech, and lack comprehensive, discriminative evaluation across multiple dimensions. To address these gaps, we present Voice Chat Bot Bench (VCB Bench) -- a high-quality Chinese benchmark built entirely on real human speech. VCB Bench evaluates LALMs from three complementary perspectives…

Geometric inequalities for electrostatic systems with boundary
Allan Freitas, Benedito Leandro, Ernani Ribeiro Jr, Guilherme Sabo
https://arxiv.org/abs/2508.10258 https://

Geometric inequalities for electrostatic systems with boundary
In this article, we investigate electrostatic systems with a nonzero cosmological constant on compact manifolds with boundary. We establish new geometric properties for electrostatic manifolds in higher dimensions, extending previous results in the literature. Moreover, we prove sharp boundary estimates and isoperimetric-type inequalities for electrostatic manifolds, as well as volume and boundary inequalities involving the Brown-York and Hawking masses.

Approach to zigzag and checkerboard patterns in spatially extended systems
Manoj C. Warambhe, Prashant M. Gade
https://arxiv.org/abs/2510.10723 https://arx…

Approach to zigzag and checkerboard patterns in spatially extended systems
Zigzag patterns in one dimension or checkerboard patterns in two dimensions occur in a variety of pattern-forming systems. We introduce an order parameter `phase defect' to identify this transition and help to recognize the associated universality class on a discrete lattice. In one dimension, if $x_{i}(t)$ is a variable value at site $i$ at time $t$. We assign spin $s_i(t)=1$ for $x_{i}(t)>x_{i-1}(t)$, $s_i(t)=-1$ if $x_{i}(t)

On the existence of self-similar solutions to the steady Navier-Stokes equations in high dimensions
Jeaheang Bang, Changfeng Gui, Hao Liu, Yun Wang, Chunjing Xie
https://arxiv.org/abs/2510.10488

On the existence of self-similar solutions to the steady Navier-Stokes equations in high dimensions
We prove that the steady incompressible Navier-Stokes equations with any given $(-3)$-homogeneous, locally Lipschitz external force on $\mathbb{R}^n\setminus\{0\}$, $4\leq n\leq 16$, have at least one $(-1)$-homogeneous solution which is scale-invariant and regular away from the origin. The global uniqueness of the self-similar solution is obtained as long as the external force is small. The key observation is to exploit a nice relation between the radial component of the velocity and the total…

Andr\'e-Quillen homology and ascent of complete intersection flat dimensions
Keri Ann Sather-Wagstaff, Tirdad Sharif
https://arxiv.org/abs/2508.07097 https://

André-Quillen homology and ascent of complete intersection flat dimensions
Using André-Quillen homology, we prove an ascent result for different types of complete intersection flat dimensions along an essentially of finite type flat local homomorphism with complete intersection closed fiber. As an application of our result, we extend a result of Majadas Soto and of Avramov, Henriques and Şega on the André-Quillen dimension of surjective local homomorphisms to that of essentially of finite types.

Minimality of Tree Tensor Network Ranks
Jana Jovcheva, Tim Seynnaeve, Nick Vannieuwenhoven
https://arxiv.org/abs/2509.09463 https://arxiv.org/pdf/2509.0946…

Minimality of Tree Tensor Network Ranks
For a given tree tensor network $G$, we call a tuple of bond dimensions minimal if there exists a tensor $T$ that can be represented by this network but not on the same tree topology with strictly smaller bond dimensions. We establish necessary and sufficient conditions on the bond dimensions of a tree tensor network to be minimal, generalizing a characterization of Carlini and Kleppe about existence of tensors with a given multilinear rank. We also show that in a minimal tree tensor network, t…

Analysis of bio-nanofluid flow over a stretching sheet with slip boundaries
Bahram Jalili, Salar Ghadiri Alamdari, Payam Jalili, Davood Domiri Ganji
https://arxiv.org/abs/2510.11149

Analysis of bio-nanofluid flow over a stretching sheet with slip boundaries
A viscous, incompressible, micropolar bio-nanofluid flowing across a stretching sheet in three dimensions while being driven to convect several slip boundaries in the presence of a magnetic field was studied. With the assistance of the relevant transformations, a mathematical model is presented. The finite difference method numerically solves the converted non-linear ordinary differential equations. A comprehensive assessment was conducted to examine the impact of governing parameters on dimens…

Instant Folded Strings, Dark Energy and a Cyclic Bouncing Universe
Nissan Itzhaki, Uri Peleg, Paul J. Steinhardt
https://arxiv.org/abs/2508.09745 https://a…

Instant Folded Strings, Dark Energy and a Cyclic Bouncing Universe
We present a wholly self-consistent, complete cyclic bouncing cosmology based on components drawn from string theory and constructed in a way that is under perturbative control throughout (e.g., with temperature much less than the string scale and string coupling $g_s \ll 1$ at all times). The cyclic evolution is governed by standard dilaton-gravity in $(3+1)$-dimensions with a perturbatively generated potential and a coupling between the dilaton and a second field that becomes massless at $ϕ=…

Timeliness, Consensus, and Composition of the Crowd: Community Notes on X
Olesya Razuvayevskaya, Adel Tayebi, Ulrikke Dybdal S{\o}rensen, Kalina Bontcheva, Richard Rogers
https://arxiv.org/abs/2510.12559

Timeliness, Consensus, and Composition of the Crowd: Community Notes on X
This study presents the first large-scale quantitative analysis of the efficiency of X's Community Notes, a crowdsourced moderation system for identifying and contextualising potentially misleading content. Drawing on over 1.8 million notes, we examine three key dimensions of crowdsourced moderation: participation inequality, consensus formation, and timeliness. Despite the system's goal of collective moderation, we find substantial concentration effect, with the top 10% of contributors produci…

Scaling High-Performance Nanoribbon Transistors with Monolayer Transition Metal Dichalcogenides
Tara Pe\~na, Anton E. O. Persson, Andrey Krayev, \'Ashildur Fri{\dh}riksd\'ottir, Kathryn Neilson, Zhepeng Zhang, Anh Tuan Hoang, Jerry A. Yang, Lauren Hoang, Andrew J. Mannix, Paul C. McIntyre, Eric Pop
https://arxiv.org/abs/2509.09964

Scaling High-Performance Nanoribbon Transistors with Monolayer Transition Metal Dichalcogenides
Nanoscale transistors require aggressive reduction of all channel dimensions: length, width, and thickness. While monolayer two-dimensional semiconductors (2DS) offer ultimate thickness scaling, good performance has largely been achieved only in micrometer-wide channels. Here, we demonstrate both $\it{n}$- and $\it{p}$-type nanoribbon transistors based on monolayer 2DS, fabricated using a multi-patterning process, reaching channel widths down to 25 nm and lengths down to 50 nm. 'Anchored' conta…

Recognizing Penny and Marble Graphs is Hard for Existential Theory of the Reals
Anna Lubiw, Marcus Schaefer
https://arxiv.org/abs/2508.10136 https://arxiv.…

Recognizing Penny and Marble Graphs is Hard for Existential Theory of the Reals
We show that the recognition problem for penny graphs (contact graphs of unit disks in the plane) is $\exists\mathbb{R}$-complete, that is, computationally as hard as the existential theory of the reals, even if a combinatorial plane embedding of the graph is given. The exact complexity of the penny graph recognition problem has been a long-standing open problem. We lift the penny graph result to three dimensions and show that the recognition problem for marble graphs (contact graphs of unit …

The Fractional Two-Sided Quaternionic Dunkl Transform and Heisenberg-Type Inequalities
Mohamed Essenhajy
https://arxiv.org/abs/2510.11597 https://arxiv.org…

The Fractional Two-Sided Quaternionic Dunkl Transform and Heisenberg-Type Inequalities
This report investigates the main definitions and fundamental properties of the fractional two-sided quaternionic Dunkl transform in two dimensions. We present key results concerning its structure and emphasize its connections to classical harmonic analysis. Special attention is given to inversion, boundedness, spectral behavior, and explicit formulas for structured functions such as radial or harmonic functions. Within this framework, we establish a generalized form of the classical Heisenberg…

Replaced article(s) found for math.SG. https://arxiv.org/list/math.SG/new
[1/1]:
- Legendrian non-isotopic unit conormal bundles in high dimensions
Yukihiro Okamoto

Phonon interference effects in GaAs-GaP superlattice nanowires
Chaitanya Arya, Johannes Trautvetter, Jose M. Sojo-Gordillo, Yashpreet Kaur, Valentina Zannier, Fabio Beltram, Tommaso Albrigi, Alicia Ruiz-Caridad, Lucia Sorba, Riccardo Rurali, Ilaria Zardo
https://arxiv.org/abs/2508.09556

Phonon interference effects in GaAs-GaP superlattice nanowires
Fine-tuning the functional properties of nanomaterials is crucial for technological applications. Superlattices, characterized by periodic repetitions of two or more materials in different dimensions, have emerged as a promising area of investigation. We present a study of the phonon interference effect on thermal transport in GaAs-GaP superlattice nanowires with sharp interfaces between the GaAs and GaP layers, as confirmed by high-resolution transmission electron microscopy. We performed ther…

Conformal Data for the O(3) Wilson-Fisher CFT from Fuzzy Sphere Realization of Quantum Rotor Model
Arjun Dey, Loic Herviou, Christopher Mudry, Andreas Martin L\"auchli
https://arxiv.org/abs/2510.09755

Conformal Data for the O(3) Wilson-Fisher CFT from Fuzzy Sphere Realization of Quantum Rotor Model
We present a model for strongly interacting fermions with internal O(3) symmetry on the fuzzy-sphere that (i) preserves the rotational symmetry of the fuzzy sphere and (ii) undergoes a quantum phase transition in the (2+1)-dimensional O(3) Wilson-Fisher universality class. Using exact diagonalization (ED) and density matrix renormalization group (DMRG), we locate the quantum critical point via conformal perturbation theory and obtain scaling dimensions from finite-size spectra. We identify 24 p…

Spectral and Dynamical Analysis of Fractional Discrete Laplacians on the Half-Lattice
Nassim Athmouni
https://arxiv.org/abs/2510.10680 https://arxiv.org/pd…

Spectral and Dynamical Analysis of Fractional Discrete Laplacians on the Half-Lattice
We investigate discrete fractional Laplacians defined on the half-lattice in several dimensions, allowing possibly different fractional orders along each coordinate direction. By expressing the half-lattice operator as a boundary restriction of the full-lattice one plus a bounded correction that is relatively compact with respect to it, we show that both operators share the same essential spectrum and the same interior threshold structure. For perturbations by a decaying potential, the conjugat…

On Carrollian and Celestial Correlators in General Dimensions
Harshal Kulkarni, Romain Ruzziconi, Akshay Yelleshpur Srikant
https://arxiv.org/abs/2508.06602 https://

On Carrollian and Celestial Correlators in General Dimensions
Carrollian holography is a framework for flat space holography, suggesting that gravity in asymptotically flat spacetime in $D$ dimensions is dual to a conformal Carrollian field theory in $D - 1$ dimensions living at null infinity. In this work, we elaborate on the definition of Carrollian amplitudes for massless scalar fields in general dimensions and provide explicit expressions for the two-, three-, and four-point functions. We show that these amplitudes naturally arise from Lorentzian holo…

Approximation and orthogonality on fully symmetric domains
Yuan Xu
https://arxiv.org/abs/2509.10342 https://arxiv.org/pdf/2509.10342

Approximation and orthogonality on fully symmetric domains
We study orthogonal polynomials on a fully symmetric planar domain $Ω$ that is generated by a certain triangle in the first quadrant. For a family of weight functions on $Ω$, we show that orthogonal polynomials that are even in the second variable on $Ω$ can be identified with orthogonal polynomials on the unit disk composed with a quadratic map, and the same phenomenon can be extended to the domain generated by the rotation of $Ω$ in higher dimensions. The connection allows an immediate de…

Partial Self-Correction in Layer Codes
Dominic J. Williamson
https://arxiv.org/abs/2510.09218 https://arxiv.org/pdf/2510.09218

Partial Self-Correction in Layer Codes
The storage of large-scale quantum information at finite temperature requires an autonomous and reliable quantum hard drive, also known as a self-correcting quantum memory. It is a long-standing open problem to find a self-correcting quantum memory in three dimensions. The recently introduced Layer Codes achieve the best possible scaling of code parameters and logical energy barrier in three dimensions, these are tantalizing features for the purposes of self-correction. In this work we show tha…

Towards a Taxonomy of Sustainability Requirements for Software Design
Mandira Roy, Novarun Deb, Nabendu Chaki, Agostino Cortesi
https://arxiv.org/abs/2510.08990 https://

Towards a Taxonomy of Sustainability Requirements for Software Design
Software systems are a significant contributor to global sustainability concerns, demanding that environmental, social, technical, and economic factors be systematically addressed from the initial requirements engineering phase. Although existing research provides various sustainability requirements (SRs), these contributions are often fragmented, specific to certain dimensions, or limited to particular application domains, resulting in a critical lack of a unified, comprehensive taxonomy for t…

from my link log —
Programming languages and dimensions of units of measure.
https://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-391.html
saved 2025-07-30

Never Compromise to Vulnerabilities: A Comprehensive Survey on AI Governance
Yuchu Jiang, Jian Zhao, Yuchen Yuan, Tianle Zhang, Yao Huang, Yanghao Zhang, Yan Wang, Yanshu Li, Xizhong Guo, Yusheng Zhao, Jun Zhang, Zhi Zhang, Xiaojian Lin, Yixiu Zou, Haoxuan Ma, Yuhu Shang, Yuzhi Hu, Keshu Cai, Ruochen Zhang, Boyuan Chen, Yilan Gao, Ziheng Jiao, Yi Qin, Shuangjun Du, Xiao Tong, Zhekun Liu, Yu Chen, Xuankun Rong, Rui Wang, Yejie Zheng, Zhaoxin Fan, Hongyuan Zhang, Pan Zhou, Lei Jin, Hao Z…

Never Compromise to Vulnerabilities: A Comprehensive Survey on AI Governance
The rapid advancement of AI has expanded its capabilities across domains, yet introduced critical technical vulnerabilities, such as algorithmic bias and adversarial sensitivity, that pose significant societal risks, including misinformation, inequity, security breaches, physical harm, and eroded public trust. These challenges highlight the urgent need for robust AI governance. We propose a comprehensive framework integrating technical and societal dimensions, structured around three interconne…

Demystifying and Navigating AI Ethics in Power Electronics
Fanfan Lin, Peter Wilson, Xinze Li, Alan Mantooth
https://arxiv.org/abs/2510.09439 https://arxiv…

Demystifying and Navigating AI Ethics in Power Electronics
Artificial intelligence (AI) is rapidly transforming power electronics, with AI-related publications in IEEE Power Electronics Society selected journals increasing more than fourfold from 2020 to 2025. However, the ethical dimensions of this transformation have received limited attention. This article underscores the urgent need for an ethical framework to guide responsible AI integration in power electronics, not only to prevent AI-related incidents but also to comply with legal and regulatory…

Training Spatial Ability in Virtual Reality
Yiannos Demetriou, Manasvi Parikh, Sara Eskandari, Westley Weimer, Madeline Endres
https://arxiv.org/abs/2508.10195 https://

Training Spatial Ability in Virtual Reality
Background: Spatial reasoning has been identified as a critical skill for success in STEM. Unfortunately, under-represented groups often have lower incoming spatial ability. Courses that improve spatial skills exist but are not widely used. Virtual reality (VR) has been suggested as a possible tool for teaching spatial reasoning since students are more accurate and complete spatial tasks more quickly in three dimensions. However, no prior work has developed or evaluated a fully-structured VR sp…

Two-loop anomalous dimensions for baryon-number-violating operators in SMEFT
Sumit Banik, Andreas Crivellin, Luca Naterop, Peter Stoffer
https://arxiv.org/abs/2510.08682 https:/…

Two-loop anomalous dimensions for baryon-number-violating operators in SMEFT
We compute the two-loop renormalization-group equations for the baryon-number-violating dimension-six operators in the SMEFT. This includes all three gauge interactions, the Yukawa, and Higgs self-interaction contributions. In addition, we present the one-loop matching of the $S_1$ scalar leptoquark on the SMEFT, which can generate the Wilson coefficients of all four gauge-invariant baryon-number-violating SMEFT operators. Using this example, we demonstrate the cancellation of scheme and matchi…

Nash Equilibria of Noncooperative/Miexd Differential Games with Density Constraints in Infinite Dimensions
Zhun Gou, Nan-Jing Huang, Jian-Hao Kang, Jen-Chih Yao
https://arxiv.org/abs/2508.07623

Nash Equilibria of Noncooperative/Miexd Differential Games with Density Constraints in Infinite Dimensions
Motivated by Cournot models, this paper proposes novel models of the noncooperative and cooperative differential games with density constraints in infinite dimensions, where markets consist of infinite firms and demand dynamics are governed by controlled differential equations. Markets engage in noncooperative competition with each other, while firms within each market engage in noncooperative or cooperative games. The main problems are to find the noncooperative Nash equilibrium (NNE) of the n…

Anomalous Critical Behavior of Driven Disordered Systems Beyond the Overdamped Limit
Giuseppe Petrillo, Eduardo Jagla, Eugenio Lippiello, Alberto Rosso
https://arxiv.org/abs/2508.09617

Anomalous Critical Behavior of Driven Disordered Systems Beyond the Overdamped Limit
We investigate the role of relaxation mechanisms in the driven response of elastic disordered interfaces in finite dimensions, focusing on the interplay between dimensionality and interaction range. Through extensive numerical simulations, we identify two distinct dynamical regimes. In two-dimensional systems with long-range interactions, we observe a regime of coexistence between pinned and flowing states. In contrast, for one-dimensional interfaces with long-range elasticity, as well as for s…

Multidimensional Poverty Mapping for Small Areas
Soumojit Das, Dilshanie Deepawansa, Partha Lahiri
https://arxiv.org/abs/2510.08898 https://arxiv.org/pdf/2…

Multidimensional Poverty Mapping for Small Areas
Many countries measure poverty based only on income or consumption. However, there is a growing awareness of measuring poverty through multiple dimensions that captures a more reasonable status of poverty. Estimating poverty measure(s) for small geographical areas, commonly referred to as poverty mapping, is challenging due to small or no sample for the small areas. While there is a huge literature available on unidimensional poverty mapping, only a limited effort has been made to address speci…

Fourier interpolation in dimensions 3 and 4 and real-variable Kloosterman sums
Danylo Radchenko, Qihang Sun
https://arxiv.org/abs/2510.04873 https://arxiv.…

Fourier interpolation in dimensions 3 and 4 and real-variable Kloosterman sums
We give a construction of radial Fourier interpolation formulas in dimensions 3 and 4 using Maass--Poincaré type series. As a corollary we obtain explicit formulas for the basis functions of these interpolation formulas in terms of what we call real-variable Kloosterman sums, which were previously introduced by Stoller. We also improve the bounds on the corresponding basis functions $a_{n,d}(x)$, $d=3,4$, for fixed $x$, in terms of the index $n$.

High SNR Probabilities of Continuous Fluid Antenna Systems in Ricean Environments
Amy S. Inwood, Peter J. Smith, Rajitha Senanayake, Michail Matthaiou
https://arxiv.org/abs/2508.10485

High SNR Probabilities of Continuous Fluid Antenna Systems in Ricean Environments
We consider a single-user (SU) continuous fluid antenna system (CFAS) employing matched filtering (MF) operating over a Ricean fading channel. Focusing on the upper tail of the received signal-to-noise ratio (SNR) distribution (the high SNR probability (HSP)), we derive accurate approximations for the HSP in 1, 2, and 3 dimensions using the expected Euler characteristic (EEC), presenting the first analytical results for a CFAS in a Ricean environment. In the process, we provide the first closed…

The Ricci tensor of a gradient Ricci soliton with harmonic Weyl tensor
Valter Borges, Matheus Andrade Ribeiro de Moura Hor\'acio, Jo\~ao Paulo dos Santos
https://arxiv.org/abs/2510.11939

The Ricci tensor of a gradient Ricci soliton with harmonic Weyl tensor
In this article, we give a new proof of a result due to J. Kim, which states that the Ricci tensor of a gradient Ricci soliton with dimension $n \geq 4$ and harmonic Weyl tensor has at most three distinct eigenvalues. This result constitutes an essential step in the classification of such manifolds, originally established by J. Kim in dimension $4$ and subsequently extended to dimensions $n\geq5$. Our proof offers two notable advantages: it is shorter and does not require the use of any special…

Bounds on skew dimensions and characters of symmetric groups via thick hook decompositions
Lucas Teyssier
https://arxiv.org/abs/2508.06770 https://arxiv.or…

Bounds on skew dimensions and characters of symmetric groups via thick hook decompositions
We bound the number of standard tableaux of skew shapes via thick hook decompositions in the Naruse hook length formula. Combining this with elementary counting arguments in the Murnaghan--Nakayama rule, we establish a uniform bound on characters of symmetric groups $\mathfrak{S}_n$. In the case of balanced representations, this improves on the character bounds of Féray and Śniady for permutations with support size at least $n^{2/3}$, and is sharp for permutations with support size of order $…

Transport properties of stochastic fluids
Chandrodoy Chattopadhyay, Josh Ott, Thomas Schaefer, Vladimir V. Skokov
https://arxiv.org/abs/2510.12557 https://…

Transport properties of stochastic fluids
We study heat conduction and momentum transport in the context of stochastic fluid dynamics. We consider a fluid described by model H in the classification of Hohenberg and Halperin. We study both non-critical and critical fluids, and we investigate transport properties in two as well as three dimensions. Our results are based on numerical simulations of model H using a Metropolis algorithm, and we employ Kubo relations to extract transport coefficients. We observe the expected logarithmic dive…

Fractal depth-first search paths in statistical physics models
Qiyuan Shi, Youjin Deng, Ming Li
https://arxiv.org/abs/2508.10502 https://arxiv.org/pdf/2508…

Fractal depth-first search paths in statistical physics models
We study the fractal properties of depth-first search (DFS) paths in critical configurations of statistical physics models, including the two-dimensional $O(n)$ loop model for various $n$, and bond percolation in dimensions $d = 2$ to $6$. In the $O(n)$ loop model, the fractal dimension of the DFS path consistently matches that of the external perimeter, suggesting DFS as a convenient alternative for probing interface geometry. For bond percolation, the DFS path exhibits nontrivial fractal scal…

LR-WaveHoltz: A Low-Rank Helmholtz Solver
Andreas Granath, Daniel Appel\"o, Siyang Wang
https://arxiv.org/abs/2510.09352 https://arxiv.org/pdf/2510.09…

LR-WaveHoltz: A Low-Rank Helmholtz Solver
We propose a low-rank method for solving the Helmholtz equation. Our approach is based on the WaveHoltz method, which computes Helmholtz solutions by applying a time-domain filter to the solution of a related wave equation. The wave equation is discretized by high-order multiblock summation-by-parts finite differences. In two dimensions we use the singular value decomposition and in three dimensions we use tensor trains to compress the numerical solution. To control rank growth we use step-trun…

Review of Steiner formulas in Fractal Geometry via Support measures and Complex Dimensions
Goran Radunovi\'c (University of Zagreb, Faculty of Science)
https://arxiv.org/abs/2509.05227

Review of Steiner formulas in Fractal Geometry via Support measures and Complex Dimensions
We review the theoretical framework that establishes a crucial bridge between the general Steiner-type formula of Hug, Last, and Weil and the theory of complex (fractal) dimensions of Lapidus et all. Two novel families of geometric functionals are introduced based on the support measures of the set itself as well as of its parallel sets, respectively. The associated scaling exponents provide new tools for extracting geometric information of the set, beyond its classical fractal dimensions while…

Multi-dimensional Neural Decoding with Orthogonal Representations for Brain-Computer Interfaces
Kaixi Tian, Shengjia Zhao, Yuhan Zhang, Shan Yu
https://arxiv.org/abs/2508.08681 …

Multi-dimensional Neural Decoding with Orthogonal Representations for Brain-Computer Interfaces
Current brain-computer interfaces primarily decode single motor variables, limiting their ability to support natural, high-bandwidth neural control that requires simultaneous extraction of multiple correlated motor dimensions. We introduce Multi-dimensional Neural Decoding (MND), a task formulation that simultaneously extracts multiple motor variables (direction, position, velocity, acceleration) from single neural population recordings. MND faces two key challenges: cross-task interference whe…

Exploring the Technical Knowledge Interaction of Global Digital Humanities: Three-decade Evidence from Bibliometric-based perspectives
Jiayi Li, Chengxi Yan, Yurong Zeng, Zhichao Fang, Huiru Wang
https://arxiv.org/abs/2508.08347

Exploring the Technical Knowledge Interaction of Global Digital Humanities: Three-decade Evidence from Bibliometric-based perspectives
Digital Humanities (DH) is an interdisciplinary field that integrates computational methods with humanities scholarship to investigate innovative topics. Each academic discipline follows a unique developmental path shaped by the topics researchers investigate and the methods they employ. With the help of bibliometric analysis, most of previous studies have examined DH across multiple dimensions such as research hotspots, co-author networks, and institutional rankings. However, these studies hav…

Quantum recurrences and the arithmetic of Floquet dynamics
Amit Anand, Dinesh Valluri, Jack Davis, Shohini Ghose
https://arxiv.org/abs/2508.09933 https://a…

Quantum recurrences and the arithmetic of Floquet dynamics
The Poincaré recurrence theorem shows that conservative systems in a bounded region of phase space eventually return arbitrarily close to their initial state after a finite amount of time. An analogous behavior occurs in certain quantum systems where quantum states can recur after sufficiently long unitary evolution, a phenomenon known as quantum recurrence. Periodically driven (i.e. Floquet) quantum systems in particular exhibit complex dynamics even in small dimensions, motivating the study …

(Anti)Gravitron: A Statistical Physics Perspective on Multidimensional Metrics of Polarizing Inequality
Rolando Gonzales Martinez
https://arxiv.org/abs/2510.09436 https://

(Anti)Gravitron: A Statistical Physics Perspective on Multidimensional Metrics of Polarizing Inequality
This paper introduces a novel framework for measuring multidimensional inequality based on a statistical physics reinterpretation of centrifugal and centripetal forces in rotating systems. Inspired by the mechanics of the Gravitron and extended via the conceptual AntiGravitron, this study proposes a new class of inequality metrics grounded in multivariate mixtures of Beta distributions. These composite metrics capture three key structural dimensions of polarizing inequality: the number and bala…

Replaced article(s) found for math.PR. https://arxiv.org/list/math.PR/new
[1/1]:
- A para-controlled approach to the stochastic Yang-Mills equation in two dimensions
Bjoern Bringmann, Sky Cao

Auto-Prompt Ensemble for LLM Judge
Jiajie Li, Huayi Zhang, Peng Lin, Jinjun Xiong, Wei Xu
https://arxiv.org/abs/2510.06538 https://arxiv.org/pdf/2510.06538…

Auto-Prompt Ensemble for LLM Judge
We present a novel framework that improves the reliability of LLM judges by selectively augmenting LLM with auxiliary evaluation dimensions. Existing LLM judges often miss crucial evaluation dimensions because they fail to recognize the implicit standards underlying human assessments. To address this challenge, we propose the Auto-Prompt Ensemble (APE), an adaptive framework that automatically learns evaluation dimensions from its failure cases. APE incorporates a confidence-based ensemble mech…

Semi-discrete multi-to -one dimensional variational problems
Omar Abdul Halim, Daniyar Omarov, Brendan Pass
https://arxiv.org/abs/2508.09490 https://arxiv.…

Semi-discrete multi-to -one dimensional variational problems
We study a class of semi-discrete variational problems that arise in economic matching and game theory, where agents with continuous attributes are matched to a finite set of outcomes with a one dimensional structure. Such problems appear in applications including Cournot-Nash equilibria, and hedonic pricing, and can be formulated as problems involving optimal transport between spaces of unequal dimensions. In our discrete strategy space setting, we establish analogues of results developed for …

A Comprehensive Evaluation of Multilingual Chain-of-Thought Reasoning: Performance, Consistency, and Faithfulness Across Languages
Raoyuan Zhao, Yihong Liu, Hinrich Sch\"utze, Michael A. Hedderich
https://arxiv.org/abs/2510.09555

A Comprehensive Evaluation of Multilingual Chain-of-Thought Reasoning: Performance, Consistency, and Faithfulness Across Languages
Large reasoning models (LRMs) increasingly rely on step-by-step Chain-of-Thought (CoT) reasoning to improve task performance, particularly in high-resource languages such as English. While recent work has examined final-answer accuracy in multilingual settings, the thinking traces themselves, i.e., the intermediate steps that lead to the final answer, remain underexplored. In this paper, we present the first comprehensive study of multilingual CoT reasoning, evaluating three key dimensions: per…

Intersection cohomology without spaces
Tom Braden, Nicholas Proudfoot
https://arxiv.org/abs/2510.09488 https://arxiv.org/pdf/2510.09488

Intersection cohomology without spaces
We survey three settings in which dimensions of intersection cohomology groups of algebraic varieties provide deep combinatorial and representation-theoretic information, and computations of the groups themselves have been made using combinatorial sheaves on finite posets. These settings are (1) intersection cohomology of Schubert varieties, the associated Kazhdan-Lusztig polynomials and their realizations via moment graph sheaves and Soergel bimodules; (2) intersection cohomology of toric vari…

Geometric study of non-constant vector fields making hyperbolic space Ricci-Bourguignon solitons
Mafal Ndiaye Diop, Abdou Bousso, Cheikh Khoule, Ameth Ndiaye
https://arxiv.org/abs/2510.12745

Geometric study of non-constant vector fields making hyperbolic space Ricci-Bourguignon solitons
The objective of this paper is to deepen the study of vector fields on hyperbolic spaces $\mathbb{H}^n$ that transform them into a Ricci-Bourguignon soliton. Starting from a recent work in \cite{bousso2025ricci} which characterizes these fields as Killing fields of a specific shape, we propose a detailed geometric study of their structure and behavior in the dimensions $n=2, 3$ and $n\geq 3$. In odd dimension we show that the dual form of these vectors are contact forms. This work aims to enric…

Non-Decaying Solutions to the 2D Dissipative Quasi-Geostrophic Equations
David M. Ambrose, Ryan Aschoff, Elaine Cozzi, James P. Kelliher
https://arxiv.org/abs/2508.10254 https:/…

Non-Decaying Solutions to the 2D Dissipative Quasi-Geostrophic Equations
We consider the surface quasi-geostrophic equation in two spatial dimensions, with subcritical diffusion (i.e. with fractional diffusion of order $2α$ for $α>\frac{1}{2}$.) We establish existence of solutions without assuming either decay at spatial infinity or spatial periodicity. One obstacle is that for $L^{\infty}$ data, the constitutive law may not be applicable, as Riesz transforms are unbounded. However, for $L^{\infty}$ initial data for which the constitutive law does converge, we dem…

Augmentation categories in higher dimensions
Hanming Liu
https://arxiv.org/abs/2508.06822 https://arxiv.org/pdf/2508.06822…

Augmentation categories in higher dimensions
For an exact symplectic manifold \(M\) and a Legendrian submanifold \(Λ\) of the contactification \(M\times \mathbb{R}\), we construct the augmentation category (over a field of characteristic 2), a unital \(A_\infty\)-category whose objects are augmentations of the Chekanov-Eliashberg differential graded algebra. This extends the construction of the augmentation category by Ng-Rutherford-Shende-Sivek-Zaslow to contact manifolds of dimension greater than 3. This paper is a step in generalising…

4D de Sitter from 6D gauged supergravity with Green-Schwarz counterterm
Xu Guo, Yi Pang, Ergin Sezgin
https://arxiv.org/abs/2510.11794 https://arxiv.org/pd…

4D de Sitter from 6D gauged supergravity with Green-Schwarz counterterm
Taking into account the Green-Schwarz anomaly counterterm in R-symmetry gauged $N=(1,0)$ supergravity in six dimensions, and the associated modification in the Maxwell kinetic term and potential, we observe that the theory admits half-supersymmetric Minkowski$_4\times S^2$ and non-supersymmetric dS$_4 \times S^2$ as exact solutions with a monopole on $S^2$. The monopole charge and the anomaly coefficients play key roles in the vacuum structure and it turns out that a diagonal gauging in which a…

On elastic and non-elastic wave superpositions for the Euler system
{\L}ukasz Chomienia, Alfred Michel Grundland
https://arxiv.org/abs/2510.09576 https://a…

On elastic and non-elastic wave superpositions for the Euler system
The paper contains an analysis of the conditions for the existence of elastic versus non-elastic wave superpositions governed by the Euler system in (1+1)-dimensions. This system admits entropic solutions and two types of sound wave solutions. It is shown that the smallest real Lie algebra containing vector fields (associated with these waves) is isomorphic to a semidirect sum of the infinite-dimensional Abelian real Lie algebra and the non-Abelian finite-dimensional real Lie algebra. Based on …

Distributed Stochastic Model Predictive Control with Temporal Aggregation for the Joint Dispatch of Cascaded Hydropower and Renewables
Luca Santosuosso, Sonja Wogrin
https://arxiv.org/abs/2510.11998

Distributed Stochastic Model Predictive Control with Temporal Aggregation for the Joint Dispatch of Cascaded Hydropower and Renewables
This paper addresses the real-time energy dispatch of a hybrid system comprising cascaded hydropower plants, wind, and solar units, jointly participating in the day-ahead energy market under inflow, renewable generation, and price uncertainties. Traditional scenario-based stochastic model predictive control (MPC) faces severe computational bottlenecks due to the complexity arising from the temporal, asset, and scenario dimensions of this control problem. To address this, we propose a novel cont…

Superresolution for two incoherent optical sources with arbitrary intensities in two dimensions
Junyan Li, Shengshi Pang
https://arxiv.org/abs/2508.08049 https://

Superresolution for two incoherent optical sources with arbitrary intensities in two dimensions
The Rayleigh criterion has long served as a fundamental limit for the resolution of classical optical imaging. However, recent advances in quantum metrology have led to the quantum superresolution technique that can break Rayleigh's curse and estimate the separation between a pair of incoherent point sources with nonvanishing precision. For two-dimensional optical systems, the precision limit of estimating the whole separation, i.e., the distance, between two point sources remains unknown so fa…

Momentum-Resolved Relaxation-Time Approach for Size-Dependent Conductivity in Anisotropic Metallic Films
YoungJun Lee, Jin Soo Lee, Seungjun Lee, Seoung-Hun Kang, Young-Kyun Kwon
https://arxiv.org/abs/2508.08622

Momentum-Resolved Relaxation-Time Approach for Size-Dependent Conductivity in Anisotropic Metallic Films
Shrinking CMOS interconnect dimensions to the nanometer scale intensifies electron scattering at surfaces, interfaces, and grain boundaries, causing severe conductivity loss and challenging copper-based designs. Here we present a momentum-resolved relaxation time framework that integrates density functional theory with the semiclassical Boltzmann transport equation to predict size-dependent resistivity in metallic thin films. Electron phonon interactions are computed from first principles, and …

Whipped and mixed warm clouds in the deep sea
Hans van Haren (Km3NeT Collaboation)
https://arxiv.org/abs/2510.09470 https://arxiv.org/pdf/2510.09470…

Whipped and mixed warm clouds in the deep sea
Turbulence is indispensable to redistribute nutrients for all life forms larger than microbial, on land and in the ocean. Yet, the development of deep-sea turbulence has not been studied in three dimensions (3D). As a disproportionate laboratory, an array of nearly 3000 high-resolution temperature sensors had been installed for three years on the flat 2500-m deep bottom of the Mediterranean Sea. The time series from the half-cubic hectometer 3D mooring-array allows for the creation of unique mo…

A no-contact result for a plate-fluid interaction system in dimension three
Mario Bukal, Igor Kukavica, Linfeng Li, Boris Muha
https://arxiv.org/abs/2510.09992 https://

A no-contact result for a plate-fluid interaction system in dimension three
We address the fluid-structure interaction between a viscous incompressible fluid and an elastic plate forming its moving upper boundary in three dimensions. The fluid is described by the incompressible Navier-Stokes equations with a free upper boundary that evolves according to the motion of the structure, coupled via the velocity- and stress-matching conditions. Under the natural energy bounds and additional regularity assumptions on the weak solutions, we prove a non-contact property with a …

Replaced article(s) found for hep-th. https://arxiv.org/list/hep-th/new
[1/1]:
- Comment on the cosmological constant for $\lambda \phi^4$ theory in $d$ spacetime dimensions
Andr\'e LeClair

Triadic Fusion of Cognitive, Functional, and Causal Dimensions for Explainable LLMs: The TAXAL Framework
David Herrera-Poyatos, Carlos Pel\'aez-Gonz\'alez, Cristina Zuheros, Virilo Tejedor, Rosana Montes, Francisco Herrera
https://arxiv.org/abs/2509.05199

Triadic Fusion of Cognitive, Functional, and Causal Dimensions for Explainable LLMs: The TAXAL Framework
Large Language Models (LLMs) are increasingly being deployed in high-risk domains where opacity, bias, and instability undermine trust and accountability. Traditional explainability methods, focused on surface outputs, do not capture the reasoning pathways, planning logic, and systemic impacts of agentic LLMs. We introduce TAXAL (Triadic Alignment for eXplainability in Agentic LLMs), a triadic fusion framework that unites three complementary dimensions: cognitive (user understanding), functio…

On the dichotomy of $p$-walk dimensions on metric measure spaces
Meng Yang
https://arxiv.org/abs/2509.08641 https://arxiv.org/pdf/2509.08641

On the dichotomy of $p$-walk dimensions on metric measure spaces
On a volume doubling metric measure space endowed with a family of $p$-energies such that the Poincaré inequality and the cutoff Sobolev inequality with $p$-walk dimension $β_p$ hold, for $p$ in an open interval $I\subseteq (1,+\infty)$, we prove the following dichotomy: either $β_p=p$ for all $p\in I$, or $β_p>p$ for all $p\in I$.

Beyond Tag Collision: Cluster-based Memory Management for Tag-based Sanitizers
Mengfei Xie, Yan Lin, Hongtao Wu, Jianming Fu, Chenke Luo, Guojun Peng
https://arxiv.org/abs/2509.09089

Beyond Tag Collision: Cluster-based Memory Management for Tag-based Sanitizers
Tag-based sanitizers attach a small "key" to each pointer and a matching "lock" tag to its target memory object, enabling runtime verification of pointer-object consistency and helping developers to detect potential memory violations. However, the limited tag encoding space challenges existing studies in assigning distinct tags to memory objects across temporal and spatial dimensions, leading to potential tag collisions. In this paper, we present ClusterTag, a novel cluster-based memory allocat…

Hamiltonian analysis of an Effective action coupled to the Palatini action in 4 dimensions
Ricardo Escobedo, Roberto Santos-Silva, Claudia Moreno, Rafael Hern\'andez-Jim\'enez
https://arxiv.org/abs/2508.04006

Hamiltonian analysis of an Effective action coupled to the Palatini action in 4 dimensions
We carry out the canonical analysis of the coupling of a $4$-dimensional effective action that arises from a dimensional reduction of a $7$-dimensional BF theory to the Palatini action in $4$-dimensions with cosmological constant, focusing on homogeneity and isotropy in all involved fields. We employ Ostrogradsky's methodology because of the presence of second time derivatives. Through the analysis of consistency conditions, we identify three distinct and consistent possibilities. In all these …

Multi-Qubit Golden Gates
Rahul Dalal, Shai Evra, Ori Parzanchevski
https://arxiv.org/abs/2509.09047 https://arxiv.org/pdf/2509.09047

Multi-Qubit Golden Gates
Our goal in this paper is to construct optimal topological generators for compact unitary Lie groups, extending the work of a letter of Sarnak and arXiv:1704.02106 on golden and super-golden gates to higher dimensions. To do so we consider a variant of the Sarnak--Xue Density Hypotheses in the weight aspect for definite projective unitary groups and prove it using the endoscopic classification of automorphic representations. Our main motivation is to construct efficient multi-qubit universal …

Sequestered Conformal Anomaly Mediation (SCAM)
Michael Nee, Lisa Randall
https://arxiv.org/abs/2510.11784 https://arxiv.org/pdf/2510.11784

Sequestered Conformal Anomaly Mediation (SCAM)
Supersymmetric models in singular extra dimensional spaces feature prominently in many interesting phenomenological models, including those derived from string theory. In this paper we explicitly derive the low energy theory of phenomenologically viable supersymmetric theories in five dimensions, and highlight several aspects of these models that are not obvious from working solely in the 4d effective theory. Important deviations arise for anomaly mediation, which is purported to be a predictiv…

Replaced article(s) found for math-ph. https://arxiv.org/list/math-ph/new
[1/1]:
- Numerical Analysis of the Causal Action Principle in Low Dimensions
Felix Finster, Robert H. Jonsson, Niki Kilbertus

Optical Link Tomography: First Field Trial and 4D Extension
Takeo Sasai, Giacomo Borraccini, Yue-Kai Huang, Hideki Nishizawa, Zehao Wang, Tingjun Chen, Yoshiaki Sone, Minami Takahashi, Tatsuya Matsumura, Masanori Nakamura, Etsushi Yamazaki, Koichi Takasugi, Ting Wang, Yoshiaki Kisaka
https://arxiv.org/abs/2510.09384

Optical Link Tomography: First Field Trial and 4D Extension
Optical link tomography (OLT) is a rapidly evolving field that allows the multi-span, end-to-end visualization of optical power along fiber links in multiple dimensions from network endpoints, solely by processing signals received at coherent receivers. This paper has two objectives: (1) to report the first field trial of OLT, using a commercial transponder under standard DWDM transmission, and (2) to extend its capability to visualize across 4D (distance, time, frequency, and polarization), al…

On the uniqueness of strong solution to the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system
Lingxin Jiang, Jiahong Wu, Fuyi Xu
https://arxiv.org/abs/2508.09761 …

On the uniqueness of strong solution to the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system
This paper is mainly concerned with an initial-boundary value problem of the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system with the Landau potential in a two and three dimensions. Global existence of strong solutions with bounded and strictly positive density for this system was proven by Giorgini and Temam \cite{GT}; however, an additional smoothness assumption on the initial density was needed to prove uniqueness in \cite{GT1}. Whether uniqueness holds without this addition…

Universality of the chiral soliton lattice in the low energy limit of QCD
Fabrizio Canfora, Nicol\'as Grandi, Marcela Lagos, Luis Urrutia-Reyes, Aldo Vera
https://arxiv.org/abs/2510.11946

Universality of the chiral soliton lattice in the low energy limit of QCD
In this paper, we show that the chiral soliton lattice (ChSL) is, in a precise sense, a universal feature of the low-energy limit of QCD minimally coupled to Maxwell theory. Here, we disclose that not only can the ChSL be obtained from the gauged Skyrme model in $3+1$ dimensions, including the back-reaction of the Maxwell $U(1)$ gauge field, we also show that the ChSL remains unchanged if the sub-leading corrections to the Skyrme model in the 't Hooft large $N_c$ expansion are included. Taking …

Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system
Ruifang Yan, Huihui Cao, Kailiang Wu
https://arxiv.org/abs/2508.08913 https://…

Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system
This paper proposes a numerical method, termed PosDiv-CDG, that provably preserves both positivity and the globally divergence-free (DF) condition at arbitrarily high order in multiple dimensions. It resolves the fundamental structural incompatibility between standard positivity-preserving limiters and global DF enforcement in the central discontinuous Galerkin (CDG) framework. The method integrates a novel positivity-limiting strategy, a modified dissipation mechanism guided by convex decompos…

Rare event probabilities in Random Geometric Graphs
Prabhanka Deka, Fangzhou Luo, Baichuan Wu
https://arxiv.org/abs/2510.09196 https://arxiv.org/pdf/2510.0…

Rare event probabilities in Random Geometric Graphs
In this paper, we study rare events in spherical and Gaussian random geometric graphs in high dimensions. In these models, the vertices correspond to points sampled uniformly at random on the $d$ dimensional unit sphere or correspond to $d$ dimensional standard Gaussian vectors, and edges are added between two vertices if the inner-product between their corresponding points are greater than a threshold $t_p$, chosen such that the probability of having an edge is equal to $p$. We focus on two pr…

A Compact Story of Positivity in de Sitter
Priyesh Chakraborty, Timothy Cohen, Daniel Green, Yiwen Huang
https://arxiv.org/abs/2508.08359 https://arxiv.org…

A Compact Story of Positivity in de Sitter
Recent developments have yielded significant progress towards systematically understanding loop corrections to de Sitter (dS) correlators. In close analogy with physics in Anti-de Sitter (AdS), large logarithms can result from loops that can be interpreted as corrections to the dimensions of operators. In contrast with AdS, these dimensions are not manifestly real. This implies that the theoretical constraints on the associated correlators are less transparent, particularly in the presence of l…

Hodge theoretic results for nearly K\"ahler manifolds in all dimensions
Michael Albanese, Spiro Karigiannis, Luc\'ia Mart\'in-Merch\'an, Aleksandar Milivojevi\'c
https://arxiv.org/abs/2509.06664

Hodge theoretic results for nearly Kähler manifolds in all dimensions
We generalize to nearly Kähler manifolds of arbitrary dimensions most of the Hodge-theoretic results for nearly Kähler $6$-manifolds that were established by Verbitsky. In particular, for a compact nearly Kähler manifold of any dimension, the (appropriately defined) Hodge numbers are related to the Betti numbers in the same way as on a compact Kähler manifold. In the $6$-dimensional case, Verbitsky was able to say slightly more using the induced $\mathrm{SU}(3)$ structure. We discuss potent…

Early Explorations of Recommender Systems for Physical Activity and Well-being
Alan Said
https://arxiv.org/abs/2508.07980 https://arxiv.org/pdf/2508.07980

Early Explorations of Recommender Systems for Physical Activity and Well-being
As recommender systems increasingly guide physical actions, often through wearables and coaching tools, new challenges arise around how users interpret, trust, and respond to this advice. This paper introduces a conceptual framework for tangible recommendations that influence users' bodies, routines, and well-being. We describe three design dimensions: trust and interpretation, intent alignment, and consequence awareness. These highlight key limitations in applying conventional recommender logi…

Counting Salem numbers arising from arithmetic hyperbolic orbifolds
Michelle Chu, Plinio G. P. Murillo, Otto Romero, Lola Thompson
https://arxiv.org/abs/2508.08003 https://

Counting Salem numbers arising from arithmetic hyperbolic orbifolds
The relationship between Salem numbers and short geodesics has been fruitful in quantitative studies of arithmetic hyperbolic orbifolds, particularly in dimensions 2 and 3. In this article, we push these connections even further. The primary goals are: (1) to bound the proportion of Salem numbers of degree up to $n+1$ in the commensurability class of classical arithmetic lattices in any odd dimension $n$; (2) to improve lower bounds for the strong exponential growth of averages of multiplicitie…

Classification and Birational Equivalence of Dimer Integrable Systems for Reflexive Polygons
Minsung Kho, Norton Lee, Rak-Kyeong Seong
https://arxiv.org/abs/2510.12290 https://

Classification and Birational Equivalence of Dimer Integrable Systems for Reflexive Polygons
Brane tilings are bipartite periodic graphs on the 2-torus and realize a large family of 4d N=1 supersymmetric gauge theories corresponding to toric Calabi-Yau 3-folds. We present a complete classification of dimer integrable systems corresponding to the 30 brane tilings whose toric Calabi-Yau 3-folds are given by the 16 reflexive polygons in 2 dimensions. For each dimer integrable system associated to a reflexive polygon, we present the Casimirs, the single Hamiltonian built from 1-loops, the …

Geometry of supergravity and the Batalin--Vilkovisky formulation of the $\mathcal N=1$ theory in ten dimensions
Julian Kupka, Charles Strickland-Constable, Fridrich Valach
https://arxiv.org/abs/2508.06398

Geometry of supergravity and the Batalin--Vilkovisky formulation of the $\mathcal N=1$ theory in ten dimensions
We provide full details of a BV formulation of $\mathcal N=1$ supergravity in ten dimensions, to all orders in fermions, built from the generalised geometry description of the theory. In contrast to standard treatments, we introduce neither the degrees of freedom corresponding to orthonormal frames for the metric nor the local Lorentz symmetries that remove them again. Instead, we observe that the field space has a fibred structure, with the fermionic degrees of freedom spanning the fibres. We …

The gyromagnetic factor of charged rotating black holes in various dimensions from scattering amplitudes
Claudio Gambino, Fabio Riccioni, Victor Sanz Sanchis
https://arxiv.org/abs/2509.08456

The gyromagnetic factor of charged rotating black holes in various dimensions from scattering amplitudes
Classical black hole spacetimes can be recovered from the classical limit of quantum scattering amplitudes in a low-energy effective field theory of gravity. In this work we compute, at first post-Minkowskian and dipole order, the metric and the electromagnetic potential for charged and rotating black holes in general spacetime dimensions from amplitudes describing the emission of either a graviton or a photon from a massive and charged Dirac fermion field up to one loop. In addition, we introd…

Non-linear stability of shock profiles in dissipative hyperbolic-hyperbolic systems
Matthias Sroczinski, Kevin Zumbrun
https://arxiv.org/abs/2510.09287 https://

Non-linear stability of shock profiles in dissipative hyperbolic-hyperbolic systems
We give the first proof of nonlinear stability for smooth shock profiles of second-order dissipative hyperbolic-hyperbolic systems under the assumption of spectral stability, showing stability of smooth small-amplitude profiles in dimensions greater than or equal to two. This class of systems notably includes the two types of causal viscous relativistic gas models introduced respectively by Freistühler-Temple and Bemfica-Disconzi-Noronha, and (the equivalent second-order form of) a class of fi…

Conformal four-point ladder integrals in diverse dimensions and polylogarithms
S. E. Derkachov, A. P. Isaev, L. A. Shumilov
https://arxiv.org/abs/2510.04235 https://

Conformal four-point ladder integrals in diverse dimensions and polylogarithms
In the paper, the family of conformal four-point ladder diagrams in arbitrary space-time dimensions is considered. We use the representation obtained via explicit calculation using the operator approach and conformal quantum mechanics to study their properties, such as symmetries, loop and dimensional shift identities. In even integer dimensions, latter allows one to reduce the problem to two-dimensional case, where the notable factorization holds. Additionally, for a specific choice of propaga…

Anomalous dimensions and critical exponents for the Gross-Neveu-Yukawa model at five loops
J. A. Gracey, A. Maier, P. Marquard, Y. Schr\"oder
https://arxiv.org/abs/2507.22594

Anomalous dimensions and critical exponents for the Gross-Neveu-Yukawa model at five loops
We renormalize the Gross-Neveu-Yukawa model with an $O(N)$ symmetry to $\mathcal{O}(ε^5)$ in $d=4-ε$ dimensions and determine the anomalous dimensions of the fermion and scalar fields, $β$-functions as well as the scalar field's mass operator. These are used to construct several $N$ dependent critical exponents relevant for quantum transitions in semi-metals and in particular those connected with graphene in three dimensions when $N=2$. Improved exponent estimates for scalar fermion transiti…

Supersymmetric lattice theories on curved space
David Berenstein, Simon Catterall
https://arxiv.org/abs/2509.08885 https://arxiv.org/pdf/2509.08885

Supersymmetric lattice theories on curved space
We show how to construct Hamiltonian lattice theories with one exact supersymmetry on arbitrary triangulations of curved space in any number of dimensions. Both bosons and fermions satisfy discrete Kähler-Dirac equations. The quantization of the fermions proceeds by imposing conventional anti-commutation relations while the bosons require a modification of the usual canonical commutator. On regular lattices we construct parity, time reversal and translation-by-one (shift) symmetries. We argue …