Tootfinder

Hypersheaves and bases
Tobias Dyckerhoff, Till Heine, Simon Schneider
https://arxiv.org/abs/2506.14007 https://arxiv.org/pdf/2506.140…

Hypersheaves and bases
Let $X$ be a topological space equipped with a basis. We prove that, for every $\infty$-category $\mathcal{C}$ with limits, the restriction functor from $\mathcal{C}$-valued hypersheaves on $X$ to basic hypersheaves is an equivalence of $\infty$-categories.

Testing the Quantum Equivalence Principle with Gravitational Waves
Saurya Das, Mitja Fridman, Gaetano Lambiase
https://arxiv.org/abs/2506.14049 https://

Testing the Quantum Equivalence Principle with Gravitational Waves
We study modifications of gravitational wave observables, such as the wave amplitude and frequency, which follow from the quantum equivalence principle, and are expressed in terms of the inertial, gravitational and rest masses of the LIGO/Virgo mirrors. We provide bounds on the violations of the quantum equivalence principle by comparing the results with the most resolved gravitational wave events observed by the LIGO/Virgo collaboration. The formalism is equally applicable to other future grou…

An augmented Lagrangian method for strongly regular minimizers in a class of convex composite optimization problems
Chengjing Wang, Peipei Tang
https://arxiv.org/abs/2507.12040

An augmented Lagrangian method for strongly regular minimizers in a class of convex composite optimization problems
In this paper, we study a class of convex composite optimization problems. We begin by characterizing the equivalence between the primal/dual strong second-order sufficient condition and the dual/primal nondegeneracy condition. Building on this foundation, we derive a specific set of equivalent conditions for the perturbation analysis of the problem. Furthermore, we employ the augmented Lagrangian method (ALM) to solve the problem and provide theoretical guarantees for its performance. Specific…

Automorphic equivalence within gapped phases of infinitely extended fermion systems
Lennart Becker, Stefan Teufel, Marius Wesle
https://arxiv.org/abs/2507.13321

Automorphic equivalence within gapped phases of infinitely extended fermion systems
We prove automorphic equivalence within gapped phases of infinitely extended lattice fermion systems (as well as spin systems) with super-polynomially decaying interactions. As a simple application, we prove a version of Goldstone's theorem for such systems: if an infinite volume interaction is invariant under a continuous symmetry, then any gapped ground state is also invariant under that symmetry.

Extensional Independence
Taishi Kurahashi, Albert Visser
https://arxiv.org/abs/2506.13524 https://arxiv.org/pdf/2506.13524

Extensional Independence
Joel Hamkins asks whether there is a $Π^0_1$-formula $ρ(x)$ such that $ρ(ϕ)$ is independent over ${\sf PA}+ϕ$, if this theory is consistent, where this construction is extensional in $ϕ$ with respect to {\sf PA}-provable equivalence. We show that there can be no such extensional Rosser formula of any complexity. We give a positive answer to Hamkins' question for the case where we replace Extensionality by a weaker demand \emph{Consistent Extensionality}. We also prove that we can demand…

New characterization of full weight spectrum one-orbit cyclic subspace codes
Minjia Shi, Wenhao Song
https://arxiv.org/abs/2506.13418 https://

New characterization of full weight spectrum one-orbit cyclic subspace codes
Castello $\textit{et al}$. [J. Comb. Theory Ser. A, 212, 106005 (2025)] provided a complete classification for full weight spectrum (FWS) one-orbit cyclic subspace codes. In this paper, we determine the weight distributions of a family of FWS codes and exhibit some equivalence classes of FWS codes under certain conditions. Furthermore, we provide a complete classification for $r$-FWS codes.

Oriented hypergraphs and generalizing the Harary-Sachs theorem to integer matrices
Blake Dvarishkis, Josephine Reynes, Lucas J. Rusnak
https://arxiv.org/abs/2506.12271

Oriented hypergraphs and generalizing the Harary-Sachs theorem to integer matrices
Incidence-based generalizations of cycle covers, called contributors, extend the Harary-Sachs coefficient theorem for characteristic polynomials of the adjacency matrix of graphs. All minors of the Laplacian resulting from an integer matrix are characterized using their associated oriented hypergraph through a new minimal collection of contributors to produce the coefficients of the total-minor polynomial. We prove that the natural grouping of contributors via tail-equivalence is necessarily ca…

Formal Verification for JavaScript Regular Expressions: a Proven Semantics and its Applications
Aur\`ele Barri\`ere, Victor Deng, Cl\'ement Pit-Claudel
https://arxiv.org/abs/2507.13091

Formal Verification for JavaScript Regular Expressions: a Proven Semantics and its Applications
We present the first mechanized, succinct, practical, complete, and proven-faithful semantics for a modern regular expression language with backtracking semantics. We ensure its faithfulness by proving it equivalent to a preexisting line-by-line embedding of the official ECMAScript specification of JavaScript regular expressions. We demonstrate its practicality by presenting two real-world applications. First, a new notion of contextual equivalence for modern regular expressions, which we use t…

Segre Characteristic Equivalence
Jessie Pitsillides
https://arxiv.org/abs/2506.12065 https://arxiv.org/pdf/2506.12065

Segre Characteristic Equivalence
Given only the dimension, $n$, of a square matrix $A \in M(n,\mathbb{C})$, how many Segre Characteristic equivalent matrices are there? Jordan Normal Form Theorem states that any linear operator over $\mathbb{C}$ is similar to a matrix in Jordan Normal Form. As such, this is a question of counting the number of possible Jordan Normal Forms for a given dimension. So, equivalently, how many Jordan Normal Forms can an $n\times n$ matrix possibly have?

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…

A simple formalization of alpha-equivalence
Kalmer Apinis, Danel Ahman
https://arxiv.org/abs/2507.10181 https://arxiv.org/pdf/2507.10…

A simple formalization of alpha-equivalence
While teaching untyped $λ$-calculus to undergraduate students, we were wondering why $α$-equivalence is not directly inductively defined. In this paper, we demonstrate that this is indeed feasible. Specifically, we provide a grounded, inductive definition for $α$-equivalence and show that it conforms to the specification provided in the literature. The work presented in this paper is fully formalized in the Rocq Prover.

Quadratic Volatility from the P\"oschl-Teller Potential and Hyperbolic Geometry
Joel Saucedo
https://arxiv.org/abs/2507.12501 https://arxiv.org/pdf/25…

Quadratic Volatility from the Pöschl-Teller Potential and Hyperbolic Geometry
This investigation establishes a formal equivalence between the generalized Black-Scholes equation under a Quadratic Normal Volatility (QNV) specification and the stationary Schrödinger equation for a hyperbolic Pöschl-Teller potential. A sequence of canonical transformations maps the financial pricing operator to a quantum Hamiltonian, revealing the volatility smile as a direct manifestation of diffusion on a hyperbolic manifold whose geometry is classified by the discriminant of the QNV pol…

Entropy production rate and time-reversibility for general jump diffusions on $\mathbb{R}^n$
Qi Zhang, Yubin Lu
https://arxiv.org/abs/2506.13135 https://…

Entropy production rate and time-reversibility for general jump diffusions on $\mathbb{R}^n$
This paper investigates the entropy production rate and time-reversibility for general jump diffusions (Lévy processes) on $\mathbb{R}^n$. We first formulate the entropy production rate and explore its associated thermodynamic relations for jump diffusions. Subsequently, we derive the entropy production rate using the relative entropy between the forward and time-reversed path measures for stationary jump diffusions via the Girsanov transform. Furthermore, we establish the equivalence among ti…

On the K-theory of algebraic tori
Qingyuan Bai, Shachar Carmeli, Branko Juran, Florian Riedel
https://arxiv.org/abs/2507.12954 https://

On the K-theory of algebraic tori
Given an algebraic torus $T$ over a field $F$, its lattice of characters $Λ$ gives rise to a topological torus $\mathfrak{T}(T)=Λ_{\mathbb R}/Λ$ with a continuous action of the absolute Galois group $G$. We construct a natural equivalence between the algebraic $K$-theory $K_{\ast}(T)$ and the equivariant homology $H^{G}_{\ast}(\mathfrak{T}(T);K_G(F))$ of the topological torus $\mathfrak{T}(T)$ with coefficients in the $G$-equivariant $K$-theory of $F$. This generalizes a computation of $K_0(…

Temperley-Lieb Categories on Non-Orientable Surfaces
Dionne Ibarra, Gabriel Montoya-Vega, Benjamin Morris
https://arxiv.org/abs/2506.14319 https://

Temperley-Lieb Categories on Non-Orientable Surfaces
In this paper we present the construction of a skeletal diagram category, which we call the square with bands category. This category extends the Temperley-Lieb (TL) category, where morphisms now include diagrams of embedded curves on (possibly) non-orientable bounded surfaces, and involves three parameters associated to simple closed curves. Such diagrams utilise handle decompositions for surfaces and are considered up to a handle slide equivalence. We define a tensor product on this category,…

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…

Levy Laplacian on manifold and heat flows of differential forms
Boris Volkov
https://arxiv.org/abs/2507.13013 https://arxiv.org/pdf/2…

Levy Laplacian on manifold and heat flows of differential forms
The Levy Laplacian is an infinite-dimensional differential operator, which is interesting for its connection with the Yang-Mills gauge fields. The article proves the equivalence of various definitions of the Levy Laplacian on the manifold of $H^1$-paths on a Riemannian manifold. The heat equation with the Levy Laplacian is considered. The tendency of some solutions of this heat equation to the locally constant functionals as time tends to infinity is studied. These solutions are constructed usi…

New characterization of full weight spectrum one-orbit cyclic subspace codes
Minjia Shi, Wenhao Song
https://arxiv.org/abs/2506.13418 https://

New characterization of full weight spectrum one-orbit cyclic subspace codes
Castello $\textit{et al}$. [J. Comb. Theory Ser. A, 212, 106005 (2025)] provided a complete classification for full weight spectrum (FWS) one-orbit cyclic subspace codes. In this paper, we determine the weight distributions of a family of FWS codes and exhibit some equivalence classes of FWS codes under certain conditions. Furthermore, we provide a complete classification for $r$-FWS codes.

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.

Measurement Incompatibility Based In-equivalence Between Bell and Network Nonlocality
Kaushiki Mukherjee, Biswajit Paul
https://arxiv.org/abs/2508.10670 https://

Measurement Incompatibility Based In-equivalence Between Bell and Network Nonlocality
It is a well-known fact that measurement incompatibility is a necessary resource to generate nonlocal correlations in usual Bell scenario that typically involves single quantum source. We can provide with some contrasting findings if we consider connected structure of multiple quantum sources. Precisely, we demonstrate that non n-locality can be detected in standard quantum network even when only a single party performs incompatible measurements. More interestingly, for any finite n greater tha…

Second-Order Parameterizations for the Complexity Theory of Integrable Functions
Aras Bacho, Martin Ziegler
https://arxiv.org/abs/2506.11210 https://

Second-Order Parameterizations for the Complexity Theory of Integrable Functions
We develop a unified second-order parameterized complexity theory for spaces of integrable functions. This generalizes the well-established case of second-order parameterized complexity theory for spaces of continuous functions. Specifically we prove the mutual linear equivalence of three natural parameterizations of the space $\Lrm{p}$ of $p$-integrable complex functions on the real unit interval: (binary) $\Lrm{p}$-modulus, rate of convergence of Fourier series, and rate of approximation by s…

Arrow reductions for the finitistic dimension conjecture
Odysseas Giatagantzidis
https://arxiv.org/abs/2507.12978 https://arxiv.org/p…

Arrow reductions for the finitistic dimension conjecture
We present new techniques for removing arrows of bound quiver algebras, reducing thus the Finitistic Dimension Conjecture $\mathsf{(FDC)}$ for a given algebra to a smaller one. Unlike the classic arrow removal operation of Green-Psaroudakis-Solberg, our methods allow for removing arrows even when they occur in every generating set for the defining admissible ideal of the algebra. Our first main result establishes an equivalence for the finiteness of the finitistic (and global) dimensions of a r…

Mutual-Supervised Learning for Sequential-to-Parallel Code Translation
Changxin Ke, Rui Zhang, Shuo Wang, Li Ding, Guangli Li, Yuanbo Wen, Shuoming Zhang, Ruiyuan Xu, Jin Qin, Jiaming Guo, Chenxi Wang, Ling Li, Qi Guo, Yunji Chen
https://arxiv.org/abs/2506.11153

Mutual-Supervised Learning for Sequential-to-Parallel Code Translation
The rise of GPU-based high-performance computing (HPC) has driven the widespread adoption of parallel programming models such as CUDA. Yet, the inherent complexity of parallel programming creates a demand for the automated sequential-to-parallel approaches. However, data scarcity poses a significant challenge for machine learning-based sequential-to-parallel code translation. Although recent back-translation methods show promise, they still fail to ensure functional equivalence in the translate…

Structural Characterizations of Marginal Policy Effects
Zhixin Wang, Yu Zhang, Zhengyu Zhang
https://arxiv.org/abs/2506.11694 https://

Structural Characterizations of Marginal Policy Effects
This paper investigates the structural interpretation of the marginal policy effect (MPE) within nonseparable models. We demonstrate that, for a smooth functional of the outcome distribution, the MPE equals its functional derivative evaluated at the outcome-conditioned weighted average structural derivative. This equivalence is definitional rather than identification-based. Building on this theoretical result, we propose an alternative identification strategy for the MPE that complements existi…

Clapping propulsion and thin vortex rings: a computational study of vortex dynamics, energy equivalence, and core potential energy
Suyog V. Mahulkar, Jaywant H. Arakeri
https://arxiv.org/abs/2507.11491

Clapping propulsion and thin vortex rings: a computational study of vortex dynamics, energy equivalence, and core potential energy
We present a numerical study on clapping propulsion using a body consisting of two rigid plates hinged at one end, with a 60-degree interplate cavity. The closing of the cavity generates a thrust-producing jet. Our previous experimental study (Mahulkar and Arakeri, PRF, 2024) compared the flow fields of the clapping body in two cases: free-moving (dynamic) and forward-constrained (stationary). The experiments revealed significant differences in body motion and flow structures. This numerical st…

C*-submodule preserving module mappings on Hilbert C*-modules
Michael Frank
https://arxiv.org/abs/2507.11206 https://arxiv.org/pdf/25…

C*-submodule preserving module mappings on Hilbert C*-modules
Let $A$ be a (non-unital, in general) C*-algebra with center $Z(M(A))$ of its multiplier algebra, and let $X$ be a full Hilbert $A$-module. Then any injective bounded module morphism $T$, for which every norm-closed $A$-submodule of $X$ is invariant, is of the form $T=c \cdot {\rm id}_X$ where $c \in Z(M(A))$. The same is true if the restriction to be norm-closed is dropped. At the other extrem, for two given strongly Morita equivalent C*-algebras $A$ and $B$ and an $A$-$B$ equivalence bimodule…

Decidable Reversible Equivalences for Finite Petri Nets
Roberto Gorrieri, Ivan Lanese
https://arxiv.org/abs/2506.11517 https://arxiv.…

Decidable Reversible Equivalences for Finite Petri Nets
In the setting of Petri nets, we prove that {\em causal-net bisimilarity} \cite{G15,Gor22,Gor25a}, which is a refinement of history-preserving bisimilarity \cite{RT88,vGG89,DDM89}, and the novel {\em hereditary} causal-net bisimilarity, which is a refinement of hereditary history-preserving bisimilarity \cite{Bed91,JNW96}, do coincide. This means that causal-net bisimilarity is a {\em reversible behavioral equivalence}, as causal-net bisimilar markings not only are able to match each other's fo…

Cosmological effect of coherent oscillation of ultralight scalar fields in a multicomponent universe
Priyanka Saha, Dipanjan Dey, Kaushik Bhattacharya
https://arxiv.org/abs/2506.12863

Cosmological effect of coherent oscillation of ultralight scalar fields in a multicomponent universe
The idea that coherent oscillations of a scalar field, oscillating over a time period that is much shorter than the cosmological timescale, can exhibit cold dark matter (CDM) like behavior was previously established. In our work we first show that this equivalence between the oscillating scalar field model and the CDM sector is exact only in a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime in the absence of cosmological constant and any other possible matter components in the univers…

Categorical-algebraic aspects of Heyting semilattices
Xabier Garc\'ia-Mart\'inez, James R. A. Gray, Michael A. Hoefnagel, Tim Van der Linden, Corentin Vienne
https://arxiv.org/abs/2508.11250

Categorical-algebraic aspects of Heyting semilattices
This article gives an overview of some key categorical-algebraic properties of the variety of Heyting semilattices, with the aim of correcting a misconception in the literature. We confirm that the category of Heyting semilattices is not algebraically coherent, even though it satisfies a strong version of the so-called Smith is Huq condition (on the equivalence of two types of commutators). We also prove that Higgins commutators of normal subobjects are normal, as a consequence of the fact th…

$C^\infty$-superrings and $C^\infty$-superschemes
Cristian Danilo Olarte, Pedro Rizzo, Alexander Torres-Gomez
https://arxiv.org/abs/2508.09900 https://arxi…

$C^\infty$-superrings and $C^\infty$-superschemes
This paper develops a theory of $C^\infty$-superrings and their associated $C^\infty$-superschemes. We prove a key equivalence between the category of fair affine $C^\infty$-superschemes and the category of fair $C^\infty$-superrings. We place special emphasis on split $C^\infty$-superrings, which generalize the function algebras of supermanifolds and serve as building blocks for more complex, non-split structures.

Replaced article(s) found for math-ph. https://arxiv.org/list/math-ph/new
[1/1]:
Quantum concentration inequalities and equivalence of the thermodynamical ensembles: an optimal m...

Two improvements upon the paper "Wiener--Luxemburg amalgam spaces"
Dalimil Pe\v{s}a
https://arxiv.org/abs/2508.10825 https://arxiv.org/pdf/2508.1…

Two improvements upon the paper "Wiener--Luxemburg amalgam spaces"
This short note seeks to present two new results that essentially improve the corresponding statements from the author's paper ``Wiener--Luxemburg amalgam spaces''. Specifically, in our first result, we show that when both the local and the global components of a pair of r.i. quasi-Banach function spaces are appropriately ordered, then both their sum and intersection can be characterised as the appropriate amalgam of said spaces, up to equivalence of quasinorms. Then, in our second result, we p…

Replaced article(s) found for math.CA. https://arxiv.org/list/math.CA/new
[1/1]:
- Equivalence of linear and trilinear Kakeya conjectures in three dimensions
Cristian Rios, Eric T. Sawyer

Subcategories of Module Categories via Restricted Yoneda Embeddings
Dylan Fillmore, Jonas T. Hartwig
https://arxiv.org/abs/2507.12778 https://

Subcategories of Module Categories via Restricted Yoneda Embeddings
We propose a framework for producing interesting subcategories of the category ${}_A\mathsf{Mod}$ of left $A$-modules, where $A$ is an associative algebra over a field $k$. The construction is based on the composition, $Y$, of the Yoneda embedding of ${}_A\mathsf{Mod}$ with a restriction to certain subcategories $\mathcal{B}\subset {}_A\mathsf{Mod}$, typically consisting of cyclic modules. We describe the subcategories on which $Y$ provides an equivalence of categories. This also provides a way…

Correlation functions of von Neumann entropy
Mathew W. Bub, Allic Sivaramakrishnan
https://arxiv.org/abs/2506.10917 https://arxiv.org…

Correlation functions of von Neumann entropy
In this note, we study two-point correlation functions of modular Hamiltonians. We show that in general quantum systems, these correlators obey properties similar to those of von Neumann entropy and capacity of entanglement, both of which are special cases of these correlators. Then we specialize to two spacelike-separated spherical subregions in conformal field theories. We present direct computations of the vacuum two-point function that confirm its equivalence to the stress-tensor conformal …

E3-Rewrite: Learning to Rewrite SQL for Executability, Equivalence,and Efficiency
Dongjie Xu, Yue Cui, Weijie Shi, Qingzhi Ma, Hanghui Guo, Jiaming Li, Yao Zhao, Ruiyuan Zhang, Shimin Di, Jia Zhu, Kai Zheng, Jiajie Xu
https://arxiv.org/abs/2508.09023

E3-Rewrite: Learning to Rewrite SQL for Executability, Equivalence,and Efficiency
SQL query rewriting aims to reformulate a query into a more efficient form while preserving equivalence. Most existing methods rely on predefined rewrite rules. However, such rule-based approaches face fundamental limitations: (1) fixed rule sets generalize poorly to novel query patterns and struggle with complex queries; (2) a wide range of effective rewriting strategies cannot be fully captured by declarative rules. To overcome these issues, we propose using large language models (LLMs) to ge…

Equivalence of stationary dynamical solutions in a directed chain and a Delay Differential Equation of neuroscientific relevance
Giulio Colombini, Nicola Guglielmi, Armando Bazzani
https://arxiv.org/abs/2506.11654

Equivalence of stationary dynamical solutions in a directed chain and a Delay Differential Equation of neuroscientific relevance
While synchronized states, and the dynamical pathways through which they emerge, are often regarded as the paradigm to understand the dynamics of information spreading on undirected networks of nonlinear dynamical systems, when we consider directed network architectures, dynamical stationary states can arise. To study this phenomenon we consider the simplest directed network, a single cycle, and excitable FitzHugh-Nagumo (FHN) neurons. We show numerically that a stationary dynamical state emerg…

Geometric models and asymptotic dimension for infinite-type surface mapping class groups
Michael C. Kopreski, George Shaji
https://arxiv.org/abs/2508.06679 https://

Geometric models and asymptotic dimension for infinite-type surface mapping class groups
Let $S$ be an infinite-type surface and let $G \leq \operatorname{Map}(S)$ be a locally bounded Polish subgroup. We construct a metric graph $M$ of simple arcs and curves on $S$ preserved by the action of $G$ and for which the vertex orbit map $G \to V(M)$ is a coarse equivalence; if $G$ is boundedly generated, then $M$ is a Cayley--Abels--Rosendal graph for $G$ and the orbit map is a quasi-isometry. In particular, if $S$ contains a non-displaceable subsurface and $G \geq \operatorname{PMap}_c(…

On Propositional Program Equivalence (extended abstract)
Tobias Kapp\'e
https://arxiv.org/abs/2507.07480 https://arxiv.org/pdf/25…

On Propositional Program Equivalence (extended abstract)
General program equivalence is undecidable. However, if we abstract away the semantics of statements, then this problem becomes not just decidable, but practically feasible. For instance, a program of the form "if $b$ then $e$ else $f$" should be equivalent to "if not $b$ then $f$ else $e$" - no matter what $b$, $e$ and $f$ are. This kind of equivalence is known as propositional equivalence. In this extended abstract, we discuss recent developments in propositional program equivalence from the …

Thomason-Type Model Structures on Simplicial Complexes and Graphs
Emilio Minichiello
https://arxiv.org/abs/2508.08195 https://arxiv.org/pdf/2508.08195

Thomason-Type Model Structures on Simplicial Complexes and Graphs
In this paper we show that the Matsushita model structure on loop graphs, which is right-transferred from the Kan-Quillen model structure on simplicial sets, factors through two other right-transferred model structures on simplicial complexes and reflexive graphs. We show that each Quillen adjunction between these right-transferred model categories is a Quillen equivalence. These model structures are analogous to the Thomason model structure on small categories, and we prove that they are all c…

What One Cannot, Two Can: Two-Layer Transformers Provably Represent Induction Heads on Any-Order Markov Chains
Chanakya Ekbote, Marco Bondaschi, Nived Rajaraman, Jason D. Lee, Michael Gastpar, Ashok Vardhan Makkuva, Paul Pu Liang
https://arxiv.org/abs/2508.07208

What One Cannot, Two Can: Two-Layer Transformers Provably Represent Induction Heads on Any-Order Markov Chains
In-context learning (ICL) is a hallmark capability of transformers, through which trained models learn to adapt to new tasks by leveraging information from the input context. Prior work has shown that ICL emerges in transformers due to the presence of special circuits called induction heads. Given the equivalence between induction heads and conditional k-grams, a recent line of work modeling sequential inputs as Markov processes has revealed the fundamental impact of model depth on its ICL capa…

Elementary equivalence and diffeomorphism groups of smooth manifolds
Sang-hyun Kim, Thomas Koberda, J. de la Nuez Gonz\'alez
https://arxiv.org/abs/2507.07427

Elementary equivalence and diffeomorphism groups of smooth manifolds
Let two smooth manifolds $M$ and $N$ be given, with $M$ closed and connected. If the $C^r$--diffeomorphism group of $M$ is elementarily equivalent to the $C^s$--diffeomorphism group of $N$ for some $r,s\in[1,\infty)\cup\{0,\infty\}$, then $r=s$ and $M$ and $N$ are $C^r$--xdiffeomorphic. This strengthens a previously known result by Takens and Filipkiewicz, which implies that a group isomorphism between diffeomorphism groups of closed manifolds necessarily arises from a diffeomorphism of the und…

Equivalence of two component spinor mechanism and four component spinor mechanism in top quark pair production
Malvika Deo, Anuradha Misra, Sharada Subramanian, Radhika Vinze
https://arxiv.org/abs/2506.09094

Equivalence of two component spinor mechanism and four component spinor mechanism in top quark pair production
We calculate the $S$-matrix elements for the process $e^{+} e^{-}\rightarrow t \bar{t}$ mediated by SM photon, $Z$ boson and an additional $Z^{'}$ boson indicating the contribution from new physics. We calculate the amplitude square using two component spinor formalism and four component spinor formalism and show the equivalance of the results using the two formalisms. We also establish the relations between the couplings of $Z^{'}$ boson to fermions in the two component spinor formalism and in…

Structural results on idealistic equivalence relations
Filippo Calderoni, Luca Motto Ros
https://arxiv.org/abs/2506.08217 https://arx…

Structural results on idealistic equivalence relations
We address some fundamental problems concerning the structure of idealistic equivalence relations. In particular, we show that, under analytic determinacy, there are continuum many idealistic analytic equivalence relations that are not classwise Borel isomorphic to an orbit equivalence relation. Moreover, we also discuss alternative formulations of the E1 conjecture, and present an elementary counterexample to one of its earliest variants proposed by Hjorth and Kechris in 1997.

When isometry and equivalence for skew constacyclic codes coincide
Monica Nevins, Susanne Pumpluen
https://arxiv.org/abs/2508.06695 https://arxiv.org/pdf/2…

When isometry and equivalence for skew constacyclic codes coincide
We show that the notions of $(n,σ)$-isometry and $(n,σ)$-equivalence introduced by Ou-azzou et al coincide for most skew $(σ,a)$-constacyclic codes of length $n$. To prove this, we show that all Hamming-weight-preserving homomorphisms between their ambient algebras must have degree one when those algebras are nonassociative. We work in the general setting of commutative base rings $S$. As a consequence, we propose new definitions of equivalence and isometry of skew constacyclic codes that ex…

Equivalence of Optical Theorems
Edwin A. Marengo, Mohammadrasoul Taghavi
https://arxiv.org/abs/2506.08943 https://arxiv.org/pdf/2506.…

Equivalence of Optical Theorems
We demonstrate, in the full vector formulation of electromagnetic fields, that the well-known optical theorem pertinent for the characterization of a scatterer's extinction power and associated cross section can be expressed in a multitude of alternative equivalent forms. These alternatives involve different forms of projective field measurements or detectors. The inherent nonuniqueness of such optical-theorem-based detectors stems from the nonuniqueness of an associated inverse source problem,…

Quantum-symmetric equivalence for superpotential algebras
Hongdi Huang, Van C. Nguyen, Kent B. Vashaw, Padmini Veerapen, Xingting Wang
https://arxiv.org/abs/2507.05612

Quantum-symmetric equivalence for superpotential algebras
We study superpotential algebras by introducing the notion of quantum-symmetric equivalence defined relatively to two fixed Hopf coactions. This concept relies on the non-vanishing of a bi-Galois object for the two coacting Hopf algebras, where the cotensor product with this object provides a Morita--Takeuchi equivalence between their comodule categories, mapping one superpotenial algebra to the other as comodule algebras. In particular, we investigate $\mathcal{GL}$-type and $\mathcal{SL}$-typ…

Mal'cev clones over a three-element set up to minor-equivalence
Stefano Fioravanti, Michael Kompatscher, Bernardo Rossi, Albert Vucaj
https://arxiv.org/abs/2508.06918 https:…

Mal'cev clones over a three-element set up to minor-equivalence
We classify all Mal'cev clones over a three-element set up to minion homomorphisms. This is another step toward the complete classification of three-element relational structures up to pp-constructability. We furthermore provide an alternative proof of Bulatov's result that all Mal'cev clones over a three-element set have an at most 4-ary relational basis.

Learning-Based Stable Optimal Control for Infinite-Time Nonlinear Regulation Problems
Han Wang, Di Wu, Lin Cheng, Shengping Gong, Xu Huang
https://arxiv.org/abs/2506.10291

Learning-Based Stable Optimal Control for Infinite-Time Nonlinear Regulation Problems
Infinite-time nonlinear optimal regulation control is widely utilized in aerospace engineering as a systematic method for synthesizing stable controllers. However, conventional methods often rely on linearization hypothesis, while recent learning-based approaches rarely consider stability guarantees. This paper proposes a learning-based framework to learn a stable optimal controller for nonlinear optimal regulation problems. First, leveraging the equivalence between Pontryagin Maximum Principle…

Equivalence between Gromov-Witten invariants: Domain dependent perturbation and Kuranishi structure approaches
Yuguo Qin
https://arxiv.org/abs/2507.04798 h…

Equivalence between Gromov-Witten invariants: Domain dependent perturbation and Kuranishi structure approaches
We prove that the homology class induced by the rational pseudocycle constructed via domain-dependent perturbations by Cieliebak and Mohnke coincides with the homology class induced by the virtual fundamental class defined through Kuranishi structures by Fukaya, Oh, Ohta, and Ono.

Likelihood Matching for Diffusion Models
Lei Qian, Wu Su, Yanqi Huang, Song Xi Chen
https://arxiv.org/abs/2508.03636 https://arxiv.org/pdf/2508.03636

Likelihood Matching for Diffusion Models
We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To efficiently compute the reverse sample likelihood, a quasi-likelihood is considered to approximate each reverse transition density by a Gaussian distribution with matched conditional mean and covariance, respectively. The score and Hessian functions for the diffusion…

Wave Mechanics and C-equivalence
Satyanad Kichenassamy (LMR)
https://arxiv.org/abs/2507.07069 https://arxiv.org/pdf/2507.07069…

Wave Mechanics and C-equivalence
We establish that de Broglie's wave, as it is introduced in his Thesis, is not a wave on a given space, but on the contrary itself determines a system in which Special Relativity is locally valid. This local system is a physical object, that defines its own units of length and time. C-equivalence provides a natural framework both for its mathematical description and its physical interpretation.

This https://arxiv.org/abs/2412.05561 has been replaced.
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Can the Rookies Cut the Tough Cookie? Exploring the Use of LLMs for SQL Equivalence Checking
Equivalence checking of SQL queries is an intractable problem often encountered in settings ranging from grading SQL submissions to debugging query optimizers. Despite recent work toward developing practical solutions, only simple queries written using a small subset of SQL are supported, leaving the equivalence checking of sophisticated SQL queries at the mercy of intensive, potentially error-prone, manual analysis. In this paper, we explore how LLMs can be used to reason with SQL queries to a…

Number of orbits of $k$-subsets of permutations
Ludovick Bouthat, Raghavendra Tripathi
https://arxiv.org/abs/2508.07463 https://arxiv.org/pdf/2508.07463

Number of orbits of $k$-subsets of permutations
Let $S_n$ denote the symmetric group of order $n$. Say that two subsets $x, y\subseteq S_n$ are \emph{equivalent} if there exist permutations $g_1, g_2\in S_n$ such that $g_1xg_2=y$, where multiplication is understood elementwise. Recently, [Tripathi, 2024] and [Kushwaha and Triathi, 2025] asked for the asymptotics of $T(n,k)$, the number of subsets of $S_n$ of size $k$ up to this equivalence. It is easy to see that $T(n,0)=T(n, 1)=1$ and $T(n, 2)=p(n)-1$, where $p(n)$ is the number of integer …

Hyper-u-amenablity and Hyperfiniteness of Treeable Equivalence Relations
Petr Naryshkin, Andrea Vaccaro
https://arxiv.org/abs/2507.07891 https://

Hyper-u-amenablity and Hyperfiniteness of Treeable Equivalence Relations
We introduce the notions of u-amenability and hyper-u-amenability for countable Borel equivalence relations, strong forms of amenability that are implied by hyperfiniteness. We show that treeable, hyper-u-amenable countable Borel equivalence relations are hyperfinite. One of the corollaries that we get is that if a countable Borel equivalence relation is measure-hyperfinite and equal to the orbit equivalence relation of a free continuous action of a free group (with $k \ge 2$ or $k = \infty$ ge…

Poset-enriched pretoposes and compact ordered spaces
J\'er\'emie Marqu\`es, Luca Reggio
https://arxiv.org/abs/2508.09944 https://arxiv.org/pdf/2508…

Poset-enriched pretoposes and compact ordered spaces
We provide a characterisation of the category $\mathsf{KOrd}$ of Nachbin's compact ordered spaces as a poset-enriched category. Up to equivalence, $\mathsf{KOrd}$ is the only non-degenerate poset-enriched pretopos whose terminal object is a (discrete) generator and in which every object is covered by an order-filtral object. Order-filtral objects satisfy an appropriate form of compactness and separation. Throughout, we make extensive use of the internal language of poset-enriched pretoposes.

This https://arxiv.org/abs/2412.02003 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Polynomial algorithm for alternating link equivalence
Link equivalence up to isotopy in a 3-space is the problem that lies at the root of knot theory, and is important in 3-dimensional topology and geometry. We consider its restriction to alternating links, given by two alternating diagrams with $n_1$ and $n_2$ crossings, and show that this problem has polynomial algorithm in terms of $max\{n_1, n_2\}$. For the proof, we use Tait flyping conjectures, observations stemming from the work of Lackenby, Menasco, Sundberg and Thistlethwaite on alternati…

From Lipschitz embedding to Lipschitz equivalence between dust-like self-similar sets
Huo-Jun Ruan, Jian-Ci Xiao
https://arxiv.org/abs/2508.07670 https://a…

From Lipschitz embedding to Lipschitz equivalence between dust-like self-similar sets
Let $K,F\subset\mathbb{R}^d$ be two dust-like self-similar sets sharing the same Hausdorff dimension. We consider when the mere existence of a Lipschitz embedding from $K$ to $F$ already implies their Lipschitz equivalence. Our main result is threefold: (1) if the Lipschitz image of $K$ intersects $F$ in a set of positive Hausdorff measure, then $K$ admits a Lipschitz surjection onto $F$; (2) if $F$ is in addition homogeneous, then the generating iterated function systems of $K, F$ should have …

Endoscopy for Modular Hecke Categories
Colton Sandvik
https://arxiv.org/abs/2508.10214 https://arxiv.org/pdf/2508.10214

Endoscopy for Modular Hecke Categories
Generalizing the theory of parity sheaves on complex algebraic stacks due to Juteau-Mautner-Williamson, we develop a theory of twisted equivariant parity sheaves. We use this formalism to construct a modular incarnation of Lusztig and Yun's monodromic Hecke category. We then give two applications: (1) a modular categorification of the monodromic Hecke algebra, and (2) a monoidal equivalence between the monodromic Hecke category of parity sheaves and the ordinary Hecke category of parity sheaves…

Low degree subvarieties of universal hypersurfaces
Yifeng Huang, Borys Kadets, Olivier Martin
https://arxiv.org/abs/2506.08848 https://

Low degree subvarieties of universal hypersurfaces
We study irreducible subvarieties $Z$ of the universal hypersurface $\mathcal{X}/B$ of degree $d$ and dimension $n$. We prove that when $d$ is sufficiently large, degree $kd$ subvarieties $Z$ which dominate $B$ come from intersection with a family of degree $k$ projective varieties parametrized by $B$. This answers a question raised independently by Farb and Ma. Our main tools consist of a Grassmannian technique due to Riedl and Yang, a theorem of Mumford-Roitman on rational equivalence of zero…

DHoTT: A Temporal Extension of Homotopy Type Theory for Semantic Drift
Iman Poernomo
https://arxiv.org/abs/2506.09671 https://arxiv.o…

DHoTT: A Temporal Extension of Homotopy Type Theory for Semantic Drift
We introduce Dynamic Homotopy Type Theory (DHoTT), a temporal extension of Homotopy Type Theory (HoTT) designed to reason formally about concepts whose meanings evolve continuously or rupture discontinuously over time. While traditional HoTT captures identity and equivalence within a fixed semantic landscape, DHoTT enriches this framework by explicitly indexing types with a temporal parameter, allowing types themselves to deform, rupture, and reassemble as contexts shift. Formally, we show th…

Queue Replacement Approach to Dynamic User Equilibrium Assignment with Route and Departure Time Choice
Takara Sakai, Takashi Akamatsu, Koki Satsukawa
https://arxiv.org/abs/2508.07159

Queue Replacement Approach to Dynamic User Equilibrium Assignment with Route and Departure Time Choice
This study develops a hybrid analytical and numerical approach for the dynamic user equilibrium (DUE) assignment with route and departure time choice (RDTC) for homogeneous users. The core concept of the proposed approach is the generalized queue replacement principle (GQRP). The GQRP is an equivalence between the equilibrium queueing delay pattern and the solution to a linear programming (LP) problem obtained by relaxing certain conditions in the original DUE-RDTC problem. We present a systema…

Dowker's theorem for higher-order relations
Vin de Silva, Chad Giusti, Vladimir Itskov, Michael Robinson, Radmila Sazdanovic, Nikolas Schonsheck, Melvin Vaupel, Iris H. R. Yoon
https://arxiv.org/abs/2506.10909

Dowker's theorem for higher-order relations
Given a relation $R \subseteq I \times J$ between two sets, Dowker's Theorem (1952) states that the homology groups of two associated simplicial complexes, now known as Dowker complexes, are isomorphic. In its modern form, the full result asserts a functorial homotopy equivalence between the two Dowker complexes. What can be said about relations defined on three or more sets? We present a simple generalization to multiway relations of the form $R \subseteq I_1 \times I_2 \times \cdots \times I_…

Lagrangian-based Equilibrium Propagation: generalisation to arbitrary boundary conditions & equivalence with Hamiltonian Echo Learning
Guillaume Pourcel, Debabrota Basu, Maxence Ernoult, Aditya Gilra
https://arxiv.org/abs/2506.06248

Lagrangian-based Equilibrium Propagation: generalisation to arbitrary boundary conditions & equivalence with Hamiltonian Echo Learning
Equilibrium Propagation (EP) is a learning algorithm for training Energy-based Models (EBMs) on static inputs which leverages the variational description of their fixed points. Extending EP to time-varying inputs is a challenging problem, as the variational description must apply to the entire system trajectory rather than just fixed points, and careful consideration of boundary conditions becomes essential. In this work, we present Generalized Lagrangian Equilibrium Propagation (GLEP), which e…

Dynamical dark energy in models close to $\Lambda$CDM
Saikat Chakraborty, Charlotte Louw, Peter K. S. Dunsby, Kelly MacDevette, Alvaro de la Cruz Dombriz
https://arxiv.org/abs/2508.09813

Dynamical dark energy in models close to $Λ$CDM
In this communication we address whether or not there is an equivalence between the kinematical and dynamical descriptions of the spatially flat $Λ$CDM model. We address this by investigating whether an almost $Λ$CDM expansion history ($j(z)\approx1$) corresponds to an almost $Λ$CDM model ($w_{\rm DE}(z)\approx-1$) by considering two particular explicit examples. At least for the cases considered, this turns out not to be the case. Instead, what we find is that an almost $Λ$CDM cosmic evolu…

This https://arxiv.org/abs/2505.16093 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multiple chordal SLE($κ$) and quantum Calogero-Moser system
We study multiple chordal SLE$(κ)$ systems in a simply connected domain $Ω$, where $z_1, \ldots, z_n \in \partial Ω$ are boundary starting points and $q \in \partial Ω$ is an additional marked boundary point. As a consequence of the domain Markov property and conformal invariance, we show that the presence of the marked boundary point $q$ gives rise to a natural equivalence relation on partition functions. While these functions are not necessarily conformally covariant, each equivalence c…

Ultra-Large-Scale Compilation and Manipulation of Quantum Circuits with Pandora
Ioana Moflic, Alexandru Paler
https://arxiv.org/abs/2508.05608 https://arxi…

Ultra-Large-Scale Compilation and Manipulation of Quantum Circuits with Pandora
There is an enormous gap between what quantum circuit sizes can be compiled and manipulated with the current generation of quantum software and the sizes required by practical applications such as quantum chemistry or Shor's algorithm. We present Pandora, an efficient, open-source, multithreaded, high-performance-computing-enabled tool based on circuit rewrites. Pandora can be used for quantum circuit equivalence checking, full compilations of large circuits, and scalable, streaming quantum res…

EvoGraph: Hybrid Directed Graph Evolution toward Software 3.0
Igor Costa, Christopher Baran
https://arxiv.org/abs/2508.05199 https://arxiv.org/pdf/2508.051…

EvoGraph: Hybrid Directed Graph Evolution toward Software 3.0
We introduce **EvoGraph**, a framework that enables software systems to evolve their own source code, build pipelines, documentation, and tickets. EvoGraph represents every artefact in a typed directed graph, applies learned mutation operators driven by specialized small language models (SLMs), and selects survivors with a multi-objective fitness. On three benchmarks, EvoGraph fixes 83% of known security vulnerabilities, translates COBOL to Java with 93% functional equivalence (test verified), …

High-Dimensional Unfolding in Large Backgrounds
Alexandre Falc\~ao, Adam Takacs
https://arxiv.org/abs/2507.06291 https://arxiv.org/pd…

High-Dimensional Unfolding in Large Backgrounds
We propose new methodologies in multi-dimensional unfolding in dense environments, and show that incorporating auxiliary observables can significantly improve performance. Our approach builds on the ML-based OmniFold algorithm, which we extend to account for background, detector acceptance, efficiency, and uncertainties, enabling its application in high-luminosity and heavy-ion collision settings. We derive this algorithm and demonstrate its mathematical and numerical equivalence to expectation…

Toposes with enough points as categories of \'etale spaces
Sam van Gool, J\'er\'emie Marqu\`es, Umberto Tarantino
https://arxiv.org/abs/2508.09604 https://

Toposes with enough points as categories of étale spaces
We extend Makkai duality between coherent toposes and ultracategories to a duality between toposes with enough points and ultraconvergence spaces. Our proof generalizes and simplifies Makkai's original proof. Our main result can also be seen as an extension to ionads of Barr's equivalence between topological spaces and relational modules for the ultrafilter monad. In view of the correspondence between toposes and geometric theories, we obtain a strong conceptual completeness theorem, in the sen…

Finslerian lightconvex boundaries: applications to causal simplicity and the space of cone geodesics $\mathcal{N}$
J\'onatan Herrera, Miguel S\'anchez
https://arxiv.org/abs/2506.09032

Finslerian lightconvex boundaries: applications to causal simplicity and the space of cone geodesics $\mathcal{N}$
Our outcome is structured in the following sequence: (1) a general result for indefinite Finslerian manifolds with boundary $(M,L)$ showing the equivalence between local and infinitesimal (time, light or space) convexities for the boundary $\partial M$, (2) for any cone structure $(M,\mathcal{C})$ which is globally hyperbolic with timelike boundary, the equivalence among: (a) the boundary $\partial M$ is lightconvex, (b) the interior $\mathring{M}$ is causally simple and (c) the space of the co…

Homotopy classification of $4$-manifolds with $3$-manifold fundamental group
Jonathan Hillman, Daniel Kasprowski, Mark Powell, Arunima Ray
https://arxiv.org/abs/2508.07504 https…

Homotopy classification of $4$-manifolds with $3$-manifold fundamental group
We give a criterion on a group $π$ and a homomorphism $w \colon π\to C_2$ under which closed $4$-manifolds with fundamental group $π$ and orientation character $w$ are classified up to homotopy equivalence by their quadratic $2$-types. We verify the criterion for a large class of $3$-manifold groups and orientation characters, in particular for the fundamental group $π$ of any closed, orientable $3$-manifold whose finite subgroups are cyclic, provided $w$ vanishes on every element of $π$ o…

Existence, equivalence and spectrality of infinite convolutions in $\R^d$
Junjie Miao, Hongbo Zhao
https://arxiv.org/abs/2506.06670 https://

Existence, equivalence and spectrality of infinite convolutions in $\R^d$
In this paper, we study existence, equivalence and spectrality of infinite convolutions which may not be compactly supported in $d$-dimensional Euclidean space by manipulating various techniques in probability theory. First, we define the equivalent sequences, and we prove that the infinite convolutions converges simultaneously if they are generated by equivalent sequences. Moreover, the equi-positivity keeps unchanged for infinite convolutions generated by equivalent sequences. Next, we study …

Generalised Orbifolds and G-equivariantisation
Sebastian Heinrich, Julia Plavnik, Ingo Runkel, Abigail Watkins
https://arxiv.org/abs/2506.08154 https://

Generalised Orbifolds and G-equivariantisation
In a construction motivated by topological field theory, a so-called orbifold datum $\mathbb{A}$ in a ribbon category $C$ allows one to define a new ribbon category $C_{\mathbb{A}}$. If $C$ is the neutral component of a $G$-crossed ribbon category $B$, and $\mathbb{A}$ is an orbifold datum in $C$ defined in terms of $B$, one finds that $C_{\mathbb{A}}$ is equivalent to the equivariantisation $B^G$ of $B$ as a ribbon category. We give a constructive proof of this equivalence.

On the Borel complexity of the space of left-orderings of nilpotent groups
Emir Molina Tauc\'an
https://arxiv.org/abs/2507.06953 https://

On the Borel complexity of the space of left-orderings of nilpotent groups
We give the first examples of nonabelian left-orderable groups such that the conjugacy orbit equivalence relation on its space of orders has infinity orbits, yet it is smooth in the Borel sense. The examples are all nilpotent groups and we provide a sufficient condition so that the space of orders of a nilpotent group has a smooth conjugacy orbit relation. We also show with different examples that nilpotence is not a sufficient condition for smoothness.

Componentwise Polish groupoids and equivalence relations
Ruiyuan Chen
https://arxiv.org/abs/2507.04138 https://arxiv.org/pdf/2507.041…

Componentwise Polish groupoids and equivalence relations
We study Borel equivalence relations equipped with a uniformly Borel family of Polish topologies on each equivalence class, and more generally, standard Borel groupoids equipped with such a family of topologies on each connected component. Such "componentwise Polish topologies" capture precisely the topological information determined by the Borel structure of a Polish group action, by the Becker--Kechris theorem. We prove that conversely, every abstract such Borel componentwise Polish groupoid …

Equivalence of Koopman Eigenfunctions and a Commuting Local Frame of Symmetries
Xinyuan Jiang, Yan Li
https://arxiv.org/abs/2508.02437 https://arxiv.org/pd…

Equivalence of Koopman Eigenfunctions and a Commuting Local Frame of Symmetries
This article establishes the relationship between the Koopman eigenfunctions of a first-order nonlinear ODE system and its symmetries. Specifically, a bijective mapping is obtained between i) a commuting local frame of symmetry generators, and ii) a set of Koopman eigenfunctions whose gradients form a local frame. This equivalence is used to convert the problem of finding Koopman eigenfunctions into the equivalent problem of finding commuting vector fields, which are readily given by the flow m…

On a class of quasi-Hermitian surfaces in even characteristic
Angela Aguglia, Alessandro Montinaro
https://arxiv.org/abs/2508.03907 https://arxiv.org/pdf/2…

On a class of quasi-Hermitian surfaces in even characteristic
In [1], a new quasi-Hermitian variety $\mathcal{H}_\varepsilon^r$ in $\mathrm{PG}(r, q^2)$, with $q = 2^e$ and $e \geq 3$ an odd integer, was constructed. The variety depends on a primitive element $\varepsilon$ of the underlying field $\mathrm{GF}(q^2)$.11 In the present paper, we first provide a classification of such varieties up to projective equivalence in finite projective spaces of arbitrary dimension. Then, we focus on the case $r = 3$ and study the structure of the lines contained in…

HBAR entropy of Infalling Atoms into a GUP-corrected Schwarzschild Black Hole and equivalence principle
Ali \"Ovg\"un, Reggie C. Pantig
https://arxiv.org/abs/2506.10621 …

HBAR entropy of Infalling Atoms into a GUP-corrected Schwarzschild Black Hole and equivalence principle
In this work, we have investigated the phenomenon of acceleration radiation exhibited by a two-level atom freely falling into a Generalized Uncertainty Principle (GUP)-corrected Schwarzschild black hole. We derive analytic expressions for the atom's excitation probability with simultaneous emission of a scalar quantum and observe that it satisfies the Einstein equivalence principle when compared to the excitation probability induced by a uniformly accelerating mirror, motivated by studies [10.1…

Equivalence Classes in AES -- Part 1
David Cornwell
https://arxiv.org/abs/2506.23050 https://arxiv.org/pdf/2506.23050

Equivalence Classes in AES -- Part 1
We investigate properties of equivalence classes in AES which arise naturally from properties of MixColumns and InvMixColumns. These two operations have the property that the XOR of the 4 input bytes equals the XOR of 4 output bytes. We examine the effect on equivalence classes due to the operation of SubBytes, ShiftRows, MixColumns and AddRoundKey. The next phase of research is to find a key recovery attack using known (plaintext, ciphertext) equivalence class pairs. Keywords: AES, Equivalen…

An equivalence between time-symmetry and cyclic causality in quantum theory
Eliot Jean, Ralph Silva, V. Vilasini
https://arxiv.org/abs/2508.02463 https://a…

An equivalence between time-symmetry and cyclic causality in quantum theory
Understanding the relationship between the time-symmetric nature of physical laws and the apparent directionality of causality is a central question in quantum foundations. The standard operational formulation, widely used in quantum information, imposes a definite, acyclic causal order on agents' operations, contrasting with time-symmetric dynamics. Two prominent extensions of this framework are the multi-time state (MTS) formalism, which incorporates time symmetry via arbitrary pre- and post-…

Mutual Influence of Symmetries and Topological Field Theories
Daniel Teixeira, Matthew Yu
https://arxiv.org/abs/2507.06304 https://ar…

Mutual Influence of Symmetries and Topological Field Theories
We study how the fusion 2-category symmetry of a fermionic (2+1)d QFT can be affected when one allows for stacking with TQFTs to be an equivalence relation for QFTs. Focusing on a simple kind of fermionic fusion 2-category described purely by group theoretical data, our results reveal that by allowing for stacking with $\mathrm{Spin}(n)_1$ as an equivalence relation enables a finite set of inequivalent modifications to the original fusion 2-categorical-symmetry. To put our results in a broader …

CETBench: A Novel Dataset constructed via Transformations over Programs for Benchmarking LLMs for Code-Equivalence Checking
Neeva Oza, Ishaan Govil, Parul Gupta, Dinesh Khandelwal, Dinesh Garg, Parag Singla
https://arxiv.org/abs/2506.04019

CETBench: A Novel Dataset constructed via Transformations over Programs for Benchmarking LLMs for Code-Equivalence Checking
LLMs have been extensively used for the task of automated code generation. In this work, we examine the applicability of LLMs for the related but relatively unexplored task of code-equivalence checking, i.e., given two programs, whether they are functionally equivalent or not. This is an important problem since benchmarking code equivalence can play a critical role in evaluating LLM capabilities for tasks such as code re-writing and code translation. Towards this end, we present CETBench - Code…

Birational equivalence of exponential matrices
Ryuji Tanimoto
https://arxiv.org/abs/2507.02317 https://arxiv.org/pdf/2507.02317

Birational equivalence of exponential matrices
Let $k$ be an algebraically closed field of characteristic $p \geq 0$ and let $\mathbb{G}_a$ denote the additive group of $k$. We give one-to-one correspondences between exponentional matrices and various objects, and in particular give a one-to-one correspondence between exponential matrices of size $n$-by-$n$ and $\mathbb{G}_a$-actions on the $(n - 1)$-dimensional projective space. We then introduce birational equivalence of exponential matrices and start to classify exponential matrices bira…

Invariants for sum-rank metric codes
Paolo Santonastaso, Ferdinando Zullo
https://arxiv.org/abs/2507.04158 https://arxiv.org/pdf/2507…

Invariants for sum-rank metric codes
The code equivalence problem is central in coding theory and cryptography. While classical invariants are effective for Hamming and rank metrics, the sum-rank metric, which unifies both, introduces new challenges. This paper introduces new invariants for sum-rank metric codes: generalised idealisers, the centraliser, the center, and a refined notion of linearity. These lead to the definition of nuclear parameters, inspired by those used in division algebra theory, where they are crucial for pro…

Gravitational form factors of pion in a nonlocal quark model
Vladimir Voronin
https://arxiv.org/abs/2507.06025 https://arxiv.org/pdf/…

Gravitational form factors of pion in a nonlocal quark model
Interaction with external gravitational field is introduced into a nonlocal quark model using the equivalence principle. This allows to define the energy-momentum tensor in flat space and evaluate its hadronic matrix element with external pions. It is found that bubble diagrams give a significant contribution to the corresponding gravitational form factors.

Teasing apart definitional equivalence
Jason Chen, Toby Meadows
https://arxiv.org/abs/2508.03956 https://arxiv.org/pdf/2508.03956

Teasing apart definitional equivalence
In a recent paper, Enayat and Le lyk [2024] show that second order arithmetic and countable set theory are not definitionally equivalent. It is well known that these theories are biinterpretable. Thus, we have a pair of natural theories that llustrate a meaningful difference between definitional equivalence and bi-interpretability. This is particularly interesting given that Visser and Friedman [2014] have shown that a wide class of natural foundational theories in mathematics are such that if …

Slope detection, taut foliations, and the relative L-space conjecture
Steven Boyer, Cameron McA. Gordon, Ying Hu
https://arxiv.org/abs/2508.06395 https://a…

Slope detection, taut foliations, and the relative L-space conjecture
The $L$-space conjecture asserts the equivalence, for prime $3$-manifolds, of three properties: not being an $L$-space ($NLS$), having a left-orderable fundamental group ($LO$), and admitting a co-orientable taut foliation ($CTF$). In this paper we introduce a relative version of the $L$-space conjecture for knot manifolds $M$, stated in terms of sets of slopes on $\partial M$ characterised (i.e. detected) by Heegaard Floer homology, left-orders, and foliations, respectively. We give a unified …

Shininess, strong politeness, and unicorns
Benjamin Przybocki, Guilherme V. Toledo, Yoni Zohar
https://arxiv.org/abs/2507.04445 https://

Shininess, strong politeness, and unicorns
Shininess and strong politeness are properties related to theory combination procedures. In a paper titled "Many-sorted equivalence of shiny and strongly polite theories", Casal and Rasga proved that for decidable theories, these properties are equivalent. We refine their result by showing that: (i) shiny theories are always decidable, and therefore strongly polite; and (ii) there are (undecidable) strongly polite theories that are not shiny. This line of research is tightly related to a recent…

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences
Mikhail Gorsky, Nicholas J. Williams
https://arxiv.org/abs/2506.08858

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences
We study preorders on (equivalence classes of) maximal chains in the general context of polygonal lattices endowed with suitably nice edge labellings. We show that, given a quotient of polygonal lattices, such edge labellings descend to the quotient, and that there is an induced order-preserving surjective map on the preordered sets of equivalence classes of maximal chains. Under a natural condition ensuring that the domain is a poset, the map is a contraction of preordered sets. We apply this …

Thomason's colimit theorem for the double category of elements
Andrew Gill, Maru Sarazola
https://arxiv.org/abs/2506.08246 https://

Thomason's colimit theorem for the double category of elements
We show that, for any 2-category $C$ and 2-functor $F\colon C \to Cat$, the double category of elements $\iint_C F$ introduced by Grandis and Paré satisfies a version of Thomason's colimit theorem; that is, there is a weak homotopy equivalence $B hocolim F\simeq B(\iint_C F)$.

This https://arxiv.org/abs/2408.04287 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A note on surjective cardinals
For cardinals $\mathfrak{a}$ and $\mathfrak{b}$, we write $\mathfrak{a}=^\ast\mathfrak{b}$ if there are sets $A$ and $B$ of cardinalities $\mathfrak{a}$ and $\mathfrak{b}$, respectively, such that there are partial surjections from $A$ onto $B$ and from $B$ onto $A$. $=^\ast$-equivalence classes are called surjective cardinals. In this article, we show that $\mathsf{ZF}+\mathsf{DC}_κ$, where $κ$ is a fixed aleph, cannot prove that surjective cardinals form a cardinal algebra, which gives a ne…

This https://arxiv.org/abs/2410.10946 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Equivalence checking of quantum circuits via intermediary matrix product operator
As quantum computing advances, the complexity of quantum circuits is rapidly increasing, driving the need for robust methods to aid in their design. Equivalence checking plays a vital role in identifying errors that may arise during compilation and optimization of these circuits and is a critical step in quantum circuit verification. In this work, we introduce a novel method based on Matrix Product Operators (MPOs) for determining the equivalence of quantum circuits. Our approach contracts tens…

An Effective Equivalence Model of Analyzing PLS of Multiple Eavesdroppers Facing Low-altitude Communication Systems
Yujia Zhao, Zhiyong Feng, Kan Yu, Qixun Zhang, Dong Li
https://arxiv.org/abs/2507.05878

An Effective Equivalence Model of Analyzing PLS of Multiple Eavesdroppers Facing Low-altitude Communication Systems
In low-altitude wireless communications, the increased complexity of wireless channels and the uncertainty of eavesdroppers (Eves)--caused by diverse altitudes, speeds, and obstacles--pose significant challenges to physical layer security (PLS) technologies based on fixed-position antennas (FPAs), particularly in terms of beamforming capabilities and spatial efficiency. In contrast, movable antennas (MAs) offer a flexible solution by enabling channel reconstruction through antenna movement, eff…

Torsion Balance Experiments Enable Direct Detection of Sub-eV Dark Matter
Shigeki Matsumoto, Jie Sheng, Chuan-Yang Xing, Lin Zhu
https://arxiv.org/abs/2506.07763

Torsion Balance Experiments Enable Direct Detection of Sub-eV Dark Matter
Light dark matter with sub-eV masses has a high number density in our galaxy, and its scattering cross section with macroscopic objects can be significantly enhanced by coherence effects. Repeated scattering with a target object can induce a measurable acceleration. Torsion balance experiments with geometric asymmetry are, in principle, capable of detecting such signals. Our analysis shows that existing torsion balances designed to test the Equivalence Principle already place the most stringent…

In-depth analysis of violations of the (strong) equivalence principle in scalarized Einstein-Gauss-Bonnet theories
Mart\'in G. Richarte, J\'unior D. Toniato
https://arxiv.org/abs/2507.03983

In-depth analysis of violations of the (strong) equivalence principle in scalarized Einstein-Gauss-Bonnet theories
We conducted a theoretical analysis of the violation of the equivalence principle within a broad class of scalar-Einstein-Gauss-Bonnet theories that exhibit spontaneous scalarization. Beginning with the Jordan frame, we performed a conformal mapping to identify the equivalent model in the Einstein frame. This approach revealed that the Gauss-Bonnet coupling introduces a mixed term that links the Einstein tensor to the kinetic terms, along with an additional kinetic term associated with the box …

Is Crane--Yetter fully extended?
Luuk Stehouwer
https://arxiv.org/abs/2506.04864 https://arxiv.org/pdf/2506.04864

Is Crane--Yetter fully extended?
We revisit the question of whether the Crane-Yetter topological quantum field theory (TQFT) associated to a modular tensor category admits a fully extended refinement. More specifically, we use tools from stable homotopy theory to classify extensions of invertible four-dimensional TQFTs to theories valued in symmetric monoidal 4-categories whose Picard spectrum has nontrivial homotopy only in degrees 0 and 4. We show that such extensions are classified by two pieces of data: an equivalence clas…

On the Natural Equivalence Between Canonical and Hilbert Energy Momentum Tensors via Noether's Theorem
Peir-Ru Wang
https://arxiv.org/abs/2507.05780 ht…

On the Natural Equivalence Between Canonical and Hilbert Energy Momentum Tensors via Noether's Theorem
In this work, we investigate the structure and properties of the canonical energy momentum tensor (EMT) across a range of field theories. We begin by developing a unified and systematic method that naturally yields the canonical EMT for gauge theory, without the need for artificial symmetrization or improvement terms. Our analysis highlights how Noether's theorem intrinsically emphasizes the 1-form nature of gauge potentials. We further extend to general relativity and demonstrate that the assu…

Quasi-equivalence of Gaussian states and energy estimates for functions of modular Hamiltonians
Adriano Chialastri, Ko Sanders
https://arxiv.org/abs/2506.03907

Quasi-equivalence of Gaussian states and energy estimates for functions of modular Hamiltonians
To compare two Gaussian states of the Weyl-CCR algebra of a free scalar QFT we study three closely related perspectives: (i) quasi-equivalence of the GNS-representations, (ii) differences of the total energy (on some Cauchy surface), and (iii) differences between functions of the modular Hamiltonians. (For perspective (ii) we will only consider real linear free scalar quantum fields on ultrastatic spacetimes.) These three perspectives are known to be related qualitatively, due to work of Araki …

Semi-strictification of $(\infty, n)$-categories
Cl\'emence Chanavat, Amar Hadzihasanovic
https://arxiv.org/abs/2507.00146 https://

Semi-strictification of $(\infty, n)$-categories
We prove the first equivalence between a weak non-algebraic model and a semi-strict algebraic model of $(\infty, n)$-categories. This takes the form of a natural semi-strictification, whereby a weak $(\infty, n)$-category is embedded into a semi-strict one through an acyclic cofibration, in such a way that weak functors lift to semi-strict functors; this constitutes the derived unit of a Quillen equivalence between weak model categories whose fibrant objects are, respectively, the weak $(\infty…