Tootfinder

Hopf-Galois structures on separable field extensions of degree related to Cunningham chains
Andrew Darlington
https://arxiv.org/abs/2508.03384 https://arxi…

Hopf-Galois structures on separable field extensions of degree related to Cunningham chains
The past few years have seen Hopf--Galois structures on extensions of squarefree degree studied in various contexts. The Galois case was fully explored by Alabdali and Byott in 2020, followed by a first attempt at generalising these results to include non-normal extensions by Byott and Martin-Lyons; their work looks at separable extensions of degree $pq$ with $p,q$ distinct odd primes, and $p=2q+1$. This paper extends the latter work further by considering separable extensions of squarefree deg…

Some power series extensions of Fibonacci and Lucas polynomials
Johann Cigler
https://arxiv.org/abs/2509.04881 https://arxiv.org/pdf/2509.04881

Some power series extensions of Fibonacci and Lucas polynomials
We study formal power series which can be interpreted as interpolations of Fibonacci and Lucas polynomials with even (or odd) indices.

Massey products and unipotent extensions with restricted ramification
Oussama Hamza (HIT), Donghyeok Lim (FEMTO-ST, UMLP), Christian Maire (FEMTO-ST, UMLP)
https://arxiv.org/abs/2508.03233

Massey products and unipotent extensions with restricted ramification
We fix a prime p and construct new cases of pro-p extensions of number fields with restricted ramification and splitting, whose Galois groups decompose as coproducts of pro-p absolute Galois groups of local fields. As a consequence, these pro-p extensions satisfy the strong Massey vanishing property and thus admit large unipotent quotients.

This week I have (a) enabled DNS security extensions (first documented in 1997 in RFC 2065) on a domain I control and (b) enabled IPv6 (first documented in 1995 in RFC 1883) on my home router, so I think it's time to break out "The Dream of the '90s" from Portlandia: https://youtu.be/TZt-pOc3moc…

Intertwining Algebras and Affine Hecke Algebras for Finite Central Extensions of Classical $p$-adic Groups with Application to Metaplectic Groups
Volker Heiermann, Chenyan Wu
https://arxiv.org/abs/2508.04303

Intertwining Algebras and Affine Hecke Algebras for Finite Central Extensions of Classical $p$-adic Groups with Application to Metaplectic Groups
For a finite central extension $\tilde{G}$ of a classical $p$-adic reductive group, we consider the endomorphism algebra of some induced projective generator à la Bernstein of the category of smooth representations of $\tilde{G}$. In the case where the Levi subgroups decompose, we can compute this algebra to get a result similar to the one previously obtained by the first author for classical $p$-adic groups, showing that this intertwining algebra is a twisted semi-direct product of an affine …

The Flat Cover Conjecture for Monoid Acts
Sean Cox
https://arxiv.org/abs/2507.04155 https://arxiv.org/pdf/2507.04155

The Flat Cover Conjecture for Monoid Acts
We prove that the Flat Cover Conjecture holds for the category of (right) acts over any right-reversible monoid $S$, provided that the flat $S$-acts are closed under stable Rees extensions. The argument shows that the class $\mathcal{F}$-Mono ($S$-act monomorphisms with flat Rees quotient) is cofibrantly generated in such categories, answering a question of Bailey and Renshaw. But cofibrant generation of $\mathcal{SF}$-Mono ($S$-act monomorphisms with \emph{strongly} flat Rees quotient) appears…

Performance analysis of common browser extensions for cryptojacking detection
Dmitry Tanana
https://arxiv.org/abs/2509.02083 https://arxiv.org/pdf/2509.020…

Performance analysis of common browser extensions for cryptojacking detection
This paper considers five extensions for Chromium-based browsers in order to determine how effective can browser-based defenses against cryptojacking available to regular users be. We've examined most popular extensions - MinerBlock, AdGuard AdBlocker, Easy Redirect && Prevent Cryptojacking, CoinEater and Miners Shield, which claim to be designed specifically to identify and stop illegal cryptocurrency mining. An empirically confirmed dataset of 373 distinct cryptojacking-infected websites whic…

Distance restricted matching extensions in regular non-bipartite graphs
Jun Fujisawa
https://arxiv.org/abs/2508.04507 https://arxiv.org/pdf/2508.04507

Distance restricted matching extensions in regular non-bipartite graphs
Let $m$ and $r$ be integers with $m \ge r \ge 3$ and let $G$ be an $r$-regular graph of even order. Let $M$ be a matching in $G$ of size $m$ such that each pair of edges in $M$ is at distance at least $3$. In 2023, Aldred et al. proved that if $G$ is cyclically $(mr-r+1)$-edge-connected and $G$ is bipartite, then there exists a perfect matching of $G$ containing $M$. In this paper, we present non-bipartite analogues of Aldred et al.'s theorem. An odd ear of $U \subseteq V(G)$ is a path of odd l…

Design Support for Multitape Turing Machines
Marco T. Moraz\'an (Seton Hall University), Oliwia Kempinski (University of Maryland), Andr\'es M. Garced (Seton Hall University)
https://arxiv.org/abs/2508.03638

Design Support for Multitape Turing Machines
Many Formal Languages and Automata Theory courses introduce students to Turing machine extensions. One of the most widely-used extensions endows Turing machines with multiple tapes. Although multitape Turing machines are an abstraction to simplify Turing machine design, students find them no less challenging. To aid students in understanding these machines, the FSM programming language provides support for their definition and execution. This, however, has proven insufficient for many students …

Every once in a while, I will complain about cookie modals appearing on every damn site that I visit... today is one of those days 😠
Is there no way to stop them?! I've tried a few extensions but nothing completely works

Putting Perspective into OWL [sic]: Complexity-Neutral Standpoint Reasoning for Ontology Languages via Monodic S5 over Counting Two-Variable First-Order Logic (Extended Version with Appendix)
Luc\'ia G\'omez \'Alvarez, Sebastian Rudolph
https://arxiv.org/abs/2508.00653

Putting Perspective into OWL [sic]: Complexity-Neutral Standpoint Reasoning for Ontology Languages via Monodic S5 over Counting Two-Variable First-Order Logic (Extended Version with Appendix)
Standpoint extensions of knowledge representation formalisms have been recently introduced as a means to incorporate multi-perspective modelling and reasoning through modal operators that attribute pieces of knowledge to specific entities or agents. In these extensions, the integration between conceptual modelling and perspective annotations can vary in strength, with monodic standpoint extensions offering a well-balanced approach. They allow for advanced modelling features, such as the express…

Analogue of the Galois Theory for normal fields and B-extensions (characteristic free approach)
V. V. Bavula
https://arxiv.org/abs/2509.01779 https://arxiv…

Analogue of the Galois Theory for normal fields and B-extensions (characteristic free approach)
The aim of the paper is to introduce B-extensions which are the most symmetrical finite field extensions (a finite field extension $L/K$ is called a {\it B-extension} if the endomorphism algebra ${\rm End}_K(L)$ is generated by the algebra of differential operators ${\cal D} (L/K)$ on the $K$-algebra $L$ and the automorphism group $G(L/K):={\rm Aut}_{K-{\rm alg}}(L)$) and to obtain an analogue of the Galois Theory for B-extensions. Surprisingly, the class of B-extensions coincides with the clas…

The F-pure threshold versus the a-invariant for standard graded rings
Suchitra Pande
https://arxiv.org/abs/2508.04940 https://arxiv.org/pdf/2508.04940

The F-pure threshold versus the a-invariant for standard graded rings
Hirose, Watanabe and Yoshida conjectured a criterion for a standard graded strongly $F$-regular ring to be Gorenstein in terms of the $F$-pure threshold. We complete the proof of this conjecture. We also prove natural extensions of the conjecture to section rings of normal, $F$-split projective varieties with respect to globally generated ample divisors. Our proof exploits the geometry of the Proj of the graded ring.

Extensions of the Bonnet-Myers Theorem
Ronggang Li, Shaoqing Wang
https://arxiv.org/abs/2509.02126 https://arxiv.org/pdf/2509.02126

Extensions of the Bonnet-Myers Theorem
In this paper, we present extensions of the classical Bonnet-Myers theorem for Riemannian manifolds with nonnegative Ricci curvature. Our results provide criteria for compactness and a method for estimating the diameter of such manifolds under general curvature conditions. As applications, we establish compactness theorems for manifolds whose Ricci curvature decays at polynomial or exponential rates.

Properties and Decoding of Twisted GRS Codes and Their Extensions
Yang Li, Martianus Frederic Ezerman, Huimin Lao, San Ling
https://arxiv.org/abs/2508.02382 https://

Properties and Decoding of Twisted GRS Codes and Their Extensions
Maximum distance separable (MDS) codes that are not equivalent to generalized Reed-Solomon (GRS) codes are called non-GRS MDS codes. Alongside near MDS (NMDS) codes, they are applicable in communication, cryptography, and storage systems. From theoretical perspective, it is particularly intriguing to investigate families of linear codes in which each element can be determined to be either a non-GRS MDS or an NMDS code. Two promising candidates for such families emerge from what is known as twis…

Coefficient estimates for the class of q-starlike functions
Ming Li, Ao-Li Zhu
https://arxiv.org/abs/2508.03223 https://arxiv.org/pdf/2508.03223

Coefficient estimates for the class of q-starlike functions
By employing the $q$-difference operator, various classes of $q$-extensions of starlike functions have emerged from many different viewpoints and perspectives. Ruscheweyh's work unified these $q$-extensions with convolution operations. Inspired by prior research, this paper delves into the class of $q$-starlike functions defined via convolution. First, we provide comprehensive analysis of its Taylor coefficients by using the Carathéodory-Toeplitz Theorem and its corollaries. Precise upper boun…

GOP Declares Tax-Cut Extensions 'Free' to Obscure Megabill's Cost (Richard Rubin/Wall Street Journal)
https://www.wsj.com/politics/policy/gop-declares-tax-cut-extensions-free-to-obscure-megabills-cost-4c4089bf?st=UuBkoQ&reflink=article_copyURL_share
http://www.memeorandum.com/250629/p77#a250629p77

MARVEL: An End-to-End Framework for Generating Model-Class Aware Custom RISC-V Extensions for Lightweight AI
Ajay Kumar M, Cian O'Mahoney, Pedro Kreutz Werle, Shreejith Shanker, Dimitrios S. Nikolopoulos, Bo Ji, Hans Vandierendonck, Deepu John
https://arxiv.org/abs/2508.01800

MARVEL: An End-to-End Framework for Generating Model-Class Aware Custom RISC-V Extensions for Lightweight AI
Deploying deep neural networks (DNNs) on resource-constrained IoT devices remains a challenging problem, often requiring hardware modifications tailored to individual AI models. Existing accelerator-generation tools, such as AMD's FINN, do not adequately address extreme resource limitations faced by IoT endpoints operating in bare-metal environments without an operating system (OS). To overcome these constraints, we propose MARVEL-an automated, end-to-end framework that generates custom RISC-V …

On integral extensions between the abelianization functor and its symmetric powers
Minkyu Kim, Christine Vespa
https://arxiv.org/abs/2509.02105 https://arx…

On integral extensions between the abelianization functor and its symmetric powers
This paper aims to study Ext-groups between certain functors defined on the category of finitely generated free groups. Rational Ext-groups between the abelianization functor and its symmetric powers are known, and are almost always equal to zero. Recently, using homotopical methods, Arone constructed an explicit bounded complex whose homology corresponds to the integral Ext-groups between the abelianization functor and its symmetric powers. The homology of this complex is far from being trivia…

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-…

Correspondence, Wells and Hochschild-Serre sequences for nonabelian extensions of multiplicative Lie algebras
Alexander Wires, Dev Karan Singh, Shiv Datt Kumar
https://arxiv.org/abs/2509.03019

Correspondence, Wells and Hochschild-Serre sequences for nonabelian extensions of multiplicative Lie algebras
For nonabelian $2^{\mathrm{nd}}$-cohomology of multiplicative Lie algebras, we properly generalize from the group case three classic results. We prove a Correspondence theorem which compares $2^{\mathrm{nd}}$-cohomology associated to a realized abstract kernel to the abelian $2^{\mathrm{nd}}$-cohomology group over the algebraic center. For arbitrary extensions, we prove a Wells's Theorem characterizing ideal-preserving automorphisms and establish the 1-dimensional Lyndon-Hochschild-Serre exact …

Perpetual American Standard and Lookback Options in Insider Models with Progressively Enlarged Filtrations
Pavel V. Gapeev, Libo Li
https://arxiv.org/abs/2507.03470

Perpetual American Standard and Lookback Options in Insider Models with Progressively Enlarged Filtrations
We derive closed-form solutions to the optimal stopping problems related to the pricing of perpetual American standard and lookback put and call options in the extensions of the Black-Merton-Scholes model with progressively enlarged filtrations. More specifically, the information available to the insider is modelled by Brownian filtrations progressively enlarged with the times of either the global maximum or minimum of the underlying risky asset price over the infinite time interval, which is n…

After investing $250M on Gardner, Wilson, are the Jets done spending? https://www.espn.com/nfl/story/_/id/45809435/new-york-jets-contract-extensions-breece-hall-jermaine-johnson-vera-tucker

A researcher says 245 extensions on nearly 1M devices are overriding security protections to turn browsers into engines that scrape websites for a paid service (Dan Goodin/Ars Technica)
https://arstechnica.com/security/2025/

Browser extensions turn nearly 1 million browsers into website-scraping bots
Extensions load unknown sites into invisible Windows. What could go wrong?

Lifting noncommutative principal bundles along central extensions
Stefan Wagner
https://arxiv.org/abs/2509.02263 https://arxiv.org/pdf/2509.02263

Lifting noncommutative principal bundles along central extensions
Motivated by the classical theory of spin structures, we develop a theory for lifting free C$^*$-dynamical systems, a.k.a. noncommutative principal bundles, along central extensions. This theory extends the bundle-theoretic notion of spin structures and yields a complete existence and classification result for such lifts. Using factor system techniques and Picard formalism, our approach introduces new invariants and obstruction classes, thereby unifying geometric, cohomological, and operator-al…

Micah Parsons tops list of 5 Cowboys who still need contract extensions after Jake Ferguson deal https://www.sportingnews.com/us/nfl/dallas-cowboys/news/micah-parsons-tops-list-5-cowboys-need-…

from my link log —
Postgres extensions in Rust.
https://depth-first.com/articles/2021/08/25/postgres-extensions-in-rust/
saved 2021-08-29

Postgres Extensions in Rust
Opening a new path to high-performance, domain-specific database applications.

McKinsey-Tarski algebras and Raney extensions
Guram Bezhanishvili, Ranjitha Raviprakash, Anna Laura Suarez, Joanne Walters-Wayland
https://arxiv.org/abs/2509.01233 https://

McKinsey-Tarski algebras and Raney extensions
We introduce the notion of Raney morphism between MT-algebras and show that the resulting category is equivalent to the category of Raney extensions. This is done by generalizing the construction of the Funayama envelope of a frame. The resulting notion of the $T_0$-hull of a Raney extension generalizes that of the $T_D$-hull of a frame.

Commuting self-adjoint extensions of the partial differential operators on disconnected sets
Piyali Chakraborty, Dorin Dutkay
https://arxiv.org/abs/2506.23720

Commuting self-adjoint extensions of the partial differential operators on disconnected sets
In connection with the Fuglede conjecture, we study the existence of commuting self-adjoint extensions of the partial differential operators on arbitrary, possibly disconnected domains in $\br^d$, the associated unitary group, the spectral measure and some geometric properties.

Higher-order Chern-Simons extensions to QED in $2 1$ dimensions
Ricardo Avila, Albert Yu. Petrov, Carlos M. Reyes, C\'esar Riquelme, Angel Sanchez
https://arxiv.org/abs/2508.21266

Higher-order Chern-Simons extensions to QED in $2+1$ dimensions
In this work, we investigate radiative corrections in the higher-order extension of the Maxwell-Chern-Simons model coupled to standard spinor matter in $2+1$ dimensions. We begin analyzing the higher-order gauge sector, where we find the modes and the polarizations vectors associated to a massive photon and ghost field. The higher-order gauge model is canonically quantized and as expected the resulting algebra of creation and annihilation operators corresponds to an indefinite metric in Hilbert…

I am wondering what signals does Apple need to hear to stop pretending like Safari is still a great browser.
It is a great browser iif you haven’t used any others.
Safari has the smallest number of extensions.
Safari has the biggest chances to not work on a website.
Safari is not the fastest browser.

Class of extensions of real field and their topological properties
E. V. Alexandrov
https://arxiv.org/abs/2506.14838 https://arxiv.or…

Class of extensions of real field and their topological properties
Proper classes of extensions of real field was defined and topological properties of these extensions were studied. These extensions can be connected, in this case such set is not closed under binary operations (addition and multiplication), and not connected, in this case this extension is linearly ordered field. In the future these constructions can be applied to building measure that "feels" set of zero Lebesgue measure.

Linear Complementary Pairs of Algebraic Geometry Codes via Kummer Extensions
Huang Junjie, Chen Haojie, Zhang Huachao, Zhao Chang-An
https://arxiv.org/abs/2506.23081

Linear Complementary Pairs of Algebraic Geometry Codes via Kummer Extensions
Due to their widespread applications, linear complementary pairs (LCPs) have attracted much attention in recent years. In this paper, we determine explicit construction of non-special divisors of degree $g$ and $g-1$ on Kummer extensions with specific properties. In addition, we present several methods for constructing LCPs of algebraic geometry codes (AG Codes) via Kummer extensions. These results are applied in constructing explicit LCPs of AG Codes from subcovers of the BM curve, elliptic fu…

Open 2D TFTs admit initial open-closed extensions
Shaul Barkan, Jan Steinebrunner, Adela YiYu Zhang
https://arxiv.org/abs/2509.02553 https://arxiv.org/pdf/…

Open 2D TFTs admit initial open-closed extensions
We show that any open 2-dimensional topological field theory valued in a symmetric monoidal $\infty$-category (with suitable colimits) extends canonically to an open-closed field theory whose value at the circle is the Hochschild homology object of its value at the disk. As a corollary, we obtain an action of the moduli spaces of surfaces on the Hochschild homology object of $E_1$-Calabi-Yau algebras. This provides a space level refinement of previous work of Costello over $\mathbb{Q}$ and Wahl…

Examining MPI and its Extensions for Asynchronous Multithreaded Communication
Jiakun Yan, Marc Snir, Yanfei Guo
https://arxiv.org/abs/2508.18667 https://ar…

Examining MPI and its Extensions for Asynchronous Multithreaded Communication
The increasing complexity of HPC architectures and the growing adoption of irregular scientific algorithms demand efficient support for asynchronous, multithreaded communication. This need is especially pronounced with Asynchronous Many-Task (AMT) systems. This communication pattern was not a consideration during the design of the original MPI specification. The MPI community has recently introduced several extensions to address these evolving requirements. This work evaluates two such extensio…

Quantum Cocycle Invariants of Knots from Yang-Baxter Cohomology
Masahico Saito, Emanuele Zappala
https://arxiv.org/abs/2509.04267 https://arxiv.org/pdf/250…

Quantum Cocycle Invariants of Knots from Yang-Baxter Cohomology
Yang-Baxter operators (YBOs) have been employed to construct quantum knot invariants. More recently, cohomology theories for YBOs have been independently developed, drawing inspiration from analogous theories for quandles and other discrete algebraic structures. Quandle cohomology, in particular, gives rise to cocycle invariants for knots via $2$-cocycles, which are closely related to quandle extensions, and knotted surfaces via $3$-cocycles. These quandle cocycle knot invariants have also been…

Bricks and $\tau$-tilting theory under base field extensions
Erlend D. B{\o}rve, Eric J. Hanson, Maximilian Kaipel
https://arxiv.org/abs/2508.01040 https://

Bricks and $τ$-tilting theory under base field extensions
Let $K:k$ be a field extension and let $Λ$ be a finite-dimensional $k$-algebra. We investigate the relationship between $Λ$ and $Λ_K = Λ\otimes_k K$ with particular emphasis on various aspects of $τ$-tilting theory and bricks. We show that many types of objects for $Λ$ lift injectively to the same type of object for $Λ_K$, and many common constructions in $τ$-tilting theory commute with the process of extending the base field. One of our main applications is the construction of a faithf…

Extensions of integral orthoregular sets and icubes
M\'arton Erd\'elyi, P\'eter Maga, Gergely Z\'abr\'adi
https://arxiv.org/abs/2508.01196 https://

Extensions of integral orthoregular sets and icubes
In this paper, we study the question when a (rational or Gaussian) integral vector can be extended to an integral orthogonal basis consisting of vectors of equal length. We also study when a set of integral vectors has such an extension. Some necessary conditions are given which are proven to be sufficient in dimensions $3$ and $4$.

Constraints on Logarithmic Model Extensions of Symmetric Teleparallel Gravity
Purnendu Karmakar, Sandeep Haridasu, Atsushi Nishizawa
https://arxiv.org/abs/2508.21054 https://

Constraints on Logarithmic Model Extensions of Symmetric Teleparallel Gravity
We address various cosmological phenomenologies in the symmetric teleparallel framework both in background and perturbation such as cosmic expansion, gravitational coupling constant, gravitational waves propagation. Focusing on logarithmic extensions of $f(Q)$ models, we performed Bayesian analysis using the most-recent cosmological data, DESI DR2, Pantheon+. We also utilized a compilation of redshift space distortions ($f σ_8$) dataset to constrain the growth of structures in each of the mode…

On one hand I’m super excited how Python’s packaging user land is great now.
On the other hand I don’t know if I even want everyone to know how cursed setuptools is and how everything with C/C /Fortran extensions still runs a setup.py somewhere where the sun doesn’t shine.

Interrelation among Solvable Potentials and Extensions of SWKB Quantization Condition
Yuta Nasuda
https://arxiv.org/abs/2507.22381 https://arxiv.org/pdf/25…

Interrelation among Solvable Potentials and Extensions of SWKB Quantization Condition
The exactly solvable Schrödinger equations with the conventional shape-invariant potentials are known to be related with each other through point cannonical transformations. In this paper, we extend the idea to integral formulae called the SWKB integrals. By virtue of this, we derive extended forms of the SWKB quantization condition for certain classes of Natanzon potentials. We further demonstrate that the same idea can also be applied to obtain an exact quantization rule for a subclass of qu…

i should make a build of vscodium that can install all of the proprietary extensions
my next best bet for a usable editor is sublime text, and unfortunately st4 doesn't seem like it's particularly actively developed anymore. yes, it's still maintained, but i expect a much better editor today than in 2010

Finite abelian groups acting on rationally connected threefolds II: groups of K3 type
Konstantin Loginov, Antoine Pinardin, Zhijia Zhang
https://arxiv.org/abs/2509.02531 https:/…

Finite abelian groups acting on rationally connected threefolds II: groups of K3 type
We study finite abelian groups acting on three-dimensional rationally connected varieties. We concentrate on the groups of K3 type, that is, abelian extensions by a cyclic group of groups that faithfully act on a K3 surface. In particular, if a finite abelian group faithfully acts on a threefold preserving a K3 surface (with at worst du Val singularities), then such a group is of K3 type. We prove a classification theorem for the groups of K3 type which can act on three-dimensional rationally c…

Too bad that you can't test the theme feature of #GNOME on a live distro since setting up "gnome-shell-extensions" requires a reboot to enable it.
Edit: it wasn't the "gnome-shell-extensions", reboot was required for enabling "User Themes" (via Extensions).
However, a logout/login was OK as well and it did work on my Debian live distro again (logout do…

Exponential mixing of frame flows for three dimensional manifolds of quarter-pinched negative curvature
Mark Pollicott, Daofei Zhang
https://arxiv.org/abs/2508.01593 https://

Exponential mixing of frame flows for three dimensional manifolds of quarter-pinched negative curvature
For a compact three-dimensional smooth Riemannian manifold of strictly 1/4-pinched negative sectional curvature, we establish exponential mixing of the frame flow with respect to the normalized volume. More generally this result extends to a class of torus extensions of Anosov flows, subject to assumptions on the Brin transitivity group and the smoothness of the stable subbundle. Our approach is based on a simplified dynamical model for studying the extension flow, constructed via a Young tower…

3 Great Extensions for #VSCode - #dotNet
https://improveandrepeat.com/2025/07/3

3 Great Extensions for VS Code - Improve & Repeat
None

With less than a month to go, House panel votes to extend popular cyber programs https://therecord.media/house-homeland-committee-cyber-information-sharing-law

An Algorithm for Computing Hopf--Galois Structures and Skew Bracoids of Low Degree
Andrew Darlington
https://arxiv.org/abs/2508.03372 https://arxiv.org/pdf…

An Algorithm for Computing Hopf--Galois Structures and Skew Bracoids of Low Degree
Making use of the fact that Hopf-Galois structures on separable extensions and skew bracoids are both intrinsically connected to transitive subgroups of the holomorph, we present an algorithm to classify and enumerate these objects in several low degree cases. Our approach allows us to greatly extend existing computational results for Hopf-Galois structures, while building on the existing algorithms presented in this area.

Restricted Central Extensions of Restricted Heisenberg Lie Superalgebras
Yong Yang
https://arxiv.org/abs/2509.00426 https://arxiv.org/pdf/2509.00426…

Restricted Central Extensions of Restricted Heisenberg Lie Superalgebras
Restricted Heisenberg Lie superalgebras are studied over an algebraically closed field F of characteristic p > 2. We use the ordinary 1- and 2-cohomology spaces with trivial coefficients to compute the restricted 2-cohomology spaces. As an application, the corresponding restricted one-dimensional central extensions are described.

Time Resolution Independent Operator Learning
Diab W. Abueidda, Mbebo Nonna, Panos Pantidis, Mostafa E. Mobasher
https://arxiv.org/abs/2507.02524 https://

Time Resolution Independent Operator Learning
Accurately learning solution operators for time-dependent partial differential equations (PDEs) from sparse and irregular data remains a challenging task. Recurrent DeepONet extensions inherit the discrete-time limitations of sequence-to-sequence (seq2seq) RNN architectures, while neural-ODE surrogates cannot incorporate new inputs after initialization. We introduce NCDE-DeepONet, a continuous-time operator network that embeds a Neural Controlled Differential Equation (NCDE) in the branch and a…

The @… recently released version 3 of the #PNG spec more than 2 decades after version 2 was released in 2003. The new spec largely makes official various extensions already in use like animated PNGs, HDR support, and EXIF metadata, so many browsers and graphics apps already largely suppo…

W-algebras as conformal extensions of affine VOAs
Dra\v{z}en Adamovi\'c, Tomoyuki Arakawa, Thomas Creutzig, Andrew R. Linshaw, Anne Moreau, Pierluigi M\"oseneder Frajria, Paolo Papi
https://arxiv.org/abs/2508.18889

W-algebras as conformal extensions of affine VOAs
We provide a criterion for a vertex operator superalgebra homomorphism from an affine vertex algebra to another vertex superalgebra to be conformal, and an additional criterion that guarantees that this homomorphism is surjective. This situation is applied to W-algebras and W-superalgebras and we list all cases where our criterion applies. This gives many new examples of W-algebras that collapse to affine vertex algebras or are conformal extensions. In particular, we provide many examples of si…

High-Order Schemes for Hyperbolic Conservation Laws Using Young Measures
Shaoshuai Chu, Michael Herty
https://arxiv.org/abs/2509.02107 https://arxiv.org/pd…

High-Order Schemes for Hyperbolic Conservation Laws Using Young Measures
We develop high-order numerical schemes to solve random hyperbolic conservation laws using linear programming. The proposed schemes are high-order extensions of the existing first-order scheme introduced in [{\sc S. Chu, M. Herty, M. Lukáčová-Medvi{\softd}ová, and Y. Zhou}, solving random hyperbolic conservation laws using linear programming], where a novel structure-preserving numerical method using a concept of generalized, measure-valued solutions to solve random hyperbolic systems of co…

Data driven modeling of multiple interest rates with generalized Vasicek-type models
Pauliina Ilmonen, Milla Laurikkala, Kostiantyn Ralchenko, Tommi Sottinen, Lauri Viitasaari
https://arxiv.org/abs/2509.03208

Data driven modeling of multiple interest rates with generalized Vasicek-type models
The Vasicek model is a commonly used interest rate model, and there exist many extensions and generalizations of it. However, most generalizations of the model are either univariate or assume the noise process to be Gaussian, or both. In this article, we study a generalized multivariate Vasicek model that allows simultaneous modeling of multiple interest rates while making minimal assumptions. In the model, we only assume that the noise process has stationary increments with a suitably decaying…

Replaced article(s) found for quant-ph. https://arxiv.org/list/quant-ph/new
[3/3]:
- Interrelation among Solvable Potentials and Extensions of SWKB Quantization Condition
Yuta Nasuda
…

Decidability of Extensions of Presburger Arithmetic by Hardy Field Functions
Hera Brown, Jakub Konieczny
https://arxiv.org/abs/2508.19206 https://arxiv.org…

Decidability of Extensions of Presburger Arithmetic by Hardy Field Functions
We study the extension of Presburger arithmetic by the class of sub-polynomial Hardy field functions, and show the majority of these extensions to be undecidable. More precisely, we show that the theory $\mathrm{Th}(\mathbb{Z}; <, +, \lfloor f \rceil)$, where $f$ is a Hardy field function and $\lfloor \cdot \rceil$ the nearest integer operator, is undecidable when $f$ grows polynomially faster than $x$. Further, we show that when $f$ grows sub-linearly quickly, but still as fast as some polynom…

A search for dark matter produced in association with a dark Higgs boson decaying into a Higgs boson pair in 3$b$ or 4$b$ final states using $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
ATLAS Collaboration
https://arxiv.org/abs/2507.02175

A search for dark matter produced in association with a dark Higgs boson decaying into a Higgs boson pair in 3$b$ or 4$b$ final states using $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
A search is performed for dark matter particles produced in association with a resonant pair of Higgs bosons using 140 fb$^{-1}$ of proton--proton collisions at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector at the Large Hadron Collider. This signature is expected in some extensions of the Standard Model predicting the production of dark matter particles, and is interpreted in terms of a dark Higgs model containing a $Z'$ mediator in which the dark Higgs boson $s$ decays into …

Zero Probability of the Cut Locus of a Fr\'echet Mean on a Riemannian Manifold
Alexander Lytchak, Stephan F. Huckemann
https://arxiv.org/abs/2508.00747 https://

Zero Probability of the Cut Locus of a Fréchet Mean on a Riemannian Manifold
We show that the cut locus of a Fréchet mean of a random variable on a connected and complete Riemanian manifold has zero probability, a result known previously in special cases and conjectured in general. In application, we rule out stickiness, while providing examples of nowhere smooth Fréchet functions and we discuss extensions of the statement to Fréchet $p$-means, for $p\neq 2$, as well as to noncomplete manifolds and more general metric spaces.

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[3/5]:
- Active learning for level set estimation under input uncertainty and its extensions
Yu Inatsu, Masayuki Karasuyama, Keiichi Inoue, Ichiro Takeuchi

Jets' Breece Hall on RB extensions: James Cook, Kyren Williams have 'done much more' in NFL https://www.nfl.com/news/jets-breece-hall-rb-extensions-james-cook-kyren-williams-done-much-more-in-nfl

Extensions of realizable Hamiltonian and complexity one GKM$_4$ graphs
Oliver Goertsches, Grigory Solomadin
https://arxiv.org/abs/2509.00392 https://arxiv.…

Extensions of realizable Hamiltonian and complexity one GKM$_4$ graphs
We prove that the GKM graphs of GKM$_4$ manifolds that are either Hamiltonian or of complexity one extend to torus graphs. The arguments are based on a reformulation of the extension problem in terms of a natural representation of the fundamental group of the GKM graph, using a coordinate-free version of the axial function group of Kuroki, as well as on covers of GKM graphs and acyclicity results for orbit spaces of GKM manifolds.

from my link log —
The tar archive format, its extensions, and why GNU tar extracts in quadratic time.
https://mort.coffee/home/tar/
saved 2025-07-03 http…

Passwords and FIDO2 Are Meant To Be Secret: A Practical Secure Authentication Channel for Web Browsers
Anuj Gautam, Tarun Yadav, Garrett Smith, Kent Seamons, Scott Ruoti
https://arxiv.org/abs/2509.02289

Passwords and FIDO2 Are Meant To Be Secret: A Practical Secure Authentication Channel for Web Browsers
Password managers provide significant security benefits to users. However, malicious client-side scripts and browser extensions can steal passwords after the manager has autofilled them into the web page. In this paper, we extend prior work by Stock and Johns, showing how password autofill can be hardened to prevent these local attacks. We implement our design in the Firefox browser and conduct experiments demonstrating that our defense successfully protects passwords from XSS attacks and malic…

The derivator of a dg-category
Francesco Genovese, Chiara Sava, Jan \v{S}\v{t}ov\'i\v{c}ek
https://arxiv.org/abs/2508.02612 https://arxiv.org/pdf/2508.…

The derivator of a dg-category
In this work, we construct the stable derivator associated to a homotopically complete and cocomplete dg-category by explicitly defining homotopy Kan extensions via suitable weighted homotopy limits and colimits in dg-categories. By restricting the domain of the derivator to finite direct categories, we obtain a well-defined derivator even for pretriangulated dg-categories. This definition enables an explicit description of the derivator associated to a weakly idempotent complete Frobenius exac…

Abelian extensions of five-dimensional solvable Leibniz algebras
A. Kh. Khudoyberdiyev, S. A. Sheraliyeva
https://arxiv.org/abs/2506.23528 https://

Abelian extensions of five-dimensional solvable Leibniz algebras
In this work, we extend the central extension method for solvable Leibniz algebras. Using this method, a complete classification of one-dimensional abelian extensions of five-dimensional solvable Leibniz algebras with a non-trivial three-dimensional nilradical is obtained. Furthermore, we explore extensions of solvable Leibniz algebras whose nilradical is null-filiform, establishing that, in this case, there exists a unique solvable abelian extension.

On pre-local tabularity above $\mathrm{S4}\times \mathrm{S4}$
Ilya B. Shapirovsky, Vladislav V. Sliusarev
https://arxiv.org/abs/2506.20874 https://

On pre-local tabularity above $\mathrm{S4}\times \mathrm{S4}$
We investigate pre-local tabularity in normal extensions of the logic $\mathrm{S4}\times \mathrm{S4}$. We show that there are exactly four pre-locally tabular logics in normal extensions of products of finite height, and that every non-locally tabular logic in this family is contained in one of them. We also give an axiomatic criterion of local tabularity above the logic of products with Noetherian skeletons. Then we construct examples of pre-locally tabular extensions of $\mathrm{S4}\times \ma…

A Calogero Model with root string representatives of infinite order Coxeter orbits
Andreas Fring
https://arxiv.org/abs/2509.01738 https://arxiv.org/pdf/250…

A Calogero Model with root string representatives of infinite order Coxeter orbits
We present a worked example for the new extensions of the multi-particle Calogero model endowed with infinite Weyl group symmetry of affine and hyperbolic type. Building upon the hyperbolic extension of the $A_3$-Kac-Moody algebra, we construct an explicit realisation of the model in terms of infinite root systems generated from Coxeter orbits. To address the challenge of summing over infinitely many roots, we introduce root string representatives that span the invariant root space while preser…

Ramification groups of Galois extensions over local fields of positive characteristic with Galois group isomorphic to the group of unitriangular matrices
Koto Imai
https://arxiv.org/abs/2508.21312

Ramification groups of Galois extensions over local fields of positive characteristic with Galois group isomorphic to the group of unitriangular matrices
We study the ramification groups of finite Galois extensions $L/K$ of a complete discrete valuation field $K$ of equal characteristic $p>0$ with perfect residue field and Galois group isomorphic to the group of unitriangular matrices $UT_n(\mathbb{F}_p)$ over $\mathbb{F}_p$. We show that the upper ramification breaks can be expressed as a linear function of the valuation of the entries of a matrix directly constructed from the coefficients of a defining equation of the extension. This allows us…

Improved Upper Bounds for Numerical Radius Inequalities of Operator Matrices and Their Applications
M. H. M. Rashid
https://arxiv.org/abs/2508.00845 https://

Improved Upper Bounds for Numerical Radius Inequalities of Operator Matrices and Their Applications
This study presents new upper bounds for the numerical radii of operator matrices, with a focus on $n \times n$ and $2 \times 2$ block matrices acting on Hilbert space direct sums. By employing techniques such as the Hölder-McCarthy inequality, Jensen's inequality, Bohr's inequality, and extensions of the Buzano inequality, we derive improved estimates that refine classical results by Kittaneh, El-Haddad, Dragomir, Buzano, and others. Our main contributions include bounds for general operator …

Varieties and pure symbols
Alexander Vishik
https://arxiv.org/abs/2509.00592 https://arxiv.org/pdf/2509.00592

Varieties and pure symbols
In this article, we prove that the 2-isotropy of any projective variety is controlled by a pure symbol in the Milnor's K-theory (mod 2) of the flexible closure of the base field. We also show that such pure symbols control the 2-equivalence of field extensions as well as the numerical equivalence of algebraic cycles (with mod 2 coefficients).

Matt LaFleur, Brian Gutekunst on hot seat? What Packers coach, GM need to accomplish to receive extensions

https://www.cbssports.com/nfl/news/matt…

Does Micah Parsons' trade request mean things are really over for him in Dallas? https://www.nytimes.com/athletic/6531051/2025/08/01/micah-parsons-trade-request-cowboys-jerry-jones/

Trump threatens 'no extensions' on new Aug. 1 tariff deadline, warns of higher import taxes (NBC News)
https://www.nbcnews.com/business/business-news/trump-threatens-no-extensions-aug-1-tariff-deadline-what-countries-rcna217536
http://www.memeorandum.com/250709/p7#a250709p7

5 Helpful Extensions for #VisualStudio 2022 - #dotNet
https://improveandrepeat.com/2025/0…

5 Helpful Extensions for Visual Studio 2022 - Improve & Repeat
None

In Search of Homology for Quasigroups of Bol-Moufang Type
Anthony Christiana, Ben Clingenpeel, Huizheng Guo, Jinseok Oh, Jozef H. Przytycki, Anna Zamojska-Dzienio
https://arxiv.org/abs/2508.21268

In Search of Homology for Quasigroups of Bol-Moufang Type
We initiate (co)homology theory for quasigroups of Bol-Moufang type based on analysis of their extensions by affine quasigroups of the same type. We use these extensions to define second and third boundary operations, $\partial_2(x,y)$ and $\partial_3(x,y,z)$, respectively. We use these definitions to compute the second homology groups for several examples from the work of Phillips and Vojtechovsky. We speculate about the relation between these homology groups and those obtained from a small ca…

Replaced article(s) found for math.CV. https://arxiv.org/list/math.CV/new
[1/1]:
- Quasiconformal Extensions of Harmonic Univalent Mappings of the Unit Disk
Xiu-Shuang Ma

The Baum-Connes conjecture for extensions revisited
Jianguo Zhang
https://arxiv.org/abs/2506.18446 https://arxiv.org/pdf/2506.18446…

The Baum-Connes conjecture for extensions revisited
In this paper, we verify that the Baum-Connes conjecture with coefficients is closed under group extensions. More precisely, for an extension $1\rightarrow N \rightarrow Γ\rightarrow Γ/ N \rightarrow 1$ of discrete countable groups, we prove that the Baum-Connes conjecture with coefficients holds for $Γ$ if it holds for $N$ and $Γ/ N$. This result will enlarge the class of groups satisfying the Baum-Connes conjecture with coefficients.

Some Extensions of Endo-Noetherian Rings
R. M. Salem, R. E. Abdel-Khalek, N. Abdelnasser
https://arxiv.org/abs/2507.23668 https://arxiv.org/pdf/2507.23668

Some Extensions of Endo-Noetherian Rings
In this article, we proceed on the transfer of the left endo-Noetherian property on certain ring extensions. We transfer of the right (left) endo-Noetherian property to the right (left) quotient rings. For a subring $T$ of $R$ and a finite set of indeterminates $X$, we prove that $T + XR[[X]]$ is left endo-Noetherian if and only if $R[[X]]$ is left endo-Noetherian. In addition, we prove that the subring $Λ:=\{ f \in R[[S,ω]]: f(1) \in T \}$ of the skew generalized power series ring $R[[S, ω]…

Analytic Linearization and Holomorphic Extensions of Proper Groupoids
Rui Loja Fernandes, Ning Jiang
https://arxiv.org/abs/2508.18036 https://arxiv.org/pdf…

Analytic Linearization and Holomorphic Extensions of Proper Groupoids
We establish analytic linearization of s-proper analytic groupoids around invariant submanifolds. We apply this result to show that any such groupoid admits a holomorphic extension.

Projective length, phantom extensions, and the structure of flat modules
Matteo Casarosa, Martino Lupini
https://arxiv.org/abs/2506.17982 https://

Projective length, phantom extensions, and the structure of flat modules
We consider the natural generalization of the notion of the order of a phantom map from the topological setting to triangulated categories. When applied to the derived category of the category of countable flat modules over a countable Dedekind domain, this yields a notion of\emph{\ phantom extension} of order $α<ω_{1}$. We provide a complexity-theoretic characterization of the module $\mathrm{Ph}% ^{α}\mathrm{Ext}\left( C,A\right) $ of phantom extensions of order $α$ with respect to the st…

Explicit Constructions of Sum-Rank Metric Codes from Quadratic Kummer Extensions
Zhu Yunlong, Zhao Chang-An
https://arxiv.org/abs/2506.18653 https://

Explicit Constructions of Sum-Rank Metric Codes from Quadratic Kummer Extensions
This paper presents new constructions of sum-rank metric codes derived from algebraic function fields, while the existing results about such codes remain limited. A central challenge in this field involves the determination of parameters. We address this challenge through quadratic Kummer extensions, and propose two general constructions of $2\times2$ sum-rank codes. The novel sum-rank metric code constructions derived from algebraic function fields demonstrate superior code lengths compared to…

Combinatorial Extensions on Andrews and El Bachraoui's Almost-Distinct Partitions
Brian Hopkins
https://arxiv.org/abs/2508.17459 https://arxiv.org/pdf/…

Combinatorial Extensions on Andrews and El Bachraoui's Almost-Distinct Partitions
Andrews and El Bachraoui recently studied integer partitions where the smallest part is repeated a specified number of times and any other parts are distinct. Their results included two ``surprising identities'' for which they requested combinatorial proofs. We provide combinatorial proofs for an infinite family of related identities and also consider the analogous partitions where only the largest part can be repeated. The results give rise to infinite families of inequalities for the number o…

Monomial arrow removal and the finitistic dimension conjecture
Karin Erdmann, Odysseas Giatagantzidis, Chrysostomos Psaroudakis, {\O}yvind Solberg
https://arxiv.org/abs/2506.23747

Monomial arrow removal and the finitistic dimension conjecture
In this paper, we introduce the monomial arrow removal operation for bound quiver algebras, and show that it is a novel reduction technique for determining the finiteness of the finitistic dimension. Our approach first develops a general method within the theory of abelian category cleft extensions. We then demonstrate that the specific conditions of this method are satisfied by the cleft extensions arising from strict monomial arrow removals. This crucial connection is established through the …

On gap sets in arbitrary Kummer extensions of $K(x)$
Ethan Cotterill, Erik A. R. Mendoza, Pietro Speziali
https://arxiv.org/abs/2506.19169 https://

On gap sets in arbitrary Kummer extensions of $K(x)$
Let $K$ be an algebraically closed field, and let $F/K(x)$ be a Kummer extension of function fields of genus $g$. We provide a compact and explicit description of the gap set $G(Q)$ at any totally ramified place $Q$ of the extension $F/K(x)$. As a consequence, we deduce structural properties of the Weierstrass semigroup $H(Q)$; in particular, we determine a generating set for $H(Q)$, and we characterize its symmetry in certain cases. We also generalize a formula due to Towse that describes the …

$C$-self-adjoint contractive extensions of $C$-symmetric non-densely defined contractions
Yury Arlinskii, Konrad Schm\"udgen
https://arxiv.org/abs/2506.14357

$C$-self-adjoint contractive extensions of $C$-symmetric non-densely defined contractions
Given a conjugation (involution) $C$ on a Hilbert space, $C$-self-adjoint contractive extensions of a non-densely defined $C$-symmetric contraction are studied and parameterizations of all such extensions are obtained. As an application, a proof of an announced result of Glazman \cite{Glazman1} on the existence of maximal dissipative $C$-self-adjoint extensions of a densely defined $C$-symmetric dissipative operator is given.

The Galois Theory (a ring theoretic approach)
V. V. Bavula
https://arxiv.org/abs/2509.01284 https://arxiv.org/pdf/2509.01284…

The Galois Theory (a ring theoretic approach)
The fundamental concepts in the Galois Theory are separable, normal and Galois field extensions. These concepts are central in proofs of the Galois Theory. In the paper, we introduce a new approach, a ring theoretic approach, to the Galois Theory which is based on central simple algebras and none of the above concepts are used or even mentioned. The only concept which is used is `G-extension' (a finite field extension $L/K$ is called a {\em G-extension} if the endomorphism algebra ${\rm End}_K(…

Orlando Brown expects more from 'special' Bengals offense after Ja'Marr Chase, Tee Higgins deals https://www.nfl.com/news/orlando-brown-expecting-more-from-special-bengals-offense-following-ja-…

Transformations of Triads and Seventh Chords: Group Extensions and Duality
Thomas M. Fiore, Thomas Noll, Ethan Bonnell, Hayden Pyle, No\'e Rodriguez, Meredith Williams, Sonia Cannas, Moreno Andreatta
https://arxiv.org/abs/2507.20811

Transformations of Triads and Seventh Chords: Group Extensions and Duality
Transformational music theory, pioneered by David Lewin, uses simply transitive group actions to analyze music. In this paper, we construct a simply transitive group action on a disjoint union of two sets, built from a simply transitive action on each set and an equivariant bijection connecting them. Motivational examples are the omnibus progression and the reflected omnibus progression, which involve the consonant triads and the dominant/half-diminished seventh chords, connected by the inclusi…

Extensions of Abelian Schemes and the Additive Group
Gabriel Ribeiro, Zev Rosengarten
https://arxiv.org/abs/2506.17393 https://arxiv.…

Extensions of Abelian Schemes and the Additive Group
We compute extension sheaves of abelian schemes and of the additive group by the multiplicative group in the fppf topology. Our main results include a generalized and streamlined proof of the Barsotti--Weil formula, the vanishing of $\underline{\operatorname{Ext}}^2(A,\mathbb{G}_m)$ for an abelian scheme $A$ over a general base, and a description of $\underline{\operatorname{Ext}}^1(\mathbb{G}_a,\mathbb{G}_m)$ in characteristic zero.

Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- On $\omega$-strongly measurable cardinals in $\mathbb{P}_{\max}$ extensions
Navin Aksornthong, Takehiko Gappo, James Holland, Grigor Sargsyan

Determining class groups as Galois modules up to equivalence for some nonabelian extensions
Cornelius Greither, Takenori Kataoka
https://arxiv.org/abs/2508.15242 https://…

Determining class groups as Galois modules up to equivalence for some nonabelian extensions
In previous papers, the Galois module structure of minus class groups was studied for abelian CM extensions. In this paper, we discuss some nonabelian cases, focusing on metacyclic extensions. For a certain class of these, we obtain a complete description of the Galois modules that occur as minus class groups, modulo a certain equivalence relation on modules, which was introduced earlier by the same authors.

NFL offseason report cards: Let's grade every team's signings, trades, draft picks and hires https://www.espn.com/nfl/story/_/id/45690070/nfl-offseason-grades-2025-free-agency-draft-trades-extensions-coaching-chang…

Families of p-adic fields
Jordi Gu\`ardia R\'ubies, John W. Jones, Kevin Keating, Sebastian Pauli, David P. Roberts, David Roe
https://arxiv.org/abs/2507.02360

Families of p-adic fields
We improve the database of $p$-adic fields in the LMFDB by systematically using Krasner-Monge polynomials and working relatively as well as absolutely. These improvements organize $p$-adic fields into families. They thereby make long lists of fields more manageable and various theoretical structures more evident. In particular, the database now includes all degree $n$ extensions of $\mathbb{Q}_p$, for $p<200$ and $n \leq 23$.

Cohomological rigidity of conformal Galilei algebras and their central extensions
Abror Khudoyberdiyev, Doston Jumaniyozov
https://arxiv.org/abs/2508.17752 https://

Cohomological rigidity of conformal Galilei algebras and their central extensions
In this paper, we study the second adjoint cohomology of the compexification of the real conformal Galilei algebras \(\mathfrak{cga}_\ell(d,\mathbb{R})\) and their central extensions. These algebras are non-semisimple Lie algebras that appear as non-relativistic analogues of conformal Lie algebras. Using cohomological methods, including the Hochschild-Serre factorization theorem, we compute the space \(H^2(\mathfrak{g}, \mathfrak{g})\) and examine conditions under which these algebras are cohom…

Streamlined WZ method proofs of Van Hamme supercongruences
Andres Valloud
https://arxiv.org/abs/2508.00343 https://arxiv.org/pdf/2508.00343

Streamlined WZ method proofs of Van Hamme supercongruences
Using the WZ method to prove supercongruences critically depends on an inspired WZ pair choice. This paper demonstrates a procedure for finding WZ pair candidates to prove a given supercongruence. When suitable WZ pairs are thus obtained, coupling them with the $p$-adic approximation of $Γ_p$ by Long and Ramakrishna enables uniform proofs for the Van Hamme supercongruences B.2, C.2, D.2, E.2, F.2, G.2, and H.2. This approach also yields the known extensions of G.2 modulo $p^4$, and of H.2 modu…

Courtland Sutton contract: Broncos WR reveals he left money on the table so team could remain competitive

https://www.cbssports.com/nfl/news/courtla

Counting biquadratic number fields with quaternionic and dihedral extensions
Louis M. Gaudet, Siman Wong
https://arxiv.org/abs/2506.21522 https://

Counting biquadratic number fields with quaternionic and dihedral extensions
We establish asymptotic formulae for the number of biquadratic number fields of bounded discriminant that can be embedded into a quaternionic or a dihedral extension. To prove these results, we express the solvability of these inverse Galois problems in terms of Hilbert symbols, and then apply a method of Heath-Brown to bound sums of linked quadratic characters.

Hasse norm principle for extensions of prime squared degree
Yasuhiro Oki
https://arxiv.org/abs/2508.10706 https://arxiv.org/pdf/2508.10706

Hasse norm principle for extensions of prime squared degree
We give an equivalent condition for the validity of the Hasse norm principle for finite separable extensions of prime squared degree of global fields. Our theorem recovers the result of Drakokhrust--Platonov, which claims that the Hasse norm principle holds for adequate extensions of prime squared degree.

Equidistribution of realizable Steinitz classes for cyclic Kummer extensions
Brody Lynch
https://arxiv.org/abs/2506.12999 https://arx…

Equidistribution of realizable Steinitz classes for cyclic Kummer extensions
Let $\ell$ be prime, and $K$ be a number field containing the $\ell$-th roots of unity. We use techniques from classical algebraic number theory to prove that the Steinitz classes of $\mathbb Z/\ell\mathbb Z$ extensions of $K$ are equidistributed among realizable classes in the ideal class group of $K$. For $\ell = 2$, this was proved by Kable and Wright using the deep theory of prehomogeneous vector spaces. Foster proved that Steinitz classes are uniformly distributed between realizable classe…