Tootfinder

Characterizing Equivalence of Logically Constrained Terms via Existentially Constrained Terms (Full Version)
Kanta Takahata, Jonas Sch\"opf, Naoki Nishida, Takahito Aoto
https://arxiv.org/abs/2505.21986

Characterizing Equivalence of Logically Constrained Terms via Existentially Constrained Terms (Full Version)
Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained term rewriting. A fundamental question on constrained terms arising there is how to characterize equivalence between them. However, in the current literature only limited progress has been made on this. In this paper, we provide several sound and complete so…

Simplicial properadic homotopy
Eric Hoffbeck, Johan Leray, Bruno Vallette
https://arxiv.org/abs/2505.22004 https://arxiv.org/pdf/2505…

Simplicial properadic homotopy
In this paper, we settle the homotopy properties of the infinity-morphisms of homotopy (bial)-gebras over properads, i.e. algebraic structures made up of operations with several inputs and outputs. We start by providing the literature with characterizations for the various types of infinity-morphisms, the most seminal one being the equivalence between infinity-quasi-isomorphisms and zig-zags of quasi-isomorphisms which plays a key role in the study the formality property. We establish a simplic…

Lower Bounds on the Size of Markov Equivalence Classes
Erik Jahn, Frederick Eberhardt, Leonard J. Schulman
https://arxiv.org/abs/2506.20933 https://…

Lower Bounds on the Size of Markov Equivalence Classes
Causal discovery algorithms typically recover causal graphs only up to their Markov equivalence classes unless additional parametric assumptions are made. The sizes of these equivalence classes reflect the limits of what can be learned about the underlying causal graph from purely observational data. Under the assumptions of acyclicity, causal sufficiency, and a uniform model prior, Markov equivalence classes are known to be small on average. In this paper, we show that this is no longer the ca…

Local Type Inference for Context-Free Session Types
Bernardo Almeida (LASIGE, Faculty of Sciences, University of Lisbon, Portugal), Andreia Mordido (LASIGE, Faculty of Sciences, University of Lisbon, Portugal), Vasco T. Vasconcelos (LASIGE, Faculty of Sciences, University of Lisbon, Portugal)
https://arxiv.org/abs/2505.20855

Local Type Inference for Context-Free Session Types
We address the problem of local type inference for a language based on System F with context-free session types. We present an algorithm that leverages the bidirectional type checking approach to propagate type information, enabling first class polymorphism while addressing the intricacies brought about by the sequential composition operator and type equivalence. The algorithm improves the language's usability by eliminating the need for type annotations at type application sites.

Self-adjoint operators in Z-stable C$^*$-algebras with prescribed spectral data
Andrew S. Toms, Hao Wan
https://arxiv.org/abs/2505.22448 https://

Self-adjoint operators in Z-stable C$^*$-algebras with prescribed spectral data
We consider the variety of spectral measures that are induced by quasitraces on the spectrum of a self-adjoint operator in a simple separable unital and Z-stable C$^*$-algebra. This amounts to a continuous map from the simplex of quasitraces of the C$^*$-algebra into regular Borel probability measures on the spectrum of the operator under consideration. In the case of a connected spectrum this data determines the unitary equivalence class of the operator, and may be reduced to to the case of an…

This https://arxiv.org/abs/2502.20991 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Domains, Information Frames, Rough Sets: An Equivalence of Categories
A generalization of Scott's information systems~\cite{sco82} is presented that captures exactly all continuous domains. The global consistency predicate in Scott's definition is relativized. Now, for every atomic statement, there is a consistency predicate that states which finite sets of statements express information that is consistent with the given statement. The category of information frames is shown to be equivalent to the category of domains. Moreover, the relationship with CF-approxima…

On the isotopies of tangles in periodic 3-manifolds using finite covers
Yuka Kotorii, Sonia Mahmoudi, Elisabetta Matsumoto, Ken'ichi Yoshida
https://arxiv.org/abs/2505.20940

On the isotopies of tangles in periodic 3-manifolds using finite covers
A periodic tangle is a one-dimensional submanifold in $\mathbb{R}^3$ that has translational symmetry in one, two or three transverse directions. A periodic tangle can be seen as the universal cover of a link in the solid torus, the thickened torus, or the three-torus, respectively. Our goal is to study equivalence relations of such periodic tangles. Since all finite covers of a link lift to the same periodic tangle, it is necessary to prove that isotopies between different finite covers are pre…

This https://arxiv.org/abs/2505.01936 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Algebraic structures arising from the finite condensation on linear orders
The finite condensation $\sim_F$ is an equivalence relation defined on a linear order $L$ by $x \sim_F y$ if and only if the set of points lying between $x$ and $y$ is finite. We define an operation $\cdot_F$ on linear orders $L$ and $M$ by $L \cdot_F M = \operatorname{o.t.}\left((LM)/\!\sim_F\right)$; that is, $L \cdot_F M$ is the order type of the lexicographic product of $L$ and $M$ modulo the finite condensation. The infinite order types $L$ such that $L / \! \sim_F\, \cong 1$ are $ω, ω^*…

This https://arxiv.org/abs/2405.07671 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csFL_…

Constructing a BPE Tokenization DFA
Many natural language processing systems operate over tokenizations of text to address the open-vocabulary problem. In this paper, we give and analyze an algorithm for the efficient construction of deterministic finite automata (DFA) designed to operate directly on tokenizations produced by the popular byte pair encoding (BPE) technique. This makes it possible to apply many existing techniques and algorithms to the tokenized case, such as pattern matching, equivalence checking of tokenization d…

This https://arxiv.org/abs/2412.10066 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Non-Ground Congruence Closure
Congruence closure on ground equations is a well-established and efficient algorithm for deciding ground equalities. It constructs an explicit representation of ground equivalence classes based on a given set of input equations, allowing ground equalities to be decided by membership. In many applications, these ground equations originate from grounding non-ground equations. We propose an algorithm that directly computes a non-ground representation of ground congruence classes for non-ground e…

This https://arxiv.org/abs/2412.18206 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Topological Koszulity for Category Algebras
We give a topological description of Ext groups between simple representations of categories via a nerve type construction. We use it to show that the Koszulity of indiscretely based category algebras is equivalent to the locally bouquet property of this nerve. We also provide a class of functors which preserve the Koszulity of category algebras called almost discrete fibrations. Specializing from categories to posets, we show that the equivalence relations of V. Reiner and D. Stamate in arXiv:…

Equivalence of Landscape and Erosion Distances for Persistence Diagrams
Cagatay Ayhan, Tom Needham
https://arxiv.org/abs/2506.21488 https://

Equivalence of Landscape and Erosion Distances for Persistence Diagrams
This paper establishes connections between three of the most prominent metrics used in the analysis of persistence diagrams in topological data analysis: the bottleneck distance, Patel's erosion distance, and Bubenik's landscape distance. Our main result shows that the erosion and landscape distances are equal, thereby bridging the former's natural category-theoretic interpretation with the latter's computationally convenient structure. The proof utilizes the category with a flow framework of d…

Replaced article(s) found for math.NT. https://arxiv.org/list/math.NT/new
[1/1]:
- Number of Equivalence Classes of Rational Functions over Finite Fields
Xiang-dong Hou

The Fano of lines, the Kuznetsov component, and a flop
Kimoi Kemboi, Ed Segal
https://arxiv.org/abs/2506.20559 https://arxiv.org/pdf/…

The Fano of lines, the Kuznetsov component, and a flop
The Kuznetsov component of the derived category of a cubic fourfold is a `non-commutative K3 surface'. Its symmetric square is hence a `non-commutative hyperkaehler fourfold'. We prove that this category is equivalent to the derived category of an actual hyperkaehler fourfold: the Fano of lines in the cubic. This verifies a conjecture of Galkin. One of the key steps in our proof is a new derived equivalence for a specific 12-dimensional flop.

Stretched Horizon Dissipation and the Fate of Echoes
Seiji Terashima
https://arxiv.org/abs/2506.20462 https://arxiv.org/pdf/2506.2046…

Stretched Horizon Dissipation and the Fate of Echoes
We examine the dissipation of infalling particles near black holes under the assumption that the equivalence principle breaks down at the stretched horizon. This violation allows partial reflection of particles just outside the event horizon, as suggested by models such as the fuzzball and firewall proposals. We show that scattering with blue-shifted Hawking radiation leads to moderate dissipation when the particle energy is comparable to the Hawking temperature. The decay rate is independent o…

The linearizability of singular foliations is a Morita invariant
Marco Zambon
https://arxiv.org/abs/2506.19509 https://arxiv.org/pdf/…

The linearizability of singular foliations is a Morita invariant
Hausdorff Morita equivalence is an equivalence relation on singular foliations, which induces a bijection between their leaves. Our main statement is that linearizability along a leaf is invariant under Hausdorff Morita equivalence. The proof relies on a characterization of tubular neighborhood embeddings using Euler-like vector fields.

This https://arxiv.org/abs/2505.02548 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Modal logic for reasoning about uncertainty and confusion
We consider a modal logic that can formalise statements about uncertainty and beliefs such as `I think that my wallet is in the drawer rather than elsewhere' or `I am confused whether my appointment is on Monday or Tuesday'. To do that, we expand Gödel modal logic $\mathbf{K}\mathsf{G}$ with the involutive negation $\sim$ defined as $v({\sim}ϕ,w)=1-v(ϕ,w)$. We provide semantics with the finite model property for our new logic that we call $\mathbf{K}\mathsf{G_{inv}}$ and show its equivalence…

Computational simulation of thermal processes in ncs production plants
Pablo Cortes, Omar Lopez, Ramiro Medina, Gerardo Gordillo, Javier Guevara
https://arxiv.org/abs/2506.20885

Computational simulation of thermal processes in ncs production plants
This paper develops a computational simulation of the fluid dynamics and heat transfer phenomena that occur inside combustion chamber, and flat and semispherical open evaporators used in NCS non-centrifugal sugar industry. The study estimates the effect of primary/secondary air ratio and excess air in the combustion chamber performance resulting in an optimal value of 1.3 for the equivalence ratio in the lower section of combustion chamber. The influence of both mechanisms of heat transfer in t…

"I'm Petting the Laptop, Which Has You Inside It": Reflecting on Lived Experiences of Online Friendship
Seraphina Yong, Ashlee Milton, Evan Suma Rosenberg, Stevie Chancellor, Svetlana Yarosh
https://arxiv.org/abs/2506.20055

"I'm Petting the Laptop, Which Has You Inside It": Reflecting on Lived Experiences of Online Friendship
Online(-only) friendships have become increasingly common in daily lives post-COVID despite debates around their mental health benefits and equivalence to ''real'' relationships. Previous research has reflected a need to understand how online friends engage beyond individual platforms, and the lack of platform-agnostic inquiry limits our ability to fully understand the dynamics of online friendship. We employed an activity-grounded analysis of 25 interviews on lived experiences of close online …

Morita equivalence classes for crossed product of rational rotation algebras
Sayan Chakraborty, Pratik Kumar Kundu
https://arxiv.org/abs/2505.19869 https:/…

Morita equivalence classes for crossed product of rational rotation algebras
We study the Morita equivalence classes of crossed products of rotation algebras $A_θ$, where $θ$ is a rational number, by finite and infinite cyclic subgroups of $\mathrm{SL}(2, \mathbb{Z})$. We show that for any such subgroup $F$, the crossed products $A_θ\rtimes F$ and $A_{θ'} \rtimes F$ are strongly Morita equivalent, where both $θ$ and $θ'$ are rational. Combined with previous results for irrational values of $θ$, our result provides a complete classification of the crossed products…

Leading bounds on micro- to picometer fifth forces from neutron star cooling
Damiano F. G. Fiorillo, Alessandro Lella, Ciaran A. J. O'Hare, Edoardo Vitagliano
https://arxiv.org/abs/2506.19906

Leading bounds on micro- to picometer fifth forces from neutron star cooling
The equivalence principle and the inverse-square law of gravity could be violated at short distances ($10^{-6}$ to $10^{-12}$ meters) by scalars sporting a coupling $g_N$ to nucleons and mass $\mathrm{eV}\lesssim m_ϕ\lesssim\rm MeV$. We show for the first time that stringent bounds on the existence of these scalars can be derived from the observed cooling of nearby isolated neutron stars (NSs). Although NSs can only be used to set limits comparable to the classic SN 1987A cooling bound in the …

Generalized Verma modules over sl(m 1) induced from simple highest weight modules
Yaohui Xue, Yan Wang
https://arxiv.org/abs/2506.19625 https://

Generalized Verma modules over sl(m+1) induced from simple highest weight modules
A class of generalized Verma modules over sl(m+1) are constructed from simple highest weight gl(m)-modules. Furthermore, the simplicity criterion for these sl(m+1)-modules are determined and an equivalence between generalized Verma modules and tensor modules are established.

from my link log —
Dependent types and program equivalence.
https://www.seas.upenn.edu/~sweirich/papers/popl10-lambda-eek.pdf
saved 2025-06-10

Canonical Analysis of Eddington Gravity
J. Kluson
https://arxiv.org/abs/2506.16279 https://arxiv.org/pdf/2506.16279

Canonical Analysis of Eddington Gravity
In this short note we perform canonical analysis of Eddington gravity using L. Faddeev and Jackiw formalism. We demonstrate that resulting canonical action has the same form as General Relativity canonical action which proves an equivalence of Eddington gravity and General Relativity in Hamiltonian formalism.

TrainVerify: Equivalence-Based Verification for Distributed LLM Training
Yunchi Lu, Youshan Miao, Cheng Tan, Peng Huang, Yi Zhu, Xian Zhang, Fan Yang
https://arxiv.org/abs/2506.15961

TrainVerify: Equivalence-Based Verification for Distributed LLM Training
Training large language models (LLMs) at scale requires parallel execution across thousands of devices, incurring enormous computational costs. Yet, these costly distributed trainings are rarely verified, leaving them prone to silent errors and potentially wasting millions of GPU hours. We introduce TrainVerify, a system for verifiable distributed training of LLMs. Given a deep learning model's logical specification as the ground truth, TrainVerify formally verifies that a distributed parallel …

Iterating sine, equivalence classes of variable changes, and groups with few conjugacy classes
Pavel Etingof
https://arxiv.org/abs/2506.16364 https://

Iterating sine, equivalence classes of variable changes, and groups with few conjugacy classes
This is an expository paper about iterations of a smooth real function $f$ on $[0,\varepsilon)$ such that $f(0)=0$, $f'(0)=1$, and $f(x)0$, i.e., the sequence defined by $x_{n+1}=f(x_n)$. This sequence has interesting asymptotics, whose study leads to the question of classifying conjugacy classes in the group of formal changes of variable $y=f(x)$, i.e., formal series $f(x)=x+a_2x^2+a_3x^2+...$ with real coefficients (under composition). The same classification applies over a finite …

Towards Robust Causal Effect Identification Beyond Markov Equivalence
Kai Z. Teh, Kayvan Sadeghi, Terry Soo
https://arxiv.org/abs/2506.15561 https://

Towards Robust Causal Effect Identification Beyond Markov Equivalence
Causal effect identification typically requires a fully specified causal graph, which can be difficult to obtain in practice. We provide a sufficient criterion for identifying causal effects from a candidate set of Markov equivalence classes with added background knowledge, which represents cases where determining the causal graph up to a single Markov equivalence class is challenging. Such cases can happen, for example, when the untestable assumptions (e.g. faithfulness) that underlie causal d…

Proper cocycles, measure equivalence and $L_p$-Fourier multipliers
Simeng Wang, Runlian Xia, Gan Yao
https://arxiv.org/abs/2506.18320 https://

Proper cocycles, measure equivalence and $L_p$-Fourier multipliers
We develop a new transference method for completely bounded $L_p$-Fourier multipliers via proper cocycles arising from probability measure-preserving group actions. This method extends earlier results by Haagerup and Jolissaint, which were limited to the case $p = \infty$. Based on this approach, we present a new and simple proof of the main result in [Hong-Wang-Wang, Mem. Amer. Math. Soc. 2024] regarding the pointwise convergence of noncommutative Fourier series on amenable groups, refining th…

Scaling GR(1) Synthesis via a Compositional Framework for LTL Discrete Event Control
Hern\'an Gagliardi, Victor Braberman, Sebastian Uchitel
https://arxiv.org/abs/2506.16557

Scaling GR(1) Synthesis via a Compositional Framework for LTL Discrete Event Control
We present a compositional approach to controller synthesis of discrete event system controllers with linear temporal logic (LTL) goals. We exploit the modular structure of the plant to be controlled, given as a set of labelled transition systems (LTS), to mitigate state explosion that monolithic approaches to synthesis are prone to. Maximally permissive safe controllers are iteratively built for subsets of the plant LTSs by solving weaker control problems. Observational synthesis equivalence i…

Mld versus lct near zero
Florin Ambro
https://arxiv.org/abs/2506.18507 https://arxiv.org/pdf/2506.18507

Mld versus lct near zero
We study the equivalence of approaching zero for two invariants of a singularity: the minimal log discrepancy and the log canonical threshold of the general hyperplane section.

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.

A residual a posteriori error estimate for the Stabilization-free Virtual Element Method
Stefano Berrone, Andrea Borio, Davide Fassino, Francesca Marcon
https://arxiv.org/abs/2506.17947

A residual a posteriori error estimate for the Stabilization-free Virtual Element Method
In this work, we present the a posteriori error analysis of Stabilization-Free Virtual Element Methods for the 2D Poisson equation. The abscence of a stabilizing bilinear form in the scheme allows to prove the equivalence between a suitably defined error measure and standard residual error estimators, which is not obtained in general for stabilized virtual elements. Several numerical experiments are carried out, confirming the expected behaviour of the estimator in the presence of different mes…

Correspondence among congruence families for generalized Frobenius partitions via modular permutations
Rong Chen, Xiao-Jie Zhu
https://arxiv.org/abs/2506.16823

Correspondence among congruence families for generalized Frobenius partitions via modular permutations
In 2024, Garvan, Sellers and Smoot discovered a remarkable symmetry in the families of congruences for generalized Frobenius partitions $cψ_{2,0}$ and $cψ_{2,1}$. They also emphasized that the considerations for the general case of $cψ_{k,β}$ are important for future work. In this paper, for each $k$ we construct a vector-valued modular form for the generating functions of $cψ_{k,β}$, and determine an equivalence relation among all $β$. Within each equivalence class, we can identify modu…

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.

This https://arxiv.org/abs/2211.15412 has been replaced.
link: https://scholar.google.com/scholar?q=a

STE-QUEST -- Space Time Explorer and QUantum Equivalence principle Space Test: The 2022 medium-class mission concept
Space-borne quantum technologies, particularly those based on atom interferometry, are heralding a new era of strategic and robust space exploration. The unique conditions of space, characterized by low noise and low gravity environments, open up diverse possibilities for applications ranging from precise time and frequency transfer to Earth Observation and the search of new Physics. In this paper, we summarise the M-class mission proposal in response to the 2022 call in ESA's science program: …

Thin homotopy and the signature of piecewise linear surfaces
Francis Bischoff, Darrick Lee
https://arxiv.org/abs/2506.16657 https://a…

Thin homotopy and the signature of piecewise linear surfaces
We introduce a crossed module of piecewise linear surfaces and study the signature homomorphism, defined as the surface holonomy of a universal translation invariant $2$-connection. This provides a transform whereby surfaces are represented by formal series of tensors. Our main result is that the signature uniquely characterizes a surface up to translation and thin homotopy, also known as tree-like equivalence in the case of paths. This generalizes a result of Chen and positively answers a ques…

Large-amplitude periodic solutions to the steady Euler equations with piecewise constant vorticity
Alex Doak, Karsten Matthies, Jonathan Sewell, Miles H. Wheeler
https://arxiv.org/abs/2506.17002

Large-amplitude periodic solutions to the steady Euler equations with piecewise constant vorticity
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation theory, we rigorously construct curves of solutions that terminate either with stagnation on the interface or when the conformal equivalence between one of the layers and a strip breaks down in a $C^1$ sense. We give numerical evidence that, depending on paramet…

Homomorphism Indistinguishability and Game Comonads for Restricted Conjunction and Requantification
Georg Schindling
https://arxiv.org/abs/2506.19746 https…

Homomorphism Indistinguishability and Game Comonads for Restricted Conjunction and Requantification
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph classes, two structures agree on all homomorphism counts from the class if and only if they satisfy the same sentences in a corresponding logic. This perspective often reveals connections between the combinatorial properties of graph classes and the syntactic struc…

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…

This https://arxiv.org/abs/2412.05561 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDB_…

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…

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?

Self-Equivalent Voting Rules
H\'ector Hermida-Rivera
https://arxiv.org/abs/2506.15310 https://arxiv.org/pdf/2506.15310

Self-Equivalent Voting Rules
In this paper, I introduce a novel stability axiom for stochastic voting rules, called self-equivalence, by which a society considering whether to replace its voting rule using itself will choose not do so. I then show that under the unrestricted strict preference domain, a voting rule satisfying the democratic principles of anonymity, optimality, monotonicity, and neutrality is self-equivalent if and only if it assigns to every voter equal probability of being a dictator (i.e., uniform random …

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…

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…

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…

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…

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…

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...

Spectra and invariant subspaces of compressed shifts on nearly invariant subspaces
Y. Liang, J. R. Partington
https://arxiv.org/abs/2506.18646 https://

Spectra and invariant subspaces of compressed shifts on nearly invariant subspaces
While the spectral properties and invariant subspaces of compressed shifts on model spaces are well understood, their behaviour on nearly $S^*$-invariant subspaces, a natural generalization with weaker structural constraints, remains largely unexplored. In this paper, we completely characterize the point spectrum, whole spectrum and invariant subspace structure for such compressed shifts by unitary equivalence, using the Frostman shift, Crofoot transform, and Sz.-Nagy--Foias theory. Our results…

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,…

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…

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,…

Replaced article(s) found for physics.class-ph. https://arxiv.org/list/physics.class-ph/new
[1/1]:
- Equivalence of Lagrangian and Multisymplectic Hamiltonian Formalisms for the Description of Class...
Jos\'e Francisco P\'erez-Barrag\'an

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.

This https://arxiv.org/abs/2403.17490 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Reconstruction of hypersurfaces from their invariants
Let $K$ be a field of characteristic $0$. We present an explicit algorithm that, given the invariants of a generic homogeneous polynomial $f$ under the linear action of $\mathrm{GL}_n$ or $\mathrm{SL}_n$, returns a polynomial differing from $f$ only by a linear change of variables with coefficients in a finite extension of $K$. Our approach uses the theory of covariants and the Veronese embeddings to characterize the linear equivalence class of a homogeneous polynomial through equations whose c…

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.

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…

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.

HEC: Equivalence Verification Checking for Code Transformation via Equality Saturation
Jiaqi Yin, Zhan Song, Nicolas Bohm Agostini, Antonino Tumeo, Cunxi Yu
https://arxiv.org/abs/2506.02290

HEC: Equivalence Verification Checking for Code Transformation via Equality Saturation
In modern computing systems, compilation employs numerous optimization techniques to enhance code performance. Source-to-source code transformations, which include control flow and datapath transformations, have been widely used in High-Level Synthesis (HLS) and compiler optimization. While researchers actively investigate methods to improve performance with source-to-source code transformations, they often overlook the significance of verifying their correctness. Current tools cannot provide…

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 …

Binary Self-Selective Voting Rules
H\'ector Hermida-Rivera, Toygar T. Kerman
https://arxiv.org/abs/2506.15265 https://arxiv.org/p…

Binary Self-Selective Voting Rules
This paper introduces a novel binary stability property for voting rules-called binary self-selectivity-by which a society considering whether to replace its voting rule using itself in pairwise elections will choose not to do so. In Theorem 1, we show that a neutral voting rule is binary self-selective if and only if it is universally self-selective. We then use this equivalence to show, in Corollary 1, that under the unrestricted strict preference domain, a unanimous and neutral voting rule i…

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…

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…

Morita equivalence of shifted symplectic Lie n-groupoids
Milena Weiershausen
https://arxiv.org/abs/2505.24018 https://arxiv.org/pdf/2…

Morita equivalence of shifted symplectic Lie n-groupoids
Symplectic structures on higher objects like Lie groupoids have been studied for some time now, but not all of the proposed definitions are preserved under Morita equivalence of Lie groupoids, in turn giving rise to a consistent notion of symplectic stacks. Recently, this concept has been generalized to m-shifted symplectic forms on Lie n-groupoids, which are indeed preserved under Morita equivalence of Lie n-groupoids. In this paper, we give a rigorous proof for this statement.

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 …

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 …

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 $B hocolim F\simeq B(\iint_C F)$.

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…

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…

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…

Simplicial methods in the resource theory of contextuality
Aziz Kharoof, Cihan Okay
https://arxiv.org/abs/2505.24010 https://arxiv.or…

Simplicial methods in the resource theory of contextuality
We develop a resource theory of contextuality within the framework of symmetric monoidal categories, extending recent simplicial approaches to quantum contextuality. Building on the theory of simplicial distributions, which integrates homotopy-theoretic structures with probability, we introduce event scenarios as a functorial generalization of presheaf-theoretic measurement scenarios and prove their equivalence to bundle scenarios via the Grothendieck construction. We define symmetric monoidal …

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…

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…

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…

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…

Isotypic blocks of finite groups algebras that are not $p$-permutation equivalent
John Revere McHugh
https://arxiv.org/abs/2506.03446 https://

Isotypic blocks of finite groups algebras that are not $p$-permutation equivalent
We show that Kessar's isotypy between Galois conjugate blocks of finite group algebras does not always lift to a $p$-permutation equivalence. We also provide examples of Galois conjugate blocks which are isotypic but not $p$-permutation equivalent. These results help to clarify the distinction between a $p$-permutation equivalence and an isotypy, and may be useful in determining necessary and sufficient conditions for when an isotypy lifts to a $p$-permutation equivalence.

This https://arxiv.org/abs/2207.12969 has been replaced.
link: https://scholar.google.com/scholar?q=a

Module Categories of the Generic Virasoro VOA and Quantum Groups
In this paper, we prove the equivalence between two ribbon tensor categories. On the one hand, we consider the category of modules of the Virasoro vertex operator algebra with generic central charge (generic Virasoro VOA) generated by those simple modules lying in the first row of the Kac table. On the other hand, we take the category of finite-dimensional type I modules of the quantum group $\mathcal{U}_q (\mathfrak{sl}_{2})$ with $q$ determined by the central charge. This is a continuation of…

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…

This https://arxiv.org/abs/2205.12798 has been replaced.
link: https://scholar.google.com/scholar?q=a

An involutive dual knot surgery formula
We prove an involutive analog of the dual knot surgery formula of Eftekhary and Hedden-Levine. We also compute a small model for the local equivalence class of the involutive dual knot complex.

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 …

This https://arxiv.org/abs/2311.07459 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On homogeneous plane waves
Plane waves are a special class of Lorentzian spaces with a parallel null vector field. They are of great importance in Geometry (e.g. Lorentzian holonomy) and in Physics (General Relativity as well as alternative gravity theories). Our contribution in the present paper aims at a rigorous mathematical treatment focusing on completeness of Killing fields, and globality of coordinates. Equivalence of different approaches to plane waves is by no means easy to handle. We use here cohomogeneity one …

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_…

This https://arxiv.org/abs/2410.17407 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Morita theory for dynamical von Neumann algebras
Given a locally compact quantum group $\mathbb{G}$ and two $\mathbb{G}$-$W^*$-algebras $α: A\curvearrowleft \mathbb{G}$ and $β: B\curvearrowleft \mathbb{G}$, we study the notion of equivariant $W^*$-Morita equivalence $(A, α)\sim_{\mathbb{G}} (B, β)$, which is an equivariant version of Rieffel's notion of $W^*$-Morita equivalence. We prove that important dynamical properties of $\mathbb{G}$-$W^*$-algebras, such as (inner) amenability, are preserved under equivariant Morita equivalence. For …

Determining unit groups and $\mathrm{K}_1$ of finite rings
Tommy Hofmann
https://arxiv.org/abs/2506.00266 https://arxiv.org/pdf/2506.…

Determining unit groups and $\mathrm{K}_1$ of finite rings
We consider the computational problem of determining the unit group of a finite ring, by which we mean the computation of a finite presentation together with an algorithm to express units as words in the generators. We show that the problem is equivalent to the number theoretic problems of factoring integers and solving discrete logarithms in finite fields. A similar equivalence is shown for the problem of determining the abelianization of the unit group or the first $K$-group of finite rings.

This https://arxiv.org/abs/2312.08923 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Topology change and heterotic flux vacua
We investigate the interrelation between topology and Narain T-duality of heterotic flux vacua. We present evidence that all 5 and 4-dimensional Minkowski space heterotic flux backgrounds with 8 supercharges have a locus in the moduli space with a T-dual description in terms of a compactification on the product of a K3 surface with a circle or a torus. A test of this equivalence is provided by calculating the new supersymmetric index on both sides of the duality. We examine the implications of …

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…

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…

Phase estimation in lossy optical interferometry without a reference beam
Jun Tang, Dong-Qing Wang, Wei Zhong, Lan Zhou, Yu-Bo Sheng
https://arxiv.org/abs/2505.24770

Phase estimation in lossy optical interferometry without a reference beam
We investigate phase estimation in a lossy interferometer using entangled coherent states, with particular focus on a scenario where no reference beam is employed. By calculating the quantum Fisher information, we reveal two key results: (1) the metrological equivalence between scenarios with and without a reference beam, established under ideal lossless conditions for the two-phase-shifting configuration,breaks down in the presence of photon loss, and (2) the pronounced inferior performance of…

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…

Birational equivalence of Severi-Brauer varieties
J\'anos Koll\'ar
https://arxiv.org/abs/2505.24720 https://arxiv.org/pdf/250…

Birational equivalence of Severi-Brauer varieties
We prove Amitsur's conjecture for Severi-Brauer varieties whose index is not a prime power.

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…

On the local representation theory of symmetric groups
Greta Tendi
https://arxiv.org/abs/2506.04773 https://arxiv.org/pdf/2506.04773

On the local representation theory of symmetric groups
Given a Sylow $p$-subgroup $P$ of a symmetric group, we describe the action of its normalizer on $\mathrm{Irr}(P)$. To this end, we establish a one-to-one correspondence between the irreducible characters of $P$ and certain equivalence classes of explicitly defined functions, which are also naturally suited to describing the Galois action.

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…

An atom in front of Lorentz violating Kalb-Ramond black hole background
Anisur Rahaman
https://arxiv.org/abs/2506.01006 https://arxiv…

An atom in front of Lorentz violating Kalb-Ramond black hole background
We investigate the role of Lorentz violation in the acceleration radiation produced when an atom falls into a Kalb-Ramond (KR) black hole and observe that the amplitude and an exponential (Planck-like) factor are both shaped by the Lorentz-violating parameter, indicating a breach of the equivalence principle and resembling characteristics observed in bumblebee gravity models. We further investigate how Lorentz violation and conformal symmetry work together to determine the thermodyn…

Wild Betti sheaves
Peter Scholze
https://arxiv.org/abs/2505.24599 https://arxiv.org/pdf/2505.24599

Wild Betti sheaves
In this note, we consider the problem of constructing an enlargement of the category of Betti sheaves that supports an ``exponential local system'' on $\mathbb R$, and a Fourier equivalence defined on all sheaves. We show that there is a universal solution, recovering a construction of Tamarkin known also as ``enhanced sheaves''. The universality property implies that the category of coefficients of this theory is, in a suitable sense, a nontrivial $\mathbb R_{>0}$-torsor over $\mathrm{Spec}(\m…

An isometry theorem for persistent homology of circle-valued functions
Nathan Broomhead, Mariam Pirashvili
https://arxiv.org/abs/2506.02999 https://…

An isometry theorem for persistent homology of circle-valued functions
This paper explores persistence modules for circle-valued functions, presenting a new extension of the interleaving and bottleneck distances in this setting. We propose a natural generalisation of barcodes in terms of arcs on a geometric model associated to the derived category of quiver representations. The main result is an isometry theorem that establishes an equivalence between the interleaving distance and the bottleneck distance for circle-valued persistence modules.

When Bi-interpretability implies Synonymy
Harvey M. Friedman, Albert Visser
https://arxiv.org/abs/2506.01028 https://arxiv.org/pdf/25…

When Bi-interpretability implies Synonymy
Two salient notions of sameness of theories are synonymy, also known as definitional equivalence, and bi-interpretability. Of these two definitional equivalence is the strictest notion. In which cases can we infer synonymy from bi-interpretability? We study this question for the case of sequential theories. Our result is as follows. Suppose that two sequential theories are bi-interpretable and that the interpretations involved in the bi-interpretation are one-dimensional and identity preserving…

Simple Classes of Automatic Structures
Achim Blumensath
https://arxiv.org/abs/2505.22821 https://arxiv.org/pdf/2505.22821

Simple Classes of Automatic Structures
We study two subclasses of the class of automatic structures: automatic structures of polynomial growth and Presburger structures. We present algebraic characterisations of the groups and the equivalence structures in these two classes.

Compact symmetric triads and symmetric triads with multiplicities
Kurando Baba, Osamu Ikawa
https://arxiv.org/abs/2506.02511 https://…

Compact symmetric triads and symmetric triads with multiplicities
In this paper, we develop the theory of symmetric triads with multiplicities. First, we classify abstract symmetric triads with multiplicities. Second, we determine the symmetric triads with multiplicities corresponding to commutative compact symmetric triads. As applications, we give the classifications for commutative compact symmetric triads, which consist of two types depending on the choice of the equivalence relations.

This https://arxiv.org/abs/2412.06043 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Probing Gravity -- Fundamental Aspects of Metric Theories and their Implications for Tests of General Relativity
Guided by the Einstein equivalence principle that identifies the phenomenon of gravitation as a manifestation of the dynamics of spacetime in contrast to a localizable force, we review and explore its consequences on formulating a theory of gravity. The resulting space of metric theories of gravity may address open conceptual and observational puzzles through a wealth of effects beyond general relativity, whose traces can be searched for within today's and tomorrow's gravitational testing groun…