Tootfinder

Rashod Bateman aims to 'flip that narrative' of Ravens WRs after extension https://www.nfl.com/news/rashod-bateman-aims-to-flip-that-narrative-of-ravens-wrs-after-extension

Jets, Vilardi reach 6-year, $45 million extension https://www.espn.com/nhl/story/_/id/45771151/jets-sign-forward-gabriel-vilardi-6-year-45-million-extension

President Trump plans to sign an executive order this week to grant TikTok a 90-day extension in enforcement of the sale-or-ban law, marking his third extension (CNN)
https://www.cnn.com/2025/06/17/tech/tiktok-trump-ban-delay?Date=202506…

Trump will grant TikTok another 90-day extension in enforcement of sale-or-ban law
TikTok just got another lifeline from the White House, with President Donald Trump set to delay enforcement of the sale-or-ban law by another 90 days.

An extension of the SM with vector-like quarks and hypothetical heavy bosons: model independent parametrisation at NLO order
Chahra Rekaik, Mohamed Sadek Zidi
https://arxiv.org/abs/2506.14663

An extension of the SM with vector-like quarks and hypothetical heavy bosons: model independent parametrisation at NLO order
A model independent parameterization of an extension of the Standard Model including vector-like quarks, new heavy gauge bosons and an extra scalar, involving a minimal number of free parameters, is introduced. Theoretical constraints on the model couplings and hypothetical particle masses are established by making use of perturbative unitarity. The production of heavy charged and neutral gauge bosons which subsequently decay to vector-like quarks at the LHC are investigated at both leading-ord…

Galois cohomology of elliptic curves over anticyclotomic extensions
Dac-Nhan-Tam Nguyen, Sujatha Ramdorai
https://arxiv.org/abs/2508.11835 https://arxiv.or…

Galois cohomology of elliptic curves over anticyclotomic extensions
Let $K$ be an imaginary quadratic field and $p$ be an odd prime number. Let $E/\mathbb{Q}$ be an elliptic curve with good ordinary reduction at $p$. We study the Iwasawa theory of $E$ over the anticyclotomic $\mathbb{Z}_p$-extension of $K$ by adopting a unifying framework. We also study the Galois cohomology of the dual Selmer group of $E$ over the unique $\mathbb{Z}_p^2$-extension of $K$ as well as over the anticyclotomic extension of $K$.

Trump set to grant another extension to avoid TikTok disruption (NBC News)
https://www.nbcnews.com/news/us-news/trump-extension-tiktok-rcna213625
http://www.memeorandum.com/250617/p171#a250617p171

IzhiRISC-V -- a RISC-V-based Processor with Custom ISA Extension for Spiking Neuron Networks Processing with Izhikevich Neurons
Wiktor J. Szczerek, Artur Podobas
https://arxiv.org/abs/2508.12846

IzhiRISC-V -- a RISC-V-based Processor with Custom ISA Extension for Spiking Neuron Networks Processing with Izhikevich Neurons
Spiking Neural Network processing promises to provide high energy efficiency due to the sparsity of the spiking events. However, when realized on general-purpose hardware -- such as a RISC-V processor -- this promise can be undermined and overshadowed by the inefficient code, stemming from repeated usage of basic instructions for updating all the neurons in the network. One of the possible solutions to this issue is the introduction of a custom ISA extension with neuromorphic instructions for s…

This story is cute: A malicious "Solidity" (that's the smart contract language Ethereum and other blockchains use) extension for Cursor, the Vibe-Coding Editor included code that steals your tokens/coins.
I find it funny for two reasons:
- Blockchainers love talking about how you need to verify things you interact with but someone wasn't checking if they have the right extension
- Programming smart contracts is hard because it's a massively hostile envir…

Code highlighting with Cursor AI for $500,000
Kaspersky GReAT experts uncover malicious extensions for Cursor AI that download the Quasar backdoor and a crypto stealer.

Is there a VSCode extension that can capture OpenTelemetry metrics and show them?

Micah Parsons on Cowboys Extension Talks: 'I'm Going to Get Mine No Matter What' https://www.foxsports.com/stories/nfl/micah-parsons-cowboys-extension-talks-im-going-get-mine-no-matter-what

Tietze extension does not always work in constructive mathematics if closed sets are defined as sequentially closed sets
Shun Ding, Yang Wan, Luofei Wang, Siqi Xiao
https://arxiv.org/abs/2508.11635

Tietze extension does not always work in constructive mathematics if closed sets are defined as sequentially closed sets
We prove that Tietze Extension does not always exist in constructive mathematics if closed sets on which the function we are extending are defined as sequentially closed sets. Firstly, we take a discrete metric space as our topological space. Now all sets open and sequentially closed. Then, we form an unextendible algorithmic function transforming positive integers to 0 and 1, looking at the preimages of these values as our sequentially closed sets. Then we show that if the Tietze theorem concl…

System 0: Transforming Artificial Intelligence into a Cognitive Extension
Massimo Chiriatti, Marianna Bergamaschi Ganapini, Enrico Panai, Brenda K. Wiederhold, Giuseppe Riva
https://arxiv.org/abs/2506.14376

System 0: Transforming Artificial Intelligence into a Cognitive Extension
This paper introduces System 0, a conceptual framework for understanding how artificial intelligence functions as a cognitive extension preceding both intuitive (System 1) and deliberative (System 2) thinking processes. As AI systems increasingly shape the informational substrate upon which human cognition operates, they transform from passive tools into active cognitive partners. Building on the Extended Mind hypothesis and Heersmink's criteria for cognitive extension, we argue that AI systems…

Thoughts from the @braiduk.bsky.social event thus far (shaped through my own interests and thinking)
People's desire to shape AI in society was very present (but I missed a sense of grassroots work eg AI4LAM in GLAMs, other equivalents)
Science fiction and other creative expressions can help society think through potential models for AI
AI is an extension, intensification of existing technologies
Clearly tensions, temptations between values and efficiencies, which lin…

Micah Parsons contract update: Revisiting what Cowboys owner Jerry Jones has said about extension talks

https://www.cbssports.com/nfl/news/micah-p

H\"older extension for fractional Laplacian
Feng Li
https://arxiv.org/abs/2508.12134 https://arxiv.org/pdf/2508.12134…

Hölder extension for fractional Laplacian
In this note, we characterize the sharp boundary condition such that the fractional harmonic extensions with Hölder regularity up to the boundary is globally Hölder continuous. The proofs are based on estimates of fractional harmonic measure decay and uniform fractional fatness of the complement of the domain.

@… Hi, seems like the last Vinegar update for iOS has caused audio problems on the YouTube website. As I scroll down a page of search results, the audio of each video will start playing automatically. I have tried clearing the cache and turning the extension off/on but the problem persists. Has anybody else reported this?

LD-LAudio-V1: Video-to-Long-Form-Audio Generation Extension with Dual Lightweight Adapters
Haomin Zhang, Kristin Qi, Shuxin Yang, Zihao Chen, Chaofan Ding, Xinhan Di
https://arxiv.org/abs/2508.11074

LD-LAudio-V1: Video-to-Long-Form-Audio Generation Extension with Dual Lightweight Adapters
Generating high-quality and temporally synchronized audio from video content is essential for video editing and post-production tasks, enabling the creation of semantically aligned audio for silent videos. However, most existing approaches focus on short-form audio generation for video segments under 10 seconds or rely on noisy datasets for long-form video-to-audio zsynthesis. To address these limitations, we introduce LD-LAudio-V1, an extension of state-of-the-art video-to-audio models and it …

Ranking the top offensive QB-RB-WR/TE combos in the NFL, plus breaking down T.J. Watt's historic extension

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

So, it was good to learn it's chrome-extension:// and not extension:// if I want to pass an extension URL through a desktop shortcut or via command-line argument.

AutoBnB-RAG: Enhancing Multi-Agent Incident Response with Retrieval-Augmented Generation
Zefang Liu, Arman Anwar
https://arxiv.org/abs/2508.13118 https://a…

AutoBnB-RAG: Enhancing Multi-Agent Incident Response with Retrieval-Augmented Generation
Incident response (IR) requires fast, coordinated, and well-informed decision-making to contain and mitigate cyber threats. While large language models (LLMs) have shown promise as autonomous agents in simulated IR settings, their reasoning is often limited by a lack of access to external knowledge. In this work, we present AutoBnB-RAG, an extension of the AutoBnB framework that incorporates retrieval-augmented generation (RAG) into multi-agent incident response simulations. Built on the Backdo…

A Formalization of the Reversible Concurrent Calculus CCSKP in Beluga
Gabriele Cecilia (Augusta University)
https://arxiv.org/abs/2508.13612 https://arxiv.…

A Formalization of the Reversible Concurrent Calculus CCSKP in Beluga
Reversible concurrent calculi are abstract models for concurrent systems in which any action can potentially be undone. Over the last few decades, different formalisms have been developed and their mathematical properties have been explored; however, none have been machine-checked within a proof assistant. This paper presents the first Beluga formalization of the Calculus of Communicating Systems with Keys and Proof labels (CCSKP), a reversible extension of CCS. Beyond the syntax and semantic…

Jakobi Meyers gives 7-word answer regarding potential extension with Raiders https://raiderswire.usatoday.com/story/sports/nfl/raiders/2025/08/14/jakobi-meyers-gives-7-word-answer-on-potential-e…

Towards the Coordination and Verification of Heterogeneous Systems with Data and Time
Tim Kr\"auter, Adrian Rutle, Yngve Lamo, Harald K\"onig, Francisco Dur\'an
https://arxiv.org/abs/2508.12325

Towards the Coordination and Verification of Heterogeneous Systems with Data and Time
Modern software systems are often realized by coordinating multiple heterogeneous parts, each responsible for specific tasks. These parts must work together seamlessly to satisfy the overall system requirements. To verify such complex systems, we have developed a non-intrusive coordination framework capable of performing formal analysis of heterogeneous parts that exchange data and include real-time capabilities. The framework utilizes a linguistic extension, which is implemented as a central b…

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.

Some comparison results for one extension of the Bakry-\'Emery-Ricci tensor
Andrea M. Mota, Cristiano S. Silva, Juliana F. R. Miranda
https://arxiv.org/abs/2507.12594

Some comparison results for one extension of the Bakry-Émery-Ricci tensor
We consider generalizations of the drifted Laplacian and the Bakry-Émery-Ricci tensor, and we prove a version of the mean curvature comparison theorem. Consequently, we prove a Myers-type theorem and a generalization of the Cheeger-Gromoll splitting theorem.

Mastering Cosmological Amplitudes Using Generalized Ramanujan's Theorem
Prashanth Raman, Qinglin Yang
https://arxiv.org/abs/2508.13126 https://arxiv.or…

Mastering Cosmological Amplitudes Using Generalized Ramanujan's Theorem
We present a systematic method for computing cosmological amplitudes, including in-in correlators and wavefunction coefficients, in FRW spacetime. Specializing to cases with conformally-coupled external scalars and massive scalar exchanges, we introduce a decomposition into massive family trees, which capture the nested time structure common to these observables. We then evaluate these building blocks using the Method of Brackets (MoB), a multivariate extension of Ramanujan's master theorem tha…

@… @… I was always under the impression that there weren’t too many to begin with…
But maybe I’m mistaken, because we never had a need for any extension cards. For the applications that the multi-slot systems were intended, there obvious…

@… @… I was always under the impression that there weren’t too many to begin with…
But maybe I’m mistaken, because we never had a need for any extension cards. For the applications that the multi-slot systems were intended, there obvious…

On Exact Solutions to the Linear Bellman Equation
David Ohlin, Richard Pates, Murat Arcak
https://arxiv.org/abs/2506.15527 https://ar…

On Exact Solutions to the Linear Bellman Equation
This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the class of Linearly Solvable MDP is reformulated as a continuous-state optimal control problem. It is shown that this class naturally satisfies the conditions for explicit solution of the Bellman equation, motivating the extension of previous results to semili…

A general framework for the asymptotic analysis of moist atmospheric flows
Daniel B\"aumer, Rupert Klein, Norbert J. Mauser
https://arxiv.org/abs/2506.14450

A general framework for the asymptotic analysis of moist atmospheric flows
We deal with asymptotic analysis for the derivation of partial differential equation models for geophysical flows in the earth's atmosphere with moist process closures, and we study their mathematical properties. Starting with the Navier-Stokes equations for dry air, we put the seminal papers of Klein, Majda et al. in a unified context and then discuss the appropriate extension to moist air. In particular, we deal with the scale-independent distinguished limit for the universal parameters of at…

A second 90-day extension on Paramount's proposed sale to Skydance has been automatically triggered, allowing more time for FCC approval (Jill Goldsmith/Deadline)
https://deadline.com/2025/07/paramount-skydance-latest-90-day…

Paramount, Skydance Latest 90-Day Merger Extension Kicks Off Today
A second 90-day extension of Paramount proposed sale to David Ellison’s Skydance automatically triggered today as per the deal agreement.

'Forever chemicals' detected in 65% of sampled private wells in Pennsylvania https://phys.org/news/2025-06-chemicals-sampled-private-wells-pennsylvania.html
PFAS Found in 65% of Private Wells Sampled in Pennsylvania

'Forever chemicals' detected in 65% of sampled private wells in Pennsylvania
In Pennsylvania, 3.5 million people are served by private well systems, according to Penn State Extension. To better understand potential contamination of the groundwater feeding these systems, a team of researchers from Penn State conducted a novel three-year citizen science study of per- and poly-fluoroalkyl substances (PFAS)—often referred to as forever chemicals—in 167 private wells across Pennsylvania.

Steelers, T.J. Watt agree to terms on record three-year, $123 million extension https://www.nfl.com/news/steelers-t-j-watt-agree-to-terms-on-record-three-year-123-million-extension

Replaced article(s) found for eess.SY. https://arxiv.org/list/eess.SY/new
[1/1]:
- Input-Output Extension of Underactuated Nonlinear Systems
Mirko Mizzoni, Amr Afifi, Antonio Franchi

Construction of a cyclic $p$-extension of number fields whose unit group has prescribed Galois module structure
Manabu Ozaki
https://arxiv.org/abs/2507.12949

Construction of a cyclic $p$-extension of number fields whose unit group has prescribed Galois module structure
For any finite cyclic $p$-group $G$, we will show that every $\mathbb{Z}_p$-torsion free finitely generated $\mathbb{Z}_p[G]$-module appears as $\mathcal{O}_K^\times\otimes_{\mathbb{Z}}\mathbb{Z}_p$ up to $\mathbb{Z}_p[G]$-free direct summands for a certain $G$-extension $K/k$ of number fields.

Basis construction for polynomial spline spaces over arbitrary T-meshe
Shicong Zhong, Falai Chen, Bingru Huang
https://arxiv.org/abs/2508.12950 https://arx…

Basis construction for polynomial spline spaces over arbitrary T-meshe
This paper presents the first method for constructing bases for polynomial spline spaces over an arbitrary T-meshes (PT-splines for short). We construct spline basis functions for an arbitrary T-mesh by first converting the T-mesh into a diagonalizable one via edge extension, ensuring a stable dimension of the spline space. Basis functions over the diagoalizable T-mesh are constructed according to the three components in the dimension formula corresponding to cross-cuts, rays, and T $l$-edges i…

SDAP-based QoS Flow Multiplexing Support in Simu5G for 5G NR Simulation
Mohamed Seliem, Utz Roedig, Cormac Sreenan, Dirk Pesch
https://arxiv.org/abs/2508.12785 https://

SDAP-based QoS Flow Multiplexing Support in Simu5G for 5G NR Simulation
The Service Data Adaptation Protocol (SDAP) plays a central role in 5G New Radio (NR), acting as a bridge between the core and radio networks, by enabling QoS Flow multiplexing over shared Data Radio Bearers (DRBs). However, most 5G simulation frameworks, including the popular OMNet++-based Simu5G, lack SDAP support, limiting their ability to model realistic QoS behavior. This paper presents a modular, standardscompliant SDAP extension for Simu5G. The implementation includes core elements such …

Turbulent stretching of dumbbells with hydrodynamic interactions: an analytical study
Jason R. Picardo, Dario Vincenzi
https://arxiv.org/abs/2506.14282 htt…

Turbulent stretching of dumbbells with hydrodynamic interactions: an analytical study
We study the stretching of an elastic dumbbell in a turbulent flow, with the aim of understanding and quantifying the effect of hydrodynamic interactions (HI) between the beads of the dumbbell. Adopting the Batchelor-Kraichnan model for the flow, we derive a Fokker-Planck equation and solve it analytically to obtain the probability distribution of the dumbbell's extension. Using different formulations of the HI tensor, we find that HI preferentially enhances the stretching of stiff dumbbells, i…

Dynamics on Bi-Lagrangian Structures and Cherry maps
Bertuel Tangue Ndawa
https://arxiv.org/abs/2508.12350 https://arxiv.org/pdf/2508.12350

Dynamics on Bi-Lagrangian Structures and Cherry maps
We consider a bi-Lagrangian structure $(ω,\mathcal{F}_{1},\mathcal{F}_{2})$ on a manifold $M$, that is, $(M,ω,\mathcal{F}_{1},\mathcal{F}_{2})$ is a bi-Lagrangian manifold. We prolong bi-Lagrangian structures on $M$, and lift a dynamic on its tangent and cotangent bundles in different ways. In some cases, we show that the lifted structures are affine. In the case of the 2-dimensional torus, we find that an extension of the same dynamic on pairs of so-called Cherry vector fields induces a conj…

An introduction to representation-theoretic canonical bases of cluster algebras
Fan Qin
https://arxiv.org/abs/2508.12761 https://arxiv.org/pdf/2508.12761…

An introduction to representation-theoretic canonical bases of cluster algebras
This is an introduction to cluster algebras and their common triangular bases. These bases are Kazhdan-Lusztig-type and serve as the canonical bases of cluster algebras from the representation-theoretic point of view. We review seeds associated with signed words, cluster operations (freezing and base change), the extension technique from finite to infinite rank, which are convenient tools to study these algebras and their bases. We present recent results on the topic and provide examples. An ap…

Mechanically Interlocked Polymers in Dilute Solution under Shear and Extensional Flows: A Brownian Dynamics Study
Ali Seyedi, Alex Albaugh
https://arxiv.org/abs/2506.13968

Mechanically Interlocked Polymers in Dilute Solution under Shear and Extensional Flows: A Brownian Dynamics Study
Mechanically interlocked polymers (MIPs) are a novel class of polymer structures in which the components are connected by mechanical bonds instead of covalent bonds. We measure the single-molecule rheological properties of polyrotaxanes, daisy chains, and polycatenanes under steady shear and steady uniaxial extension using coarse-grained Brownian dynamics simulations with hydrodynamic interactions. We obtain key rheological features, including tumbling dynamics, molecular extension, stress, and…

#TACO #TACOTRUMP

Une extension browser pour exporter ses threads Claude.ia et ChatGPT
#claude

Dallas Cowboys' contract extension strategy carries risks in 2025 https://insidethestar.com/dallas-cowboys-contract-extension-strategy-carries-risks-in-2025

T.J. Watt, Steelers agree to 3-year, $123 million extension: Sources https://www.nytimes.com/athletic/6500778/2025/07/17/tj-watt-steelers-contract-extension/

Contractive upper triangular matrices with prescribed diagonals and superdiagonals
Axel Renard
https://arxiv.org/abs/2506.15444 https://

Contractive upper triangular matrices with prescribed diagonals and superdiagonals
A characterization of the matrix representation of the compressed shift acting on a finite-dimensional model space endowed with the Takenaka-Malmquist-Walsh basis, among all upper triangular matrices, is proved. For a fixed dimension, this matrix is the unique matrix with spectral norm no greater than one and with a prescribed diagonal and superdiagonal. We also discuss an extension to the setting of infinite matrices.

Interaction between skew-representability, tensor products, extension properties, and rank inequalities
Krist\'of B\'erczi, Bogl\'arka Geh\'er, Andr\'as Imolay, L\'aszl\'o Lov\'asz, Carles Padr\'o, Tam\'as Schwarcz
https://arxiv.org/abs/2507.10709 …

Interaction between skew-representability, tensor products, extension properties, and rank inequalities
Skew-representable matroids form a fundamental class in matroid theory, bridging combinatorics and linear algebra. They play an important role in areas such as coding theory, optimization, and combinatorial geometry, where linear structure is crucial for both theoretical insights and algorithmic applications. Since deciding skew-representability is computationally intractable, much effort has been focused on identifying necessary or sufficient conditions for a matroid to be skew-representable. …

SC-TPTP: An Extension of the TPTP Derivation Format for Sequent-Based Calculus
Julie Cailler, Simon Guilloud
https://arxiv.org/abs/2507.11349 https://

SC-TPTP: An Extension of the TPTP Derivation Format for Sequent-Based Calculus
Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe proofs in first-order logic: SC-TPTP. To avoid multiplication of standards, our proposed format over-specifies the TPTP derivation format by focusing on sequent formalisms. By doing so, it provides a high level of detail, is faithful to mathematical tradition, a…

Sources: Steelers make Watt highest-paid non-QB https://www.espn.com/nfl/story/_/id/45764664/steelers-tj-watt-agree-3-year-123m-extension

Inflation in the Scale Symmetric Standard Model and Weyl geometry
Z. Lalak, P. Michalak
https://arxiv.org/abs/2506.14617 https://arxi…

Inflation in the Scale Symmetric Standard Model and Weyl geometry
This work explores the possibility of inflation in a scale-symmetric extension of the Standard Model Higgs sector, where the Higgs field $ϕ_1$ is coupled to a singlet scalar, the dilaton $ϕ_0$. The two-scalar theory is formulated within Weyl geometry, which modifies the Einstein frame form of the resulting single-field inflationary potential. We extend the analysis to include quantum corrections, incorporating curvature effects in the one-loop effective potential. We find that the resulting s…

Hodge-de Rham Theory on Higher-Dimensional Level-L Sierpinski Gaskets
Sze-Man Ngai, Shui-Hong Zhou
https://arxiv.org/abs/2508.12319 https://arxiv.org/pdf/2…

Hodge-de Rham Theory on Higher-Dimensional Level-L Sierpinski Gaskets
This paper extends the Hodge-de Rham theory of Aaron \textit{et al.} [Commun. Pure Appl. Anal. {\bf 13} (2014)] to higher-dimensional level-$l$ Sierpinski gaskets $SG_{\ell}^{n},$ providing a framework for analyzing differential forms and Laplacians on these fractal structures. We construct a sequence of graphs approximating $SG_{\ell}^{n}$ and define $k$-forms, de Rham derivatives, and their duals on these graphs. We prove that the extension of a $1$-form on a generation-$m$ graph to a $1$-for…

T.J. Watt contract extension: Where Steelers star ranks among franchise's best players this century

https://www.cbssports.com/nfl/news/t-j-wat

DaRon Bland hopes to get extension before season, talks playing slot and outside CB https://www.dallascowboys.com/news/daron-bland-hopes-to-get-extension-before-season-talks-playing-slot-and-outside-cb

The superposition principle for the continuity equation with singular flux
Stefano Almi, Riccarda Rossi, Giuseppe Savar\'e
https://arxiv.org/abs/2506.15333

The superposition principle for the continuity equation with singular flux
Representation results for absolutely continuous curves $μ:[0,T]\to \mathcal{P}_p(\mathbb{R}^d)$, $p>1$, with values in the Wasserstein space $(\mathcal{P}_p(\mathbb{R}^d),W_p)$ of Borel probability measures in $\mathbb{R}^d$ with finite $p$-moment, provide a crucial tool to study evolutionary PDEs in a measure-theoretic setting. They are strictly related to the superposition principle for measure-valued solutions to the continuity equation. This paper addresses the extension of these results …

Extensions of simple modules for quantum groups at complex roots of $1$
Henning Haahr Andersen
https://arxiv.org/abs/2508.12898 https://arxiv.org/pdf/2508.…

Extensions of simple modules for quantum groups at complex roots of $1$
Let $U_q$ be the quantum group corresponding to a complex simple Lie algebra $\mathfrak g$ with root system $R$. Assume the quantum parameter $q\in \C$ is a root of unity. In this paper we study the extensions between simple modules in the category consisting of the finite dimensional modules for $U_q$. We first prove that this problem is equivalent to finding the extensions between the finitely many simple modules for the small quantum group $u_q$ in $U_q$. Then we show that the extension grou…

Steelers, T.J. Watt agree to contract extension that makes him highest-paid non QB in NFL history, per report

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

An Explicit Cohen-Style Threefield Identity
Lucas Perryman-Deskins
https://arxiv.org/abs/2508.12152 https://arxiv.org/pdf/2508.12152

An Explicit Cohen-Style Threefield Identity
In 1988, Andrews, Dyson, and Hickerson showed that a $q$-series $σ$ found in Ramanujan's lost notebook and related to partitions could be interpreted as counting ideals in $\mathbb{Q}(\sqrt{6})$, and found similar formulas for $σ$ in terms of ideals of $\mathbb{Q}(\sqrt{2})$ and $\mathbb{Q}(\sqrt{3})$. Cohen followed this by showing more generally that for certain triples of quadratic fields, there is abelian extension and conductor so that the ray class character theta series for all three f…

Extension Monads: Some Structure Theorems
Danielle Bowerman, Matt Insall
https://arxiv.org/abs/2508.05828 https://arxiv.org/pdf/2508.05828

Extension Monads: Some Structure Theorems
We investigate the behavior of extension monads, introduced in the 1990s by the second author, in terms of structure results for infinitely many finitary operations and common constructions in varieties or categories of algebras. Specifically, we see that for finite collections of algebras of the same signature there the extension monad operation commutes with the direct product operation, and that the only retractions from an enlargement or extension monad are trivial.

Trump indicates he would federalize D.C. police for longer than 30 days (April Rubin/Axios)
https://www.axios.com/2025/08/13/trump-dc-police-30-day-extension
http://www.memeorandum.com/250813/p59#a250813p59

J.J. Watt offers three-word response to T.J. Watt's historic contract extension with Steelers

https://www.cbssports.com/nfl/news/j-j-wat

DaRon Bland hopes to get extension before season, talks playing slot and outside CB https://www.dallascowboys.com/news/daron-bland-hopes-to-get-extension-before-season-talks-playing-slot-and-outside-cb

Cyclic proof theory of positive inductive definitions
Gianluca Curzi, Lukas Melgaard
https://arxiv.org/abs/2507.13057 https://arxiv.o…

Cyclic proof theory of positive inductive definitions
We study cyclic proof systems for $μ\mathsf{PA}$, an extension of Peano arithmetic by positive inductive definitions that is arithmetically equivalent to the (impredicative) subsystem of second-order arithmetic $Π^1_2$-$\mathsf{CA}_0$ by Möllefeld. The main result of this paper is that cyclic and inductive $μ\mathsf{PA}$ have the same proof-theoretic strength. First, we translate cyclic proofs into an annotated variant based on Sprenger and Dam's systems for first-order $μ$-calculus, whose…

Commanders activate WR Terry McLaurin off PUP list, still no extension https://www.nytimes.com/athletic/6557147/2025/08/16/terry-mclaurin-commanders-activate-extension/

Insider Provides Brutal Update on Cowboys, Micah Parsons https://heavy.com/sports/nfl/dallas-cowboys/micah-parsons-situation-personal/?adt_ei=[email]

Trey Smith, Chiefs finalizing record extension to make him highest-paid guard in NFL https://www.nfl.com/news/trey-smith-chiefs-finalizing-record-extension-to-make-him-highest-paid-guard-in-nfl

Jets, CB Sauce Gardner agree to terms on four-year, $120.4 million contract extension https://www.nfl.com/news/jets-cb-sauce-gardner-four-year-120-4-million-contract-extension

Characterizing NC1 with Typed Monoids
Anuj Dawar, Aidan T. Evans
https://arxiv.org/abs/2508.11019 https://arxiv.org/pdf/2508.11019

Characterizing NC1 with Typed Monoids
Krebs et al. (2007) gave a characterization of the complexity class TC0 as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to infinite monoids and hence characterize classes beyond the regular languages. We advance this line of work beyond TC0 by giving a characterization of NC1. This is obtained by first showing that NC1 can be defined as the languages expressible in an extension of …

Cowboys' Micah Parsons on negotiations for contract extension: 'I'm going to get mine no matter what'

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

$40M defender supports Micah Parsons' contract bid: 'He should get every penny he's owed' https://cowboyswire.usatoday.com/story/sports/nfl/cowboys/2025/06/16/cowboys-micah-parsons-m…

Steelers' DeShon Elliott agrees to two-year, $12.5 million extension, per report

https://www.cbssports.com/nfl/news/steelers-deshon-elliot…

How will Nik Bonitto build on his All-Pro breakthrough? https://www.espn.com/nfl/story/_/id/45984013/denver-broncos-edge-rusher-nik-bonitto-sacks-contract-year-extension

Micah Parsons’ contract extension saga sparks major criticism of Cowboys https://www.sportingnews.com/us/nfl/dallas-cowboys/news/micah-parsons-contract-extension-major-criticism-cowboys/9f407c9d91ee1a98428632…

Sources: Jets' Gardner now NFL's highest-paid CB https://www.espn.com/nfl/story/_/id/45747367/sources-jets-cb-sauce-gardner-reach-4-year-1204m-extension

James Cook, Bills agree to terms on four-year, $48 million contract extension https://www.nfl.com/news/james-cook-bills-four-year-48-million-contract-extension

Could Seahawks extend safety Coby Bryant despite drafting Nick Emmanwori? https://www.espn.com/nfl/story/_/id/45765575/could-seahawks-extend-coby-bryant-draft-nick-emmanwori

Trey Hendrickson, Bengals resume talks on longterm contract extension, per report

https://www.cbssports.com/nfl/news/trey-hendrickson-benga…

Jets make Sauce Gardner highest-paid cornerback in NFL history with $120.4 million extension, per report

https://www.cbssports.com/nfl/news/jets-ma

Chiefs make Trey Smith highest-paid offensive guard in NFL with four-year, $94 million extension

https://www.cbssports.com/nfl/news/chiefs-

Mariners' Cal Raleigh first catcher to win Home Run Derby; Jets sign Garrett Wilson to $130M extension

https://www.cbssports.com/mlb/news/mariner

Live updates from The Open; Caitlin Clark to miss WNBA All-Star Weekend; Damian Lillard returns to Blazers

https://www.cbssports.com/nfl/news/live-up…

Bills, James Cook agree 4-year, $48m contract extension: Source https://www.nytimes.com/athletic/6547384/2025/08/13/james-cook-bills-contract-extension/

After hold-in, Bills' Cook gets 4-year, $48M deal https://www.espn.com/nfl/story/_/id/45963843/james-cook-bills-reach-4-year-48m-extension-rb-hold-in

Buyer's remorse? Mike Vrabel explains Kyle Dugger benching after Patriots' hefty contract extension

https://www.cbssports.com/nfl/news/buyers-

General manager Ryan Poles, Bears agree to extension through 2029 season https://www.nfl.com/news/general-manager-ryan-poles-bears-agree-to-extension-through-2029-season

NFL news roundup: Steelers, S DeShon Elliott agree to 2-yr, $12.5 million extension https://www.nfl.com/news/nfl-news-roundup-latest-league-updates-from-monday-june-16

James Cook contract: Bills star running back agrees to four-year extension, including $30 million guaranteed

https://www.cbssports.com/nfl/news/james-c

Parsons at Cowboys minicamp, extension in limbo https://www.espn.com/nfl/story/_/id/45487664/cowboys-micah-parsons-minicamp-extension-limbo

Vikings ink TE Oliver to 3-yr., $23.25M extension https://www.espn.com/nfl/story/_/id/45485798/vikings-sign-te-josh-oliver-3-year-2325-contract-extension

Terry McLaurin not expected to report to Commanders minicamp while seeking extension https://www.nfl.com/news/terry-mclaurin-not-expected-to-report-to-commanders-minicamp-while-seeking-extension

Mack says $18M Chargers extension made sense https://www.espn.com/nfl/story/_/id/45495317/khalil-mack-los-angeles-chargers-extension

Bears, GM Ryan Poles agree to contract extension through 2029: Source https://www.nytimes.com/athletic/6488952/2025/07/11/bears-ryan-poles-contract-extension/

Jets' CB Sauce Gardner addresses potential extension while attending minicamp: 'I want to win'

https://www.cbssports.com/nfl/news/jets-cb

49ers, wide receiver Jauan Jennings 'not close' on new contract extension, per report

https://www.cbssports.com/nfl/news/49ers-wide-receiver…

Chiefs guard Trey Smith weighs in on potential contract extension ahead of franchise tag deadline https://www.nfl.com/news/chiefs-guard-trey-smith-weighs-in-on-potential-contract-extension-ahead-of-franchise-tag-deadline

'He's the heartbeat of the team': Why Terry McLaurin, Commanders can't get a deal done https://www.espn.com/nfl/story/_/id/45915121/washington-commanders-terry-mclaurin-trade-request-hold-contract-extension

Michael Dickson agrees to Seahawks extension, resumes title as NFL's highest-paid punter

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

Rams RB Williams signs 3-year, $33M extension https://www.espn.com/nfl/story/_/id/45907889/rams-top-rb-kyren-williams-signs-three-year-33m-extension

Ravens sign WR Rashod Bateman to three-year, $36.75 million extension through 2029 season https://www.nfl.com/news/rashod-bateman-ravens-sign-wr-three-year-36-million-extension-2029

Rams, RB Kyren Williams agree to terms on three-year, $33 million contract extension https://www.nfl.com/news/rams-rb-kyren-williams-agree-to-terms-contract-extension

Bills RB Cook, seeking extension, sits out again https://www.espn.com/nfl/story/_/id/45900294/bills-rb-james-cook-seeking-extension-sits-again