Tootfinder

Using nonassociative algebras to classify skew polycyclic codes up to isometry and equivalence
Susanne Pumpluen
https://arxiv.org/abs/2508.10139 https://ar…

Using nonassociative algebras to classify skew polycyclic codes up to isometry and equivalence
We propose new definitions of equivalence and isometry for skew polycyclic codes that will lead to tighter classifications than existing ones. This helps to reduce the number of previously known isometry and equivalence classes, and state precisely when these different notions coincide. In the process, we classify classes of skew $(f,σ,δ)$-polycyclic codes with the same performance parameters, to avoid duplicating already existing codes. We exploit that the generator of a skew polycyclic co…

Atiyah Classes in the Context of Generalized Complex Geometry
Dadi Ni
https://arxiv.org/abs/2508.10723 https://arxiv.org/pdf/2508.10723

Atiyah Classes in the Context of Generalized Complex Geometry
In analogy to the classical holomorphic setting, Lang, Jia and Liu introduced the notion of the Atiyah class for a generalized holomorphic vector bundle using three different approaches: leveraging $\rm{\check{C}}$ech cohomology, employing the first jet short exact sequence, and adopting the perspective of Lie algebroid pairs. The purpose of this note is to establish the equivalence among these diverse definitions of the Atiyah class.

Hurwitz space components; and the Coleman-Oort Conjecture
Michael D. Fried
https://arxiv.org/abs/2509.08904 https://arxiv.org/pdf/2509.08904

Hurwitz space components; and the Coleman-Oort Conjecture
Hurwitz spaces are moduli of isotopy classes of covers. A specific space is formed from a finite group G and C, r of its conjugacy classes and an equivalence relation \dagger. Components, interpret as a braid orbits on Nielsen classes. Fried-Völklein 1991 related absolute (corresponding to a permutation representation, T, of G) and inner equivalence classes. It noted two situations producing multiple components: #1. The action of a normalizer subgroup from $T$ on components; and #2. dist…

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" …

Oriented matroids and type $\mathbb{A}$ cluster categories
Nicholas J. Williams
https://arxiv.org/abs/2509.07883 https://arxiv.org/pdf/2509.07883

Oriented matroids and type $\mathbb{A}$ cluster categories
For any cluster-tilting object $\mathsf{T}$ in the cluster category $\mathscr{C}_{n}$ of type $\mathbb{A}_{n}$, we construct a rank-four oriented matroid $\mathcal{M}_{\mathsf{T}}$ such that stackable triangulations of $\mathcal{M}_{\mathsf{T}}$ are in bijection with equivalence classes of maximal green sequences with initial cluster $\mathsf{T}$. This generalises the result that equivalence classes of maximal green sequences of linearly oriented $\mathbb{A}_{n}$ are in bijection with triangula…

K-nonizing
Jose Beltr\'an Jim\'enez, Teodor Borislavov Vasilev, Dar\'io Jaramillo-Garrido, Antonio L. Maroto, Prado Mart\'in-Moruno
https://arxiv.org/abs/2509.07715

K-nonizing
We unveil the dynamical equivalence of field theories with non-canonical kinetic terms and canonical theories with a volume element invariant under transverse diffeomorphisms. The proof of the equivalence also reveals a subtle connection between the standard Legendre transformation and the so-called Clairaut equation. Explicit examples of canonizable theories include classes of $k$-essence, non-linear electrodynamics, or $f(R)$ theories. The equivalence can also be extended to the class of mime…

Hypergraph-Guided Regex Filter Synthesis for Event-Based Anomaly Detection
Margarida Ferreira, Victor Nicolet, Luan Pham, Joey Dodds, Daniel Kroening, Ines Lynce, Ruben Martins
https://arxiv.org/abs/2509.06911

Hypergraph-Guided Regex Filter Synthesis for Event-Based Anomaly Detection
We propose HyGLAD, a novel algorithm that automatically builds a set of interpretable patterns that model event data. These patterns can then be used to detect event-based anomalies in a stationary system, where any deviation from past behavior may indicate malicious activity. The algorithm infers equivalence classes of entities with similar behavior observed from the events, and then builds regular expressions that capture the values of those entities. As opposed to deep-learning approaches, t…

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…

Counting conjugacy classes and automorphism-conjugacy classes of ZM-groups
Marius T\u{a}rn\u{a}uceanu
https://arxiv.org/abs/2509.17004 https://arxiv.org/pd…

Counting conjugacy classes and automorphism-conjugacy classes of ZM-groups
In this paper, we count the number of conjugacy and automorphism-conjugacy classes of elements of a ZM-group. The size of a conjugacy class with respect to these two equivalence relations is also counted.

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…

Weisfeiler-Lehman meets Events: An Expressivity Analysis for Continuous-Time Dynamic Graph Neural Networks
Silvia Beddar-Wiesing, Alice Moallemy-Oureh
https://arxiv.org/abs/2508.18052

Weisfeiler-Lehman meets Events: An Expressivity Analysis for Continuous-Time Dynamic Graph Neural Networks
Graph Neural Networks (GNNs) are known to match the distinguishing power of the 1-Weisfeiler-Lehman (1-WL) test, and the resulting partitions coincide with the unfolding tree equivalence classes of graphs. Preserving this equivalence, GNNs can universally approximate any target function on graphs in probability up to any precision. However, these results are limited to attributed discrete-dynamic graphs represented as sequences of connected graph snapshots. Real-world systems, such as communica…

Cremona equivalence and log Kodaira dimension
Massimiliano Mella
https://arxiv.org/abs/2509.02277 https://arxiv.org/pdf/2509.02277

Cremona equivalence and log Kodaira dimension
Two projective varieties are said to be Cremona equivalent if there is a Cremona modification sending one onto the other. In the last decade, Cremona equivalence has been investigated widely, and we now have a complete theory for non-divisorial reduced schemes. The case of irreducible divisors is completely different, and not much is known besides the case of plane curves and a few classes of surfaces. In particular, for plane curves it is a classical result that an irreducible plane curve is C…

A Hierarchy for Constant Communication Complexity
Andris Ambainis, Hartmut Klauck, Debbie Lim
https://arxiv.org/abs/2509.22004 https://arxiv.org/pdf/2509.2…

A Hierarchy for Constant Communication Complexity
Similarly to the Chomsky hierarchy, we offer a classification of communication complexity measures such that these measures are organized into equivalence classes. Different from previous attempts of this endeavor, we consider two communication complexity measures as equivalent, if, when one is constant, then the other is constant as well, and vice versa. Most previous considerations of similar topics have been using polylogarithmic input length as a defining characteristic of equivalence. In t…

Bounds and Equivalence of Skew Polycyclic Codes over Finite Fields
Hassan Ou-azzou, Anna-Lena Horlemann, Nuh Aydin
https://arxiv.org/abs/2507.17571 https://

Bounds and Equivalence of Skew Polycyclic Codes over Finite Fields
We study skew polycyclic codes over a finite field $\mathbb{F}_q$, associated with a skew polynomial $f(x) \in \mathbb{F}_q[x;σ]$, where $σ$ is an automorphism of $\mathbb{F}_q$. We start by proving the Roos-like bound for both the Hamming and the rank metric for this class of codes. Next, we focus on the Hamming and rank equivalence between two classes of polycyclic codes by introducing an equivalence relation and describing its equivalence classes. Finally, we present examples that illustra…

$D_N$-Orthogonal Freedom in the Canonical Seesaw: Flavor Invariants and Physical Non-Equivalence of F-Classes
Jianlong Lu
https://arxiv.org/abs/2509.13363 https://

$D_N$-Orthogonal Freedom in the Canonical Seesaw: Flavor Invariants and Physical Non-Equivalence of F-Classes
This work is a companion to our previous papers showing that the data-favored $μ$-$τ$ modulus relation $|U_{μi}|=|U_{τi}|$ does not imply the ''minimal'' condition $R=PR^*$ and exhibiting six right-multiplications $F$ of the heavy-light block $R$ with $(RF)D_N(RF)^{T}=R D_N R^{T}$, leaving $m_ν$ unchanged. Here we give a complete classification and basis-invariant diagnostics that distinguish inequivalent completions with the same $m_ν$. We prove all $m_ν$-preserving …

Functorial equivalence classes of $2$-blocks of tame representation type
Robert Boltje, Serge Bouc, Deniz Y{\i}lmaz
https://arxiv.org/abs/2509.14682 https://

Functorial equivalence classes of $2$-blocks of tame representation type
For any block of a finite group over an algebraically closed field of characteristic $2$ which has dihedral, semidihedral, or generalized quaternion defect groups, we determine explicitly the decomposition of the associated diagonal $p$-permutation functor over an algebraically closed field $\mathbb{F}$ of characteristic $0$ into a direct sum of simple functors. As a consequence we see that two blocks with dihedral, semidihedral, or generalized quaternion defect groups are functorially equivale…

On a long exact sequence of groups of equivalence classes of 2d $\mathcal{N}{=}(0,1)$ SQFTs
Yuji Tachikawa
https://arxiv.org/abs/2509.12481 https://arxiv.o…

On a long exact sequence of groups of equivalence classes of 2d $\mathcal{N}{=}(0,1)$ SQFTs
Strongly motivated by a mathematical result by Lin and Yamashita (arXiv:2412.02298), we describe a long exact sequence formed by groups of equivalence classes of two-dimensional $\mathcal{N}{=}(0,1)$ supersymmetric quantum field theories (SQFTs) with and without $SU(2)$ symmetry. As an application, we study chiral fermions in heterotic compactifications with $SU(2)$ symmetry of level one to four dimensions, and show that each even-dimensional irreducible representation of $SU(2)$ appears even t…

Doubly Commuting Semigroups of Isometries
C. H. Namitha, Shankar Veerabathiran, S. Sundar
https://arxiv.org/abs/2509.00409 https://arxiv.org/pdf/2509.00409…

Doubly Commuting Semigroups of Isometries
In this paper, we discuss the structure of doubly commuting semigroups of isometries. We record a new proof of Cooper's theorem in the Hilbert module setting. We discuss the Fell topology on the set of equivalence classes of irreducible, doubly commuting isometric representations of $\mathbb{R}_{+}^{d}$. We show that if $d$ is finite, the topology is $T_0$. We indicate the pathologies that occur when $d=\infty$. In particular, we show that Wold decomposition fails for isometric representations …

Continuous colorings on compact spaces
No\'e de Rancourt (LPP), Dominique Lecomte (IMJ-PRG), Miroslav Zelen
https://arxiv.org/abs/2509.18680 https://ar…

Webification of symmetry classes of plane partitions
Ashleigh Adams, Jessica Striker
https://arxiv.org/abs/2508.16565 https://arxiv.org/pdf/2508.16565

Webification of symmetry classes of plane partitions
Webs are graphical objects that give a tangible, combinatorial way to compute and classify tensor invariants. Recently, [Gaetz, Pechenik, Pfannerer, Striker, Swanson 2023+] found a rotation-invariant web basis for $\mathrm{SL}_4$, as well as its quantum deformation $U_q(\mathfrak{sl}_4)$, and a bijection between move equivalence classes of $U_q(\mathfrak{sl}_4)$-webs and fluctuating tableaux such that web rotation corresponds to tableau promotion. They also found a bijection between the set of …

In his book Mathematica David Bessis notes this curios fact:
The _definition_ of a 'species' in biology is a bit like an equivalence relation in math: Two animals are of the same species if they can produce fertile offspring. The species are the equivalence classes.
But then, biologists are much more practically inclined to work with their definitions, or how do they know that elephants and humans are in fact distinct species? How do they check?
https://en.wikipedia.org/wiki/Species

Flexible hyperbolic cone metrics on the genus 2 surface
Katherine Chui, Jacob Russell
https://arxiv.org/abs/2507.19677 https://arxiv.org/pdf/2507.19677

Flexible hyperbolic cone metrics on the genus 2 surface
A negatively curved hyperbolic cone metric on a surface is rigid if it is determined by the support of its Liouville current. We use a theorem of Erlandsson, Leininger, and Sadanand to show that there are nine mapping class group orbits of equivalence classes of non-rigid (aka flexible) metrics in the case of the genus 2 surface.

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…

Circuit-based chatacterization of finite-temperature quantum phases and self-correcting quantum memory
Ruochen Ma, Vedika Khemani, Shengqi Sang
https://arxiv.org/abs/2509.15204 …

Circuit-based chatacterization of finite-temperature quantum phases and self-correcting quantum memory
Quantum phases at zero temperature can be characterized as equivalence classes under local unitary transformations: two ground states within a gapped phase can be transformed into each other via a local unitary circuit. We generalize this circuit-based characterization of phases to systems at finite-temperature thermal equilibrium described by Gibbs states. We construct a channel circuit that approximately transforms one Gibbs state into another provided the two are connected by a path in param…

Symmetries of the periodic Fredkin chain
Andrei G. Pronko
https://arxiv.org/abs/2507.18291 https://arxiv.org/pdf/2507.18291

Symmetries of the periodic Fredkin chain
Fredkin chain is a spin-$1/2$ model with interaction of three nearest neighbors. In the case of periodic boundary conditions the ground state is degenerated and can be described in terms of equivalence classes of the Dyck paths. We introduce two operators commuting with the Hamiltonian, which play the roles of lowering and raising operators when acting at the ground states. These operators generate the $B$- or $C$-type Lie algebras, depending on whether the number of sites $N$ is odd or even, r…

Structured Information Loss in Network Embeddings
Gabriel Chuang, Augustin Chaintreau
https://arxiv.org/abs/2509.12396 https://arxiv.org/pdf/2509.12396

Structured Information Loss in Network Embeddings
We analyze a simple algorithm for network embedding, explicitly characterizing conditions under which the learned representation encodes the graph's generative model fully, partially, or not at all. In cases where the embedding loses some information (i.e., is not invertible), we describe the equivalence classes of graphons that map to the same embedding, finding that these classes preserve community structure but lose substantial density information. Finally, we show implications for community…

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…

The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring
Beren Sanders, Yufei Zhang
https://arxiv.org/abs/2508.17603 https://arxiv.o…

The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring
We study the derived category of pseudo-coherent complexes over a noetherian commutative ring, building on prior work by Matsui-Takahashi. Our main theorem is a computation of the Balmer spectrum of this category in the case of a discrete valuation ring. We prove that it coincides with the spectral space associated to a bounded distributive lattice of asymptotic equivalence classes of monotonic sequences of natural numbers. The proof of this theorem involves an extensive study of generation beh…

Moment problems and bounds for matrix-valued smeared spectral functions
Ryan Abbott, William I. Jay, Patrick R. Oare
https://arxiv.org/abs/2508.01377 https://

Moment problems and bounds for matrix-valued smeared spectral functions
Numerical analytic continuation arises frequently in lattice field theory, particularly in spectroscopy problems. This work shows the equivalence of common spectroscopic problems to certain classes of moment problems that have been studied thoroughly in the mathematical literature. Mathematical results due to Kovalishina enable rigorous bounds on smeared matrix-valued spectral functions, which are implemented numerically for the first time. The required input is a positive-definite matrix of Eu…

The Modular Energy Function: Exact Identities and a Primality Equivalence
Es-said En-naoui
https://arxiv.org/abs/2509.10592 https://arxiv.org/pdf/2509.1059…

The Modular Energy Function: Exact Identities and a Primality Equivalence
We introduce and study the arithmetic function E_m(n), defined as the sum of the remainders of n when divided by the first m positive integers. Although the definition is elementary, the function encodes rich arithmetic structure. In this first part we develop exact algebraic and combinatorial identities, including floor-sum and divisor-sum reformulations, quotient-residue decompositions, sharp bounds and extremal classes, and symmetry relations. We also establish a diagonal identity linking E_…

Geometric models of simple Lie algebras via singularity theory
Cheol-Hyun Cho, Wonbo Jeong, Beom-Seok Kim
https://arxiv.org/abs/2507.22836 https://arxiv.or…

Geometric models of simple Lie algebras via singularity theory
It is well-known that ADE Dynkin diagrams classify both the simply-laced simple Lie algebras and simple singularities. We introduce a polygonal wheel in a plane for each case of ADE, called the Coxeter wheel. We show that equivalence classes of edges and spokes of a Coxeter wheel form a geometric root system isomorphic to the classical root system of the corresponding type. This wheel is in fact derived from the Milnor fiber of corresponding simple singularities of two variables, and the biline…

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 …

Semiorders induced by uniform random points
Csaba Bir\'o, Caroline E. Boone
https://arxiv.org/abs/2509.20274 https://arxiv.org/pdf/2509.20274

Semiorders induced by uniform random points
We study semiorders induced by points drawn from a uniform random distribution. Of particular interest in this paper are the probabilities of generating specific semiorders and the equivalence classes they produce. We present a method for calculating the asymptotic probability of inducing these semiorders and describe the qualities which group these semiorders together. We also find a class of semiorders, called \emph{ladders}, whose probabilities can be calculated using the Up/Down numbers.

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…

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…

The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures
Gustavo Jasso, Fernando Muro
https://arxiv.org/abs/2509.22625 https://arxiv…

The Derived Auslander--Iyama Correspondence II: Bimodule Calabi--Yau Structures
Let $d$ be a positive integer. In a previous article we established a bijective correspondence between the following classes of objects, considered up to the appropriate notion of equivalence: differential graded algebras with finite-dimensional $0$-th cohomology such that the canonical generator of their perfect derived category is a basic $d\mathbb{Z}$-cluster tilting object, and basic Frobenius algebras that are twisted $(d+2)$-periodic as bimodules. For $d=1$ this correspondence specialises…

Cactus flower spaces and monodromy of Bethe vectors
Joel Kamnitzer, Leonid Rybnikov
https://arxiv.org/abs/2507.12829 https://arxiv.or…

Cactus flower spaces and monodromy of Bethe vectors
We continue the study of cactus flower moduli spaces $\overline{F}_n$ and Gaudin models started in arXiv:2308.06880, arXiv:2407.06424. We show that isomorphism classes of operadic coverings of the real form $\overline{F}_n(\mathbb{R})$ are naturally one-to-one with equivalence classes of concrete coboundary monoidal categories (i.e. coboundary monoidal categories that admit a faithful monoidal functor to sets) with certain semisimplicity and finiteness conditions. Following the strategy of arXi…