Tootfinder

The Complexity of Arc-Connectedness Relation in the Plane
Yusuf Uyar
https://arxiv.org/abs/2509.24596 https://arxiv.org/pdf/2509.24596

The Complexity of Arc-Connectedness Relation in the Plane
In this paper, we show that the arc-connectedness equivalence relation on a Polish subspace of the real plane is an essentially hyperfinite Borel equivalence relation. This result provides the optimal upper bound for such a Borel equivalence relation.

An SoS Entropy Dichotomy via Windowed Hypercontractivity
Marko Lela
https://arxiv.org/abs/2509.24280 https://arxiv.org/pdf/2509.24280

An SoS Entropy Dichotomy via Windowed Hypercontractivity
We prove an entropy versus degree dichotomy for low-degree tests and the Sum-of-Squares (SoS) hierarchy on a calibrated window after a gadget layer. For a target distribution \(μ\) and a product-like proxy \(u\), we study the low-degree discrepancy \(Δ_k(μ,u)\), defined as the optimal distinguishing advantage of degree \(\le k\) polynomial tests. Using a bias-orthonormal Walsh basis and a test-moment equivalence on the window, we relate \(Δ_k\) (up to constants) to the squared \(\ell_2\) ma…

Replaced article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/1]:
- A robust BFGS algorithm for unconstrained nonlinear optimization problems
Yaguang Yang
https://arxiv.org/abs/1212.5929
- Quantum computing and the stable set problem
Alja\v{z} Krpan, Janez Povh, Dunja Pucher
https://arxiv.org/abs/2405.12845 https://mastoxiv.page/@arXiv_mathOC_bot/112483516437815686
- Mean Field Game with Reflected Jump Diffusion Dynamics: A Linear Programming Approach
Zongxia Liang, Xiang Yu, Keyu Zhang
https://arxiv.org/abs/2508.20388 https://mastoxiv.page/@arXiv_mathOC_bot/115111048711698998
- Differential Dynamic Programming for the Optimal Control Problem with an Ellipsoidal Target Set a...
Sungjun Eom, Gyunghoon Park
https://arxiv.org/abs/2509.07546 https://mastoxiv.page/@arXiv_mathOC_bot/115179281556444440
- On the Moreau envelope properties of weakly convex functions
Marien Renaud, Arthur Leclaire, Nicolas Papadakis
https://arxiv.org/abs/2509.13960 https://mastoxiv.page/@arXiv_mathOC_bot/115224514482363803
- Automated algorithm design via Nevanlinna-Pick interpolation
Ibrahim K. Ozaslan, Tryphon T. Georgiou, Mihailo R. Jovanovic
https://arxiv.org/abs/2509.21416 https://mastoxiv.page/@arXiv_mathOC_bot/115286533597711930
- Optimal Control of a Bioeconomic Crop-Energy System with Energy Reinvestment
Othman Cherkaoui Dekkaki
https://arxiv.org/abs/2510.11381 https://mastoxiv.page/@arXiv_mathOC_bot/115372322896073250
- Point Convergence Analysis of the Accelerated Gradient Method for Multiobjective Optimization: Co...
Yingdong Yin
https://arxiv.org/abs/2510.26382 https://mastoxiv.page/@arXiv_mathOC_bot/115468018035252078
- History-Aware Adaptive High-Order Tensor Regularization
Chang He, Bo Jiang, Yuntian Jiang, Chuwen Zhang, Shuzhong Zhang
https://arxiv.org/abs/2511.05788
- Equivalence of entropy solutions and gradient flows for pressureless 1D Euler systems
Jos\'e Antonio Carrillo, Sondre Tesdal Galtung
https://arxiv.org/abs/2312.04932 https://mastoxiv.page/@arXiv_mathAP_bot/111560077272113052
- Kernel Modelling of Fading Memory Systems
Yongkang Huo, Thomas Chaffey, Rodolphe Sepulchre
https://arxiv.org/abs/2403.11945 https://mastoxiv.page/@arXiv_eessSY_bot/112121123836064435
- The Maximum Theoretical Ground Speed of the Wheeled Vehicle
Altay Zhakatayev, Mukatai Nemerebayev
https://arxiv.org/abs/2502.15341 https://mastoxiv.page/@arXiv_physicsclassph_bot/114057765769441123
- Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavity
Giacomo Greco, Luca Tamanini
https://arxiv.org/abs/2504.11133 https://mastoxiv.page/@arXiv_mathPR_bot/114346453424694503
- Optimizing the ground state energy of the three-dimensional magnetic Dirichlet Laplacian with con...
Matthias Baur
https://arxiv.org/abs/2504.21597 https://mastoxiv.page/@arXiv_mathph_bot/114431404740241516
- A localized consensus-based sampling algorithm
Arne Bouillon, Alexander Bodard, Panagiotis Patrinos, Dirk Nuyens, Giovanni Samaey
https://arxiv.org/abs/2505.24861 https://mastoxiv.page/@arXiv_mathNA_bot/114612580684567066
- A Novel Sliced Fused Gromov-Wasserstein Distance
Moritz Piening, Robert Beinert
https://arxiv.org/abs/2508.02364 https://mastoxiv.page/@arXiv_csLG_bot/114976243138728278
- Minimal Regret Walras Equilibria for Combinatorial Markets via Duality, Integrality, and Sensitiv...
Alo\"is Duguet, Tobias Harks, Martin Schmidt, Julian Schwarz
https://arxiv.org/abs/2511.09021 https://mastoxiv.page/@arXiv_csGT_bot/115541243299714775
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Replaced article(s) found for physics.atom-ph. https://arxiv.org/list/physics.atom-ph/new
[1/1]:
- Perturbation-assisted Observation of the Lowest Vibrational Level of the $\mathrm{b}^{3}\Pi_{0}$ ...
Yang, Nie, Yu, Liu, Avalos, He, Klos, Kotochigova, Dieckmann
https://arxiv.org/abs/2510.17166 https://mastoxiv.page/@arXiv_physicsatomph_bot/115411364513995859
- Direct Measurement of the $5s5p\,{}^1P_1 \to 5s4d\,{}^1D_2$ Decay Rate in Strontium
Naohiro Okamoto, Takatoshi Aoki, Yoshio Torii
https://arxiv.org/abs/2510.22184 https://mastoxiv.page/@arXiv_physicsatomph_bot/115450966319591523
- Turbulence and far-from-equilibrium equation of state of Bogoliubov waves in Bose-Einstein Conden...
Ying Zhu, Giorgio Krstulovic, Sergey Nazarenko
https://arxiv.org/abs/2408.15163 https://mastoxiv.page/@arXiv_condmatquantgas_bot/113038670682163852
- Observation of quantum free fall and the consistency with the equivalence principle
Or Dobkowski, et al.
https://arxiv.org/abs/2502.14535 https://mastoxiv.page/@arXiv_quantph_bot/114040790353608831
- Microwave-field quantum metrology with inherent robustness against detection losses enabled by Ry...
Kurzyna, Niewelt, Mazelanik, Wasilewski, Demkowicz-Dobrza\'nski, Parniak
https://arxiv.org/abs/2505.01506 https://mastoxiv.page/@arXiv_quantph_bot/114459737137154531
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Morita Equivalence for Quantales
Moacyr Rodrigues, Ciro Russo
https://arxiv.org/abs/2510.07565 https://arxiv.org/pdf/2510.07565

Morita Equivalence for Quantales
We study Morita equivalence in the context of quantales with identity, in the wake of Katsov and Nam's analogous work on semirings. Among a number of other results, we prove a characterization of Morita equivalence and an Eilenberg-Watts-type Theorem for quantales.

Combinatorial equivalence of separable elements in types $A$ and $B$
Yong Liao, Yuping Yang, Houyi Yu
https://arxiv.org/abs/2510.12046 https://arxiv.org/pd…

Combinatorial equivalence of separable elements in types $A$ and $B$
We study the combinatorial equivalence of separable elements in types $A$ and $B$. A bijection is constructed from the set of separable permutations in the symmetric group $S_{n+1}$ to the set of separable signed permutations in the hyperoctahedral group $B_n$. This bijection preserves descent statistics and induces a poset isomorphism under the left weak order. As a consequence, separable signed permutations are enumerated by the large Schröder numbers, and their descent polynomials are shown…

Totally paracompact spaces and the Menger covering property
Davide Giacopello, Maddalena Bonanzinga, Piotr Szewczak
https://arxiv.org/abs/2511.10252 https://arxiv.org/pdf/2511.10252 https://arxiv.org/html/2511.10252
arXiv:2511.10252v1 Announce Type: new
Abstract: A topological space is totally paracompact if any base of this space contains a locally finite subcover. We focus on a problem of Curtis whether in the class of regular Lindel\"of spaces total paracompactness is equivalent to the Menger covering property. To this end we consider topological spaces with certain dense subsets. It follows from our results that the above equivalence holds in the class of Lindel\"of GO-spaces defined on subsets of reals. We also provide a game-theoretical proof that any regular Menger space is totally paracompact and show that in the class of first-countable spaces the Menger game and a partial open neighborhood assignment game of Aurichi are equivalent. We also show that if $\mathfrak{b}=\omega_1$, then there is an uncountable subspace of the Sorgenfrey line whose all finite powers are Lindel\"of, which is a strengthening of a famous result due to Michael.
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Completeness for Fault Equivalence of Clifford ZX Diagrams
Maximilian R\"usch, Benjamin Rodatz, Aleks Kissinger
https://arxiv.org/abs/2510.08477 https://

Completeness for Fault Equivalence of Clifford ZX Diagrams
Two circuits are considered to be equivalent under noise if the effect of faults on one circuit is no worse than the effect of faults on the other circuit. We call this relationship fault equivalence. Fault equivalence offers a way to transform circuits while provably preserving their fault-tolerant properties, enabling a framework for fault-tolerant circuit synthesis and optimisation that is correct by construction. The ZX calculus, a set of graphical rewrite rules for quantum computations, pr…

Markoff triples and Nielsen equivalence in $\text{SL}_2(\mathbb{F}_p)$
Daniel E. Martin
https://arxiv.org/abs/2510.07577 https://arxiv.org/pdf/2510.07577…

Markoff triples and Nielsen equivalence in $\text{SL}_2(\mathbb{F}_p)$
In 2013, Darryl McCullough and Marcus Wanderley made a series of conjectures that describe the Nielsen equivalence classes and $T_2$-equivalence classes of pairs of generators for $\text{SL}_2(\mathbb{F}_q)$ and the Markoff equivalence classes of triples in $\mathbb{F}_q^3$ that solve $x^2+y^2+z^2=xyz+κ$ for some $κ\in\mathbb{F}_q$. (The case $κ=0$ was originally conjectured by Baragar in 1991.) We prove that one of the McCullough--Wanderley conjectures, the ``$Q$-classification conjecture" …

On the geometric Satake equivalence for Kac-Moody groups
Alexis Bouthier, Eric Vasserot
https://arxiv.org/abs/2510.11466 https://arxiv.org/pdf/2510.11466…

On the geometric Satake equivalence for Kac-Moody groups
This article establishes a geometric Satake equivalence for affine Kac-Moody groups as an equivalence of abelian semisimple categories over algebraically closed fields. We define a well-behaved category of equivariant sheaves on the double affine grassmannian \Gr_{G}, seen as a infty-stack, that we equip with a t-structure. We obtain an Braden's hyperbolic localization theorem for such a stack and prove that the constant term functor is t-exact using dimension estimates for affine MV-cycles. We…

Fisher Information, Training and Bias in Fourier Regression Models
Lorenzo Pastori, Veronika Eyring, Mierk Schwabe
https://arxiv.org/abs/2510.06945 https://

Fisher Information, Training and Bias in Fourier Regression Models
Motivated by the growing interest in quantum machine learning, in particular quantum neural networks (QNNs), we study how recently introduced evaluation metrics based on the Fisher information matrix (FIM) are effective for predicting their training and prediction performance. We exploit the equivalence between a broad class of QNNs and Fourier models, and study the interplay between the \emph{effective dimension} and the \emph{bias} of a model towards a given task, investigating how these affe…

The mainstream media loves making it seam like dysfunction in Washington is coming from both parties.
Hello?
Much of the GOP no longer accepts the rule of law, or the norms of democracy, or the legitimacy of the opposing party.
Enough of the false equivalence.
https://bsky.app/profile/rbr…

Robert Reich (@rbreich.bsky.social)
The mainstream media loves making it seam like dysfunction in Washington is coming from both parties. Hello? Much of the GOP no longer accepts the rule of law, or the norms of democracy, or the legitimacy of the opposing party. Enough of the false equivalence.

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 …

A simple proof of the coincidence of observational and labeled equivalence of processes in applied pi-calculus
Andrew M. Mironov
https://arxiv.org/abs/2510.07258 https://…

A simple proof of the coincidence of observational and labeled equivalence of processes in applied pi-calculus
This paper presents a new, significantly simpler proof of one of the main results of applied pi-calculus: the theorem that the concepts of observational and labeled equivalence of extended processes in applied pi-calculus coincide.

Gaussian Equivalence for Self-Attention: Asymptotic Spectral Analysis of Attention Matrix
Tomohiro Hayase, Beno\^it Collins, Ryo Karakida
https://arxiv.org/abs/2510.06685 https:…

Gaussian Equivalence for Self-Attention: Asymptotic Spectral Analysis of Attention Matrix
Self-attention layers have become fundamental building blocks of modern deep neural networks, yet their theoretical understanding remains limited, particularly from the perspective of random matrix theory. In this work, we provide a rigorous analysis of the singular value spectrum of the attention matrix and establish the first Gaussian equivalence result for attention. In a natural regime where the inverse temperature remains of constant order, we show that the singular value distribution of t…

Physics is simple only when analyzed locally
Matteo Luca Ruggiero
https://arxiv.org/abs/2511.07447 https://arxiv.org/pdf/2511.07447 https://arxiv.org/html/2511.07447
arXiv:2511.07447v1 Announce Type: new
Abstract: The definition of a reference frame in General Relativity is achieved through the construction of a congruence of time-like world-lines. In this framework, splitting techniques enable us to express physical phenomena in analogy with Special Relativity, thereby realizing the local description in terms of Minkowski spacetime in accordance with the equivalence principle. This approach holds promise for elucidating the foundational principles of relativistic gravitational physics, as it illustrates how its 4-dimensional mathematical model manifests in practical measurement processes conducted in both space and time. In addition, we show how, within this framework, the Newtonian gravitational force naturally emerges as an effect of the non-geodesic path of the reference frame.
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A simpler kernel for stratified Mukai flops
Ed Segal, Wei Tseu
https://arxiv.org/abs/2510.08250 https://arxiv.org/pdf/2510.08250

A simpler kernel for stratified Mukai flops
We reinvestigate the problem of describing the Fourier-Mukai kernel for the derived equivalence associated to a stratified Mukai flop. For the case of Grassmannians of planes we give a very simple geometric construction of the kernel, using the framework of matrix factorizations.

Fast radio bursts shed light on direct gravity test on cosmological scales
Shuren Zhou, Pengjie Zhang
https://arxiv.org/abs/2510.11022 https://arxiv.org/pd…

Fast radio bursts shed light on direct gravity test on cosmological scales
A key measure of gravity is the relation between the Weyl potential $Ψ+Φ$ and the matter overdensity $δ_m$, capsulized as an effective gravitational constant $G_{\rm light}$ for light motion. Its value, together with the possible spatial and temporal variation, is essential in probing physics beyond Einstein gravity. However, the lack of an unbiased proxy of $δ_m$ prohibits direct measurement of $G_{\rm light}$. We point out that the equivalence principle ensures the dispersion measure (DM)…

The equivalence between two real Seiberg-Witten homologies
Yonghan Xiao
https://arxiv.org/abs/2510.03709 https://arxiv.org/pdf/2510.03709

The equivalence between two real Seiberg-Witten homologies
We show that for a real rational homology sphere $Y$ equipped with a real $\mathrm{spin^c}$ structure $\s$, the real monopole Floer homology defined by Li and the real Seiberg-Witten Floer homology defined by Konno, Miyazawa and Taniguchi are isomorphic. As corollaries, we identify some Frøyshov-type invariants and prove two Smith-type inequalities.

Extending Games beyond the Finite Horizon
Kiri Sakahara, Takashi Sato
https://arxiv.org/abs/2510.08453 https://arxiv.org/pdf/2510.08453

Extending Games beyond the Finite Horizon
This paper argues that the finite horizon paradox, where game theory contradicts intuition, stems from the limitations of standard number systems in modelling the cognitive perception of infinity. To address this issue, we propose a new framework based on Alternative Set Theory (AST). This framework represents different cognitive perspectives on a long history of events using distinct topologies. These topologies define an indiscernibility equivalence that formally treats huge, indistinguishabl…

On-Grid Equivalence of Continuous-Time Doubly Selective Channels: A Revisit of Bello's Models
Jun Tong
https://arxiv.org/abs/2510.03626 https://arxiv.o…

On-Grid Equivalence of Continuous-Time Doubly Selective Channels: A Revisit of Bello's Models
Significant studies on communications over doubly selective channels have utilized on-grid DD channel models, which are previously investigated in Bello's seminar paper in 1963. The DD grid is typically specified by the bandwidth and time duration of the transmission frames. However, the physical channels are determined by the propagation environments and they are typically off-grid. Hence, there is often a gap between an actual physical channel and the on-grid model. This paper revisits the on…

Equivalence criteria for the two--term functional equations for Herglotz--Zagier functions
Sumukha Sathyanarayana, N. Guru Sharan
https://arxiv.org/abs/2510.10088 https://

Equivalence criteria for the two--term functional equations for Herglotz--Zagier functions
We establish Kronecker limit type formula for the generalized Mordell-Tornheim zeta function $Θ(r,r,t,x)$ as a function of the third argument around $t=1-r$. We then show that the above Kronecker limit type formula is equivalent to the two-term functional equation for the higher Herglotz function obtained by Vlasenko and Zagier. We also show the equivalence between a previously known Kronecker limit type formula for $Θ(1,1,t,x)$ around $t=0$ and the two-term functional equation for the Herglo…

Can We Hide Machines in the Crowd? Quantifying Equivalence in LLM-in-the-loop Annotation Tasks
Jiaman He, Zikang Leng, Dana McKay, Damiano Spina, Johanne R. Trippas
https://arxiv.org/abs/2510.06658

Can We Hide Machines in the Crowd? Quantifying Equivalence in LLM-in-the-loop Annotation Tasks
Many evaluations of large language models (LLMs) in text annotation focus primarily on the correctness of the output, typically comparing model-generated labels to human-annotated ``ground truth'' using standard performance metrics. In contrast, our study moves beyond effectiveness alone. We aim to explore how labeling decisions -- by both humans and LLMs -- can be statistically evaluated across individuals. Rather than treating LLMs purely as annotation systems, we approach LLMs as an alternat…

Quasi-conformal VS quasi-isometric equivalence in spaces with controlled growth
Katrin F\"Assler, Enrico Le Donne, Sebastiano Nicolussi Golo, Alessandro Ottazzi, Pierre Pansu
https://arxiv.org/abs/2510.12161

Quasi-conformal VS quasi-isometric equivalence in spaces with controlled growth
We study conditions under which quasi-conformal homeomorphisms are quasi-isometries. We show that if two nilpotent geodesic Lie groups are quasi-conformally homeomorphic, then they are quasi-isometrically equivalent. We also give more general results beyond the nilpotent case. In particular, we show that quasi-conformal homeomorphisms between geodesic Lie groups are quasi-isometries whenever the spaces have strict parabolic or hyperbolic conformal type. As a consequence, quasi-conformal homeomo…

Graded Lawson-Stone Duality
Roozbeh Hazrat, Zachary Mesyan
https://arxiv.org/abs/2510.06497 https://arxiv.org/pdf/2510.06497…

Graded Lawson-Stone Duality
The classical Stone duality associates to each Boolean algebra a topological space consisting of ultrafilters. Lawson's generalisation constructs a dual equivalence of categories of Boolean inverse $\land$-semigroups and Hausdorff ample topological groupoids. We further generalise the duality to the graded analogues of those categories, and provide various illustrations.

Replaced article(s) found for math.GN. https://arxiv.org/list/math.GN/new
[1/1]:
- The Complexity of Proper Homotopy Equivalence of Graphs
Hannah Hoganson, Jenna Zomback
https://arxiv.org/abs/2410.00901 https://mastoxiv.page/@arXiv_mathLO_bot/113236807267908552
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Spectral equivalence of unsymmetric kernel matrices and applications
Tizian Wenzel, Armin Iske
https://arxiv.org/abs/2509.24561 https://arxiv.org/pdf/2509.…

Spectral equivalence of unsymmetric kernel matrices and applications
Symmetric kernel matrices are a well researched topic in the literature of kernel based approximation. In particular stability properties in terms of lower bounds on the smallest eigenvalue of such symmetric kernel matrices are thoroughly investigated, as they play a fundamental role in theory and practice. In this work, we focus on unsymmetric kernel matrices and derive stability properties under small shifts by establishing a spectral equivalence to their unshifted, symmetric versions. This e…

On the Quantum Equivalence between $S|LWE\rangle$ and $ISIS$
Andr\'e Chailloux, Paul Hermouet
https://arxiv.org/abs/2510.06097 https://arxiv.org/pdf/25…

On the Quantum Equivalence between $S|LWE\rangle$ and $ISIS$
Chen, Liu, and Zhandry [CLZ22] introduced the problems $S|LWE\rangle$ and $C|LWE\rangle$ as quantum analogues of the Learning with Errors problem, designed to construct quantum algorithms for the Inhomogeneous Short Integer Solution ($ISIS$) problem. Several later works have used this framework for constructing new quantum algorithms in specific cases. However, the general relation between all these problems is still unknown. In this paper, we investigate the equivalence between $S
…

Equivalence Test for Mean Functions from Multi-population Functional Data
Chuang Xu, Andrew T. A. Wood, Yanrong Yang
https://arxiv.org/abs/2509.24242 https://

Equivalence Test for Mean Functions from Multi-population Functional Data
Most existing methods for testing equality of means of functional data from multiple populations rely on assumptions of equal covariance and/or Gaussianity. In this work we provide a new testing method based on a statistic that is distribution-free under the null hypothesis (i.e. the statistic is pivotal), and allows different covariance structures across populations, while Gaussianity is not required. In contrast to classical methods of functional mean testing, where either observations of the…

Classification for smooth manifolds looking like $\mathbb{CP}^3\times S^7$
Wen Shen
https://arxiv.org/abs/2510.00613 https://arxiv.org/pdf/2510.00613

Classification for smooth manifolds looking like $\mathbb{CP}^3\times S^7$
In this paper, we classify simply connected closed smooth $13$-dimensional manifolds whose cohomology ring is isomorphic to that of $\mb{CP}^3\times S^7$, up to diffeomorphism, homeomorphism, and homotopy equivalence. Furthermore, if such a manifold satisfies certain conditions, either itself or its connected sum with an exotic $13$-sphere $Σ^{13}$ admits a Riemannian metric of non-negative sectional curvature. As an additional application of our classification, we classify the diagonal $S^1$-…

Vandermonde Cells Through the Lens of Positive Geometry
Fatemeh Mohammadi, Sebastian Seemann
https://arxiv.org/abs/2510.11614 https://arxiv.org/pdf/2510.11…

Vandermonde Cells Through the Lens of Positive Geometry
We study the geometric and algebraic structure of Vandermonde cells, defined as images of the standard probability simplex under the Vandermonde map given by consecutive power sum polynomials. Motivated by their combinatorial equivalence to cyclic polytopes, which are well-known examples of positive geometries and tree amplituhedra, we investigate whether Vandermonde cells admit the structure of positive geometries. We derive explicit parametrizations and algebraic equations for their boundary …

Ground Stratification for a Logic of Definitions with Induction
Nathan Guermond (University of Minnesota), Gopalan Nadathur (University of Minnesota)
https://arxiv.org/abs/2510.12297

Ground Stratification for a Logic of Definitions with Induction
The logic underlying the Abella proof assistant includes mechanisms for interpreting atomic predicates through fixed point definitions that can additionally be treated inductively or co-inductively. However, the original formulation of the logic includes a strict stratification condition on definitions that is too restrictive for some applications such as those that use a logical relations based approach to semantic equivalence. Tiu has shown how this restriction can be eased by utilizing a wea…

So, “IJ” is a diphthong — capitalised together therefore, and can have its own #unicode digraph — but the equivalence with “Y” existed until 1804 and has been deprecated since.
https://en.wikipedia.org/wiki/IJ_(digr

Equivariant Eilenberg-Watts theorem for module coalgebras
Taiki Shibata (Okayama University of Science), Kenichi Shimizu (Shibaura Institute of Technology)
https://arxiv.org/abs/2510.07969

Equivariant Eilenberg-Watts theorem for module coalgebras
For coalgebras $C$ and $D$, Takeuchi proved that the category of linear functors from $\mathfrak{M}^C$ to $\mathfrak{M}^D$ preserving small coproducts is equivalent to the category of $C$-$D$-bicomodules, where $\mathfrak{M}^C$ for a coalgebra $C$ means the category of right $C$-comodules. We formulate and prove an equivariant version of this result for module coalgebras over a bialgebra. As an application, for a bialgebra $H$, we establish an equivalence of the 2-category of a particular class…

VeriEquivBench: An Equivalence Score for Ground-Truth-Free Evaluation of Formally Verifiable Code
Lingfei Zeng, Fengdi Che, Xuhan Huang, Fei Ye, Xu Xu, Binhang Yuan, Jie Fu
https://arxiv.org/abs/2510.06296

VeriEquivBench: An Equivalence Score for Ground-Truth-Free Evaluation of Formally Verifiable Code
Formal verification is the next frontier for ensuring the correctness of code generated by Large Language Models (LLMs). While methods that co-generate code and formal specifications in formal languages, like Dafny, can, in principle, prove alignment with user intent, progress is bottlenecked by specification quality evaluation. Current benchmarks rely on matching against ground-truth specifications, a manual and expertise-intensive process that has limited existing datasets to a few hundred si…

Equivariant Eilenberg-Watts theorems for locally compact quantum groups
Joeri De Ro
https://arxiv.org/abs/2510.06206 https://arxiv.org/pdf/2510.06206

Equivariant Eilenberg-Watts theorems for locally compact quantum groups
Given two von Neumann algebras $A$ and $B$, the $W^*$-algebraic Eilenberg-Watts theorem, due to M. Rieffel, asserts that there is a canonical equivalence $\operatorname{Corr}(A,B)\simeq \operatorname{Fun}(\operatorname{Rep}(B), \operatorname{Rep}(A))$ of categories, where $\operatorname{Corr}(A,B)$ denotes the category of all $A$-$B$-correspondences, $\operatorname{Rep}(A)$ is the category of all unital normal $*$-representations of $A$ on Hilbert spaces and $\operatorname{Fun}(\operatorname{Re…

Triangulated Categories Admitting Linear Generators
Marina Godinho, Dave Murphy
https://arxiv.org/abs/2510.12433 https://arxiv.org/pdf/2510.12433

Triangulated Categories Admitting Linear Generators
The main result of this paper is that there is an additive equivalence between $\overline{\mathcal{C}}_n$, the Paquette-Yildirim completion of the discrete cluster categories of Dynkin type $A_{\infty}$, and the perfect derived category of a certain DG algebra. This additive equivalence preserves some of the triangulated structure: it commutes with the suspension functor and preserves triangles with at least two indecomposable terms. In the process, we introduce the notion of a linear generator…

On the Bergman metric of Cartan-Hartogs domains
Andrea Loi, Roberto Mossa, Fabio ZUddas
https://arxiv.org/abs/2510.06405 https://arxiv.org/pdf/2510.06405…

On the Bergman metric of Cartan-Hartogs domains
We study the Bergman metric and introduce the Bergman dual on Cartan-Hartogs (CH) domains. For a bounded domain D in C^n with Bergman kernel K_D, we define the Bergman dual of (D, g_D) as (D*, g_D*), where D* is the maximal domain on which the modified kernel K_D*(z, zbar) = K_D(z, -zbar) is positive, and g_D* is the Kahler metric obtained from K_D*. For a Cartan-Hartogs domain M_{Omega, mu} we prove the equivalence of: (i) M_{Omega, mu} is biholomorphic to the unit ball; (ii) its Bergman metri…

Concentration structures on categories and horizontal categorification
Yangxiao Luo, Shunyu Wan
https://arxiv.org/abs/2510.07553 https://arxiv.org/pdf/2510…

Concentration structures on categories and horizontal categorification
We introduce a theory for encoding and manipulating algebraic data on categories via $\textit{concentration structures}$, which are equivalence relations on morphisms that satisfy certain axioms. For any category with a concentration structure we can functorially construct a $\textit{concentration monoid}$, which can be used to give a precise definition of horizontal categorification and decategorification. Moreover, by studying concentration structures on fundamental groupoids, we show that ev…

Nonlinear Optical Response in Pseudo-Hermitian Systems at Steady State
S. Sajad Dabiri, Reza Asgari
https://arxiv.org/abs/2510.06580 https://arxiv.org/pdf/…

Nonlinear Optical Response in Pseudo-Hermitian Systems at Steady State
We establish a steady-state theory for nonlinear optical conductivity in pseudo-Hermitian systems. We derive compact formulas for the first and second order conductivity tensors in both the velocity and length gauges and prove their exact equivalence through generalized sum rules and Berry connection identities by formulating the nonlinear response in terms of a biorthogonal density matrix. Utilizing the formalism on parity-time symmetric two-level systems reveals nonlinear phenomena that are n…

On some 2-binomial coefficients of binary words: geometrical interpretation, partitions of integers, and fair words
Gwena\"el Richomme (LIRMM | ESCAPE, UMPV)
https://arxiv.org/abs/2510.07159

On some 2-binomial coefficients of binary words: geometrical interpretation, partitions of integers, and fair words
The binomial notation (w u) represents the number of occurrences of the word u as a (scattered) subword in w. We first introduce and study possible uses of a geometrical interpretation of (w ab) and (w ba) when a and b are distinct letters. We then study the structure of the 2-binomial equivalence class of a binary word w (two words are 2-binomially equivalent if they have the same binomial coefficients, that is, the same numbers of occurrences, for each word of length at most 2). Especially we…

On Structured State-Space Duality
Jerry Yao-Chieh Hu, Xiwen Zhang, Weimin Wu, Han Liu
https://arxiv.org/abs/2510.04944 https://arxiv.org/pdf/2510.04944

On Structured State-Space Duality
Structured State-Space Duality (SSD) [Dao & Gu, ICML 2024] is an equivalence between a simple Structured State-Space Model (SSM) and a masked attention mechanism. In particular, a state-space model with a scalar-times-identity state matrix is equivalent to a masked self-attention with a $1$-semiseparable causal mask. Consequently, the same sequence transformation (model) has two algorithmic realizations: as a linear-time $O(T)$ recurrence or as a quadratic-time $O(T^2)$ attention. In this note,…

Replaced article(s) found for math.GR. https://arxiv.org/list/math.GR/new
[1/1]:
- Integrable measure equivalence rigidity of right-angled Artin groups via quasi-isometry
Camille Horbez, Jingyin Huang

On energy-momentum conservation in non-minimal geometry-matter coupling theories
Gonzalo J. Olmo, Miguel A. S. Pinto
https://arxiv.org/abs/2509.24890 https://

On energy-momentum conservation in non-minimal geometry-matter coupling theories
In this work, we discuss the conditions that allow the establishment of an equivalence between $f(R,T)=R+λh(T)$ gravity models and General Relativity coupled to a modified matter sector. We do so by considering a $D$-dimensional spacetime and the matter sector described by nonlinear electrodynamics and/or a scalar field.

Structural Identifiability of Graphical Continuous Lyapunov Models
Carlos Am\'endola, Tobias Boege, Benjamin Hollering, Pratik Misra
https://arxiv.org/abs/2510.04985 https:/…

Structural Identifiability of Graphical Continuous Lyapunov Models
We prove two characterizations of model equivalence of acyclic graphical continuous Lyapunov models (GCLMs) with uncorrelated noise. The first result shows that two graphs are model equivalent if and only if they have the same skeleton and equivalent induced 4-node subgraphs. We also give a transformational characterization via structured edge reversals. The two theorems are Lyapunov analogues of celebrated results for Bayesian networks by Verma and Pearl, and Chickering, respectively. Our resu…

On Nearly Frobenius Structures
William Davis, Olivia Dumitrescu
https://arxiv.org/abs/2510.03128 https://arxiv.org/pdf/2510.03128

On Nearly Frobenius Structures
Nearly Frobenius structures and 2-dimensional Almost TQFTs were introduced and shown to be in categorical equivalence in arXiv:1907.05470 in the attempt to extend the Atiyah-Segal's definition to the category of infinite dimensional vector spaces. In this paper, we investigate nearly Frobenius structures and we give a classification result for Almost TQFTs in dimension 2. In particular, the TQFTs functorial axioms become equivalent to the Edge Contraction/Construction axioms of colored ribbon g…

Black hole thermodynamics is around the corner
Gerui Chen, Wei Guo, Xin Lan, Hongbao Zhang, Wei Zhang
https://arxiv.org/abs/2510.04499 https://arxiv.org/pd…

Black hole thermodynamics is around the corner
We propose to work on the Euclidean black hole solution with a corner rather than with the prevalent conical singularity. As a result, we find that the Wald formula for black hole entropy can be readily obtained for generic F(Rabcd) gravity by using both the action without the corner term and the action with the corner term due to their equivalence to the first order variation, which implies that it is the corner rather than the corner term that encodes the entropy related information. With suc…

Replaced article(s) found for math.SG. https://arxiv.org/list/math.SG/new
[1/1]:
- Spectral equivalence of nearby Lagrangians
Johan Asplund, Yash Deshmukh, Alex Pieloch

Unitary transformation approach to the paraxial wave equation
M. Huerta-Sandoval, K. Uriostegui, I. Ramos-Prieto, F. Soto-Eguibar, H. Moya-Cessa
https://arxiv.org/abs/2510.00277

Unitary transformation approach to the paraxial wave equation
We present a framework for the paraxial wave equation based on propagation-dependent unitary transformations closely related to the Lewis-Ermakov invariant. This approach establishes a formal equivalence between free-space propagation and the dynamics in a quadratic gradient index (GRIN) medium. In this context, the dynamical invariant and the free-space Hamiltonian do not commute at the initial propagation stage due to Gaussian modulation, which imposes an effective quadratic confinement. Exac…

Combinatorial Characterizations and Branched Manifolds
Daryl Cooper, Leslie Mavrakis, Priyam Patel
https://arxiv.org/abs/2510.06514 https://arxiv.org/pdf/2…

Combinatorial Characterizations and Branched Manifolds
A family of compact n-manifolds is locally combinatorially defined (LCD) if it can be specified by a finite number of local triangulations. We show that LCD is equivalent to the existence of a compact branched n-manifold W, such that the family is precisely those manifolds that immerse into W. In subsequent papers, the equivalence will be used to show that, for each of the eight Thurston geometries, the family of closed 3-manifolds admitting that geometry is LCD.

Homomorphism Problems in Graph Databases and Automatic Structures
R\'emi Morvan
https://arxiv.org/abs/2510.07422 https://arxiv.org/pdf/2510.07422

Homomorphism Problems in Graph Databases and Automatic Structures
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures. Building on the well-known equivalence between conjunctive query evaluation and homomorphism existence, the first part focuses on conjunctive regular path queries, a standard extension of conjunctive queries that incorporates regular-path predicates. We study t…

Spline Interpolation on Compact Riemannian Manifolds
Charlie Sire, Mike Pereira, Thomas Romary
https://arxiv.org/abs/2510.11239 https://arxiv.org/pdf/2510.…

Spline Interpolation on Compact Riemannian Manifolds
Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches focus on Euclidean domains or the sphere, relying on the spectral properties of the Laplacian, this work introduces a method for spline interpolation on general manifolds by exploiting its equivalence with kriging. Specifically, the proposed approach uses finite…

Equivalence of continuous- and discrete-variable gate-based quantum computers with finite energy
Alex Maltesson, Ludvig Rodung, Niklas Budinger, Giulia Ferrini, Cameron Calcluth
https://arxiv.org/abs/2510.08546

Equivalence of continuous- and discrete-variable gate-based quantum computers with finite energy
We examine the ability of gate-based continuous-variable quantum computers to outperform qubit or discrete-variable quantum computers. Gate-based continuous-variable operations refer to operations constructed using a polynomial sequence of elementary gates from a specific finite set, i.e., those selected from the set of Gaussian operations and cubic phase gates. Our results show that for a fixed energy of the system, there is no superpolynomial computational advantage in using gate-based contin…

Well-Posedness and Efficient Algorithms for Inverse Optimal Transport with Bregman Regularization
Chenglong Bao, Zanyu Li, Yunan Yang
https://arxiv.org/abs/2510.03803 https://…

Well-Posedness and Efficient Algorithms for Inverse Optimal Transport with Bregman Regularization
This work analyzes the inverse optimal transport (IOT) problem under Bregman regularization. We establish well-posedness results, including existence, uniqueness (up to equivalence classes of solutions), and stability, under several structural assumptions on the cost matrix. On the computational side, we investigate the existence of solutions to the optimization problem with general constraints on the cost matrix and provide a sufficient condition guaranteeing existence. In addition, we propose…

Replaced article(s) found for q-fin.GN. https://arxiv.org/list/q-fin.GN/new
[1/1]:
- Robust dividend policy: Equivalence of Epstein-Zin and Maenhout preferences
Kexin Chen, Kyunghyun Park, Hoi Ying Wong

Replaced article(s) found for q-fin.MF. https://arxiv.org/list/q-fin.MF/new
[1/1]:
- Robust dividend policy: Equivalence of Epstein-Zin and Maenhout preferences
Kexin Chen, Kyunghyun Park, Hoi Ying Wong

Large Deviations Principle for Isoperimetry and Its Equivalence to Nonlinear Log-Sobolev Inequalities
Lei Yu
https://arxiv.org/abs/2510.04030 https://arxiv…

Large Deviations Principle for Isoperimetry and Its Equivalence to Nonlinear Log-Sobolev Inequalities
We investigate the large deviations principle (which concerns sequences of exponentially small sets) for the isoperimetric problem on product Riemannian manifolds $M^{n}$ equipped with product probability measures $ν^{\otimes n}$, where $M$ is a Riemannian manifold satisfying curvature-dimension bound $\mathrm{CD}(0,\infty)$. When the probability measure $ν$ satisfies a specific light-tail condition, we establish an exact characterization of the large deviations asymptotics for the isoperimet…

Crosslisted article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
- Combinatorial equivalence of separable elements in types $A$ and $B$
Yong Liao, Yuping Yang, Houyi Yu

Geometric Construction of Quiver Tensor Products
Daigo Ito, John S. Nolan
https://arxiv.org/abs/2510.05277 https://arxiv.org/pdf/2510.05277

Geometric Construction of Quiver Tensor Products
By a classic theorem of Beilinson, the perfect derived category $\operatorname{Perf}(\mathbb{P}^n)$ of projective space is equivalent to the category of derived representations of a certain quiver with relations. The vertex-wise tensor product of quiver representations corresponds to a symmetric monoidal structure $\otimes_{\mathsf{Q}}$ on $\operatorname{Perf}(\mathbb{P}^n)$. We prove that, for a certain choice of equivalence, the symmetric monoidal structure $\otimes_{\mathsf{Q}}$ may be descr…

Around the center
Maria Gorelik, Vladimir Hinich, Vera Serganova
https://arxiv.org/abs/2510.03928 https://arxiv.org/pdf/2510.03928

Around the center
The center of a semisimple Lie algebra can be described as the algebra of W-invariant functions on the dual of the Cartan subalgebra. The centers of many Lie superalgebras have a similar description, but the defining equivalence relation on the dual of the Cartan subalgebra is not given by a finite group action. Lagrangian equivalence relations that we introduce generalize the action of a subgroup of the orthogonal group. Using them, we present a new proof of a result by Ian Musson about the ce…

An algebraic approach to Latin squares of prime power order by local permutation polynomials
Ra\'ul M. Falc\'on, Jaime Guti\'errez, Jorge Jim\'enez Urroz
https://arxiv.org/abs/2510.09086

An algebraic approach to Latin squares of prime power order by local permutation polynomials
Every Latin square of prime power order $q$ is uniquely described by a local permutation polynomial (LPP) in the polynomial ring $\mathbb{F}_q[x,y]$. Despite this equivalence, one may find in the literature only some preliminary results on the relationship among Latin squares and LPPs. This paper delves into this topic by showing how the coefficients of any LPP are identified with the zeros of an algebraic set over $\mathbb{F}_q$. This allows for an algebraic description of all Latin squares of…

Abelian 3D TQFT gravity, ensemble holography and stabilizer states
Nikolaos Angelinos
https://arxiv.org/abs/2509.26052 https://arxiv.org/pdf/2509.26052

Abelian 3D TQFT gravity, ensemble holography and stabilizer states
We construct a model of 3D quantum gravity based on abelian topological quantum field theory (TQFT), by defining the gravitational path-integral as a sum over all 3D topologies with genus-$g$ boundary $Σ_g$. The path-integral of an abelian TQFT $\mathcal T$ on any single topology with boundary $Σ_g$ prepares a stabilizer state. This way, $\mathcal T$ partitions all these topologies into finitely many equivalence classes, where each topology within a class is associated with the same stabilize…

Ultra-Reliable Risk-Aggregated Sum Rate Maximization via Model-Aided Deep Learning
Hassaan Hashmi, Spyridon Pougkakiotis, Dionysis Kalogerias
https://arxiv.org/abs/2509.26311 ht…

Ultra-Reliable Risk-Aggregated Sum Rate Maximization via Model-Aided Deep Learning
We consider the problem of maximizing weighted sum rate in a multiple-input single-output (MISO) downlink wireless network with emphasis on user rate reliability. We introduce a novel risk-aggregated formulation of the complex WSR maximization problem, which utilizes the Conditional Value-at-Risk (CVaR) as a functional for enforcing rate (ultra)-reliability over channel fading uncertainty/risk. We establish a WMMSE-like equivalence between the proposed precoding problem and a weighted risk-aver…

Fermionic influence superoperator for transport through Majorana zero modes
Jia-Lin Pan, Zi-Fan Zhu, Shixuan Chen, Yu Su, Yao Wang
https://arxiv.org/abs/2510.04959 https://

Fermionic influence superoperator for transport through Majorana zero modes
In recent years, the study of Majorana signatures in quantum transport has become a central focus in condensed matter physics. Here, we present a rigorous and systematic derivation of the fermionic superoperator describing the open quantum dynamics of electron transport through Majorana zero modes, building on the techniques introduced in Phys. Rev. B 105, 035121 (2022). The numerical implementation of this superoperator is to construct its differential equivalence, the hierarchical equations o…

Groups versus quandle-like invariants of 3-manifolds
Luc Ta
https://arxiv.org/abs/2509.24098 https://arxiv.org/pdf/2509.24098

Groups versus quandle-like invariants of 3-manifolds
Risandles are nonassociative algebraic structures recently introduced to construct invariants of 3-manifolds. In this note, we show that the categories of groups and nonempty, faithful risandles are equivalent. In analogy to knot quandles, we also introduce fundamental risandles of 3-manifolds, which categorify the risandle coloring invariants of Ishii, Nakamura, and Saito. For infinitely many 3-manifolds, the equivalence of categories recovers the fundamental group from the fundamental risandl…

Moment tensors of Dirichlet distributions and learning Latent Dirichlet Allocation
Dat Do, Sunrit Chakraborty, Jonathan Terhorst, XuanLong Nguyen
https://arxiv.org/abs/2509.25441

Moment tensors of Dirichlet distributions and learning Latent Dirichlet Allocation
Understanding posterior contraction behavior in Bayesian hierarchical models is of fundamental importance, but progress in this question is relatively sparse in comparison to the theory of density estimation. In this paper, we study two classes of hierarchical models for grouped data, where observations within groups are exchangeable. Using moment tensor decomposition of the distribution of the latent variables, we establish a precise equivalence between the class of Admixture models (such as L…

Realism and the Inequivalence of the Two Quantum Pictures
Charles Alexandre B\'edard
https://arxiv.org/abs/2510.02138 https://arxiv.org/pdf/2510.02138

Realism and the Inequivalence of the Two Quantum Pictures
The standard claim that the Schrödinger and Heisenberg pictures of quantum mechanics are equivalent rests on the fact that they yield identical empirical predictions. This equivalence therefore assumes the instrumentalist worldview in which theories serve only as tools for prediction. Under scientific realism, by contrast, theories aim to describe reality. Whereas the Schrödinger picture posits a time-evolving wave function, the Heisenberg picture posits so-called descriptors, time-evolving g…

Homological epimorphisms in functor categories and singularity categories
Juan Andr\'es Orozco Guti\'errez, Valente Santiago Vargas
https://arxiv.org/abs/2510.09855 http…

Homological epimorphisms in functor categories and singularity categories
Given a homological epimorphism $π:\mathcal{C}\longrightarrow \mathcal{C}/\mathcal{I}$ between $K$-categories, we show that if the ideal $\mathcal{I}$ satisfies certain conditions, then there exists an equivalence between the singularity categories $\mathbf{D}_{sg}(\mathrm{Mod}(\mathcal{C}))$ and $ \mathbf{D}_{sg}(\mathrm{Mod}(\mathcal{C}/\mathcal{I}))$. This result generalizes the one obtained by Xiao-Wu Chen in [6]. We apply our result to the one point extension category and show that there …

Additively indecomposable quadratic forms over biquadratic and simplest cubic fields
Simona Fry\v{s}ov\'a, Magdal\'ena Tinkov\'a
https://arxiv.org/abs/2509.23857 htt…

Additively indecomposable quadratic forms over biquadratic and simplest cubic fields
In this paper, we study additively indecomposable quadratic forms over real biquadratic and simplest cubic fields. In particular, we show that over these fields, we can always find such a classical form in 2 variables, which differs from the situation for forms over integers. Moreover, for some cases, we derive a lower bound on the number of classical, additively indecomposable binary quadratic forms up to equivalence.

Special K\"ahler geometries of $\mathcal{N}=4$ superYang-Mills
Philip C. Argyres, Antoine Bourget, Julius F. Grimminger, Matteo Lotito, Mitch Weaver
https://arxiv.org/abs/2510.02057

Special Kähler geometries of $\mathcal{N}=4$ superYang-Mills
The low energy effective theory on the moduli space of vacua of 4d superYang-Mills (sYM) theory defines a special Kähler geometry. For simple sYM gauge algebras, $\mathfrak{g}$, we classify all compatible special Kähler structures by showing that they are in one-to-one correspondence with certain equivalence classes of integral symplectic representations of the Weyl group of $\mathfrak{g}$. We further demonstrate that, for principal Dirac pairing, these equivalence classes are in one-to-one c…

Tjurina Number Jumps and Unimodal Hypersurface Singularities in Positive Characteristic
Hongrui Ma, Aoyu Ying, Huaiqing Zuo
https://arxiv.org/abs/2510.02619 https://

Tjurina Number Jumps and Unimodal Hypersurface Singularities in Positive Characteristic
This paper generalizes existing methods to derive stronger bounds on the modality of hypersurface singularities. Our results demonstrate that each sudden jump in the Tjurina number necessarily increases the modality. Furthermore, we provide a full classification of unimodal isolated hypersurface singularities in characteristic p > 3 under contact equivalence. Keywords. isolated singularity, classification, modality, positive characteristic.

Provably Optimal Quantum Circuits with Mixed-Integer Programming
Harsha Nagarajan, Zsolt Szab\'o
https://arxiv.org/abs/2510.00649 https://arxiv.org/pdf…

Provably Optimal Quantum Circuits with Mixed-Integer Programming
We present a depth-aware optimization framework for quantum circuit compilation that unifies provable optimality with scalable heuristics. For exact synthesis of a target unitary, we formulate a mixed-integer linear program (MILP) that linearly handles global-phase equivalence and uses explicit parallel scheduling variables to certify depth-optimal solutions for small-to-medium circuits. Domain-specific valid constraints, including identity ordering, commuting-gate pruning, short-sequence redun…

Replaced article(s) found for math.GT. https://arxiv.org/list/math.GT/new
[1/1]:
- Stable equivalence relations on 4-manifolds
Daniel Kasprowski, John Nicholson, Simona Vesel\'a

Replaced article(s) found for math.RT. https://arxiv.org/list/math.RT/new
[1/1]:
- Representation Equivalence of Lattices in Lie Groups
Chandrasheel Bhagwat, Kaustabh Mondal

Replaced article(s) found for q-fin.MF. https://arxiv.org/list/q-fin.MF/new
[1/1]:
- Robust dividend policy: Equivalence of Epstein-Zin and Maenhout preferences
Kexin Chen, Kyunghyun Park, Hoi Ying Wong

Replaced article(s) found for q-fin.GN. https://arxiv.org/list/q-fin.GN/new
[1/1]:
- Robust dividend policy: Equivalence of Epstein-Zin and Maenhout preferences
Kexin Chen, Kyunghyun Park, Hoi Ying Wong

Holographic description of 4d Maxwell theories and their code-based ensembles
Ahmed Barbar, Anatoly Dymarsky, Alfred Shapere
https://arxiv.org/abs/2510.03392 https://

Holographic description of 4d Maxwell theories and their code-based ensembles
We formulate a precise holographic duality between an ensemble of 4d $U(1)^g$ Maxwell theories living on a spin four-manifold $M_4$ and an Abelian BF-type 2-form gauge theory of level $N$, summed over all five-manifolds with boundary $M_4$. The elements of the boundary ensemble are Abelian gauge theories specified by self-dual symplectic codes over $Z_N$, that parameterize topological boundary conditions in the 5d TQFT. Similarly, the equivalence classes of topologies distinguished by the 5d th…

Involutive Brauer groups and Poincar\'e rings
Viktor Burghardt, Noah Riggenbach, Lucy Yang
https://arxiv.org/abs/2509.25737 https://arxiv.org/pdf/2509.…

Involutive Brauer groups and Poincaré rings
We use the formalism of Poincaré $ \infty $-categories, as developed by Calmès-Dotto-Harpaz-Hebestreit-Land-Moi-Nardin-Nikolaus-Steimle, to define and study moduli stacks of line bundles with $ λ$-hermitian pairings and of Morita equivalence classes of Azumaya algebras equipped with an involution. Our moduli spaces give rise to enhancements of the ordinary Picard and Brauer groups which incorporate the data of an involution on the base; we will refer to these new invariants as the Poincaré …

Representation theory of the principal equivariant $\mathcal{W}$-algebra and Langlands duality
Damien Simon
https://arxiv.org/abs/2510.06990 https://arxiv.…

Representation theory of the principal equivariant $\mathcal{W}$-algebra and Langlands duality
The object of this article is to study some aspects of the quantum geometric Langlands program in the language of vertex algebras. We investigate the representation theory of the vertex algebra of chiral differential operators on a reductive group $\mathcal{D}_{G}^κ$ for generic levels. For instance we show that the geometric Satake equivalence degenerates. Then, we study the representation theory of the equivariant affine $\mathcal{W}$-algebra $\mathcal{W}_{G}^κ$, defined by Arakawa as the p…

3-manifold polynomials
Jos\'e Fr\'ias, Jos\'e Carlos G\'omez-Larra\~naga, Jos\'e Luis Le\'on-Medina, Fabiola Manjarrez-Guti\'errez
https://arxiv.org/abs/2510.06651

3-manifold polynomials
We propose a way to derive polynomial invariants of closed, orientable $3$-manifolds from Heegaard diagrams via cellularly embedded graphs. Given a Heegaard diagram of an irreducible $3$-manifold $M$, we associate a Heegaard graph $G\subset S$ on the Heegaard surface and restrict to those arising from minimal-genus splittings with a minimal number of vertices. We prove that, up to the natural equivalence of embedded graphs, only finitely many of such minimal Heegaard graphs occur for a fixed ma…

T-duality and bosonization as examples of continuum gauging and disentangling
Gertian Roose, Erez Zohar
https://arxiv.org/abs/2509.24630 https://arxiv.org/…

T-duality and bosonization as examples of continuum gauging and disentangling
Dualities and duality transformations form a well established methodology in various aspects of quantum many body physics and quantum field theories, allowing one to exploit equivalence between models which may naively seem completely different in order to gain access to further physical regimes, either analytically, numerically or experimentally. Recently, in the context of condensed matter physics and quantum information, it was shown that dualities can be understood very well through a gaugi…

Variation of algebraically integrable adjoint foliated structures
Paolo Cascini, Jihao Liu, Fanjun Meng, Roberto Svaldi, Lingyao Xie
https://arxiv.org/abs/2510.02498 https://

Variation of algebraically integrable adjoint foliated structures
Given a canonical algebraically integrable foliation on a klt projective variety, we study the variation of the ample models of the associated adjoint foliated structures with respect to the parameter. When the foliation is of general type, we show the finiteness of ample models if the parameter is sufficiently close to $1$. When the ambient variety is of general type, we show the finiteness of ample models for all parameters. A key ingredient in our proof is the equivalence between the existen…

Stable equivalence of Morita type and quotient fusion system
Conghui Li
https://arxiv.org/abs/2509.24795 https://arxiv.org/pdf/2509.24795

Stable equivalence of Morita type and quotient fusion system
In this note, we prove that stable equivalences of Morita type between blocks of finite groups induce identification of certain quotient fusion systems under sone assumption. We also collect some related results for separable equivalences.

Bounded $\mathfrak{sp}_4$-laminations and their intersection coordinates
Tsukasa Ishibashi, Zhe Sun, Wataru Yuasa
https://arxiv.org/abs/2509.25014 https://…

Bounded $\mathfrak{sp}_4$-laminations and their intersection coordinates
We introduce rational bounded $\mathfrak{sp}_4$-laminations on a marked surface $\boldsymbolΣ$ as a proposed topological model for the rational tropical points $\mathcal{A}_{Sp_4,\boldsymbolΣ}(\mathbb{Q}^{\mathsf{T}})$ of the Fock--Goncharov moduli space [FG06]. Our space consists of certain equivalence classes of $\mathfrak{sp}_4$-webs introduced by Kuperberg [Kup96], together with rational measures. We define tropical coordinate systems using the $\mathfrak{sp}_4$-case of the intersection n…

Derived equivalences, matrix equivalences, and homological conjectures
Xiaogang Li, Changchang Xi
https://arxiv.org/abs/2509.26353 https://arxiv.org/pdf/25…

Derived equivalences, matrix equivalences, and homological conjectures
Centralizer matrix algebras were investigated initially by Georg Ferdinand Frobenius in the Crelle's Journal around 1877. By introducing three new equivalence relations on all square matrices over a field, we completely characterize Morita, derived and almost $ν$-stable derived equivalences between centralizer matrix algebras in terms of these matrix equivalences, respectively. Thus the categorical equivalences are reduced to matrix equivalences in linear algebra. Further, we show that a deriv…