Tootfinder

Simple $\mathcal{W}\ltimes\widehat{H_4}$-modules from tensor products
Dashu Xu
https://arxiv.org/abs/2507.21927 https://arxiv.org/pdf/2507.21927

Simple $\mathcal{W}\ltimes\widehat{H_4}$-modules from tensor products
This paper investigates simple modules of the semi-direct product algebra $\mathcal{W}\ltimes\widehat{H_4}$, where $\mathcal{W}$ is the Witt algebra and $\widehat{H_4}$ is the loop Diamond algebra. We first use simple modules over the Weyl algebra to construct a family of simple $\mathcal{W}\ltimes\widehat{H_4}$-modules. Then, we classify simple $\mathcal{W}\ltimes\widehat{H_4}$-modules that are free $U(\mathbb{C}L_0\oplus\mathbb{C} a_0)$-modules of rank 1. Finally, we give a necessary and suff…

Swan modules and homotopy types after a single stabilisation
Tommy Hofmann, John Nicholson
https://arxiv.org/abs/2507.21975 https://arxiv.org/pdf/2507.2197…

Swan modules and homotopy types after a single stabilisation
We study Swan modules, which are a special class of projective modules over integral group rings, and their consequences for the homotopy classification of CW-complexes. We show that there exists a non-free stably free Swan module, thus resolving Problem A4 in the 1979 Problem List of C. T. C. Wall. As an application we show that, in all dimensions $n \equiv 3$ mod $4$, there exist finite $n$-complexes which are homotopy equivalent after stabilising with multiple copies of $S^n$, but not after …

Algebraic invariants of the special fiber ring of ladder determinantal modules
Alessandra Costantini, Louiza Fouli, Kriti Goel, Kuei-Nuan Lin, Haydee Lindo, Whitney Liske, Maral Mostafazadehfard
https://arxiv.org/abs/2507.22167

Algebraic invariants of the special fiber ring of ladder determinantal modules
We provide explicit formulas for key invariants of special fiber rings of ladder determinantal modules, that is, modules that are direct sums of ideals of maximal minors of a ladder matrix. Our results are given in terms of the combinatorial data of the associated ladder matrix. In particular, we compute its dimension, regularity, $a$-invariant, and multiplicity, which via \textsc{Sagbi} degeneration coincide with those of Hibi rings associated to a distributive lattice. Then, via Gröbner dege…

Experience converting a large mathematical software package written in C to C 20 modules
Wolfgang Bangerth
https://arxiv.org/abs/2506.21654 https://

Experience converting a large mathematical software package written in C++ to C++20 modules
Mathematical software has traditionally been built in the form of "packages" that build on each other. A substantial fraction of these packages is written in C++ and, as a consequence, the interface of a package is described in the form of header files that downstream packages and applications can then #include. C++ has inherited this approach towards exporting interfaces from C, but the approach is clunky, unreliable, and slow. As a consequence, C++20 has introduced a "module" system in which …

Simple modules of the planar Galilean conformal algebra from tensor products
Dashu Xu
https://arxiv.org/abs/2507.21930 https://arxiv.org/pdf/2507.21930

Simple modules of the planar Galilean conformal algebra from tensor products
This paper is devoted to constructing simple modules of the planar Galilean conformal algebra. We study the tensor products of finitely many simple $\mathcal{U}(\mathcal{H})$-free modules with an arbitrary simple restricted module, where $\mathcal{H}$ is the Cartan subalgebra. We establish necessary and sufficient conditions for simplicity and determine the corresponding isomorphism classes.

Chevalley property and discriminant ideals of Cayley-Hamilton Hopf Algebras
Yimin Huang, Zhongkai Mi, Tiancheng Qi, Quanshui Wu
https://arxiv.org/abs/2506.21879

Chevalley property and discriminant ideals of Cayley-Hamilton Hopf Algebras
For any affine Hopf algebra $H$ which admits a large central Hopf subalgebra, $H$ can be endowed with a Cayley-Hamilton Hopf algebra structure in the sense of De Concini-Procesi-Reshetikhin-Rosso. The category of finite-dimensional modules over any fiber algebra of $H$ is proved to be an indecomposable exact module category over the tensor category of finite-dimensional modules over the identity fiber algebra $H/\mathfrak{m}_{\overline{\varepsilon}}H$ of $H$. For any affine Cayley-Hamilton Hopf…

Safety Evaluation of Motion Plans Using Trajectory Predictors as Forward Reachable Set Estimators
Kaustav Chakraborty, Zeyuan Feng, Sushant Veer, Apoorva Sharma, Wenhao Ding, Sever Topan, Boris Ivanovic, Marco Pavone, Somil Bansal
https://arxiv.org/abs/2507.22389

Safety Evaluation of Motion Plans Using Trajectory Predictors as Forward Reachable Set Estimators
The advent of end-to-end autonomy stacks - often lacking interpretable intermediate modules - has placed an increased burden on ensuring that the final output, i.e., the motion plan, is safe in order to validate the safety of the entire stack. This requires a safety monitor that is both complete (able to detect all unsafe plans) and sound (does not flag safe plans). In this work, we propose a principled safety monitor that leverages modern multi-modal trajectory predictors to approximate forwar…

Coherent configurations and Frobenius structures
Gejza Jen\v{c}a, Anna Jen\v{c}ov\'a, Dominik Lachman
https://arxiv.org/abs/2507.21774 https://arxiv.or…

Coherent configurations and Frobenius structures
We prove that coherent configurations can be represented as modules over Frobenius structures in the category of real nonnegative matrices. We generalize the notion of admissible morphism from association schemes to coherent configurations. We show that the Frobenius structure associated to a coherent configuration can be modified to become a dagger Frobenius structure, and use this to connect the coherent configurations to groupoids and $H^*$-algebras. We examine the properties of the dagger F…

VizGenie: Toward Self-Refining, Domain-Aware Workflows for Next-Generation Scientific Visualization
Ayan Biswas, Terece L. Turton, Nishath Rajiv Ranasinghe, Shawn Jones, Bradley Love, William Jones, Aric Hagberg, Han-Wei Shen, Nathan DeBardeleben, Earl Lawrence
https://arxiv.org/abs/2507.21124

VizGenie: Toward Self-Refining, Domain-Aware Workflows for Next-Generation Scientific Visualization
We present VizGenie, a self-improving, agentic framework that advances scientific visualization through large language model (LLM) by orchestrating of a collection of domain-specific and dynamically generated modules. Users initially access core functionalities--such as threshold-based filtering, slice extraction, and statistical analysis--through pre-existing tools. For tasks beyond this baseline, VizGenie autonomously employs LLMs to generate new visualization scripts (e.g., VTK Python code),…

Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^ _{r,s}(B_2)$
Snehashis Mukherjee, Ritesh Kumar Pandey
https://arxiv.org/abs/2506.21856

Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$
We study the two-parameter quantized enveloping algebra $U^+_{r,s}(B_2)$ at roots of unity and investigate its structure and representations. We first show that when $r$ and $s$ are roots of unity, the algebra becomes a PI algebra, and we compute its PI degree explicitly using De Concini-Procesi method. We construct and classify finite-dimensional simple modules for $U^+_{r,s}(B_2)$ by analyzing a subalgebra $B\subset U^+_{r,s}(B_2)$. Simple modules are categorized into torsion-free and torsion…

Archaea Exchange review https://www.soundonsound.com/reviews/archaea-exchange?u…

Globalization and the biactegory of partial modules
Eliezer Batista, William Hautekiet, Joost Vercruysse
https://arxiv.org/abs/2506.18451 https://

Globalization and the biactegory of partial modules
We show that the category of partial modules over a Hopf algebra $H$ is a biactegory (a bimodule category) over the category of global $H$-modules. The corresponding enrichment of partial modules over global modules is described, and the close relation between the dilation of partial modules and Hom-objects arising from this enrichment is investigated. In particular, for finite-dimensional pointed Hopf algebras, the standard dilation of a partial module $M$ is isomorphic to the Hom-object from …

Prototyping of 6.2-mm-Pitch Fiber Positioner Modules for Stage-V Telescope Instrumentation
Malak Galal, Maxime Rombach, Jonathan Wei, Ricardo Ara\'ujo, Diane Chapuis, S\'ebastien Pernecker, Abby Bault, Joseph Harry Silber, Nicholas Wenner, William Van Shourt, Stefane Caseiro, Corentin Magnenat, David Schlegel, Jean-Paul Kneib
https://

Prototyping of 6.2-mm-Pitch Fiber Positioner Modules for Stage-V Telescope Instrumentation
Small-pitch populated focal planes are a critical enabling technology for the next generation of highly multiplexed astronomical instruments. This work reports on ongoing prototyping activities for 6.2 mm-pitch alpha-beta (theta-phi) fiber positioner modules. Following a concise review of the underlying concept, the performance of trillium-based and independently actuated robotic designs is compared. Key operational parameters including XY positioning repeatability, non-linearity, backlash, and…

I'm about to give up on Heltec radios; have two modules which work great, (well...... work well enough for a limited duration of time since they're battery hogs), but refuse to accept any serial data when in DFU mode.
I was able to flash a third Heltec (all V3 32-bit devices) just fine, but for whatever reason these two just refuse to play nicely.
Even tried a stupid simple application just to see if _something_ would flash and NOPE.
```
Failed to connect to ES…

Security Tensors as a Cross-Modal Bridge: Extending Text-Aligned Safety to Vision in LVLM
Shen Li, Liuyi Yao, Wujia Niu, Lan Zhang, Yaliang Li
https://arxiv.org/abs/2507.20994 h…

Security Tensors as a Cross-Modal Bridge: Extending Text-Aligned Safety to Vision in LVLM
Large visual-language models (LVLMs) integrate aligned large language models (LLMs) with visual modules to process multimodal inputs. However, the safety mechanisms developed for text-based LLMs do not naturally extend to visual modalities, leaving LVLMs vulnerable to harmful image inputs. To address this cross-modal safety gap, we introduce security tensors - trainable input vectors applied during inference through either the textual or visual modality. These tensors transfer textual safety al…

The Dolbeault geometric Langlands conjecture via limit categories
Tudor P\u{a}durariu, Yukinobu Toda
https://arxiv.org/abs/2508.19624 https://arxiv.org/pdf…

The Dolbeault geometric Langlands conjecture via limit categories
We introduce limit categories for cotangent stacks of smooth stacks as an effective version of classical limits of categories of D-modules on them. We develop their general theory and pursue their relation with categories of D-modules. In particular, we establish the functorial properties of limit categories such as the smooth pull-back and projective push-forward. Using the notion of limit categories, we propose a precise formulation of the Dolbeault geometric Langlands conjecture, proposed by…

Theta invariants and Lattice-Point Counting in Normed $\mathbb{Z}$-Modules
Mounir Hajli
https://arxiv.org/abs/2508.17406 https://arxiv.org/pdf/2508.17406…

Theta invariants and Lattice-Point Counting in Normed $\mathbb{Z}$-Modules
Euclidean lattices occupy a central position in number theory, the geometry of numbers, and modern cryptography. In the present article, the theory of Euclidean lattices is employed to investigate normed $\mathbb{Z}$-modules of finite rank. Specifically, let $\overline{E}$ be a normed $\mathbb Z$-module of finite rank. We establish several inequalities for the lattice-point counting function of $\overline{E}$, along with related results. Our arguments rely primarily on the analytic properties o…

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…

#European #Cloud Modules
https://berthub.eu/articles/posts/european-cloud-modules/…

Modular fixed points in equivariant homotopy theory
Yorick Fuhrmann
https://arxiv.org/abs/2506.21413 https://arxiv.org/pdf/2506.21413…

Modular fixed points in equivariant homotopy theory
We show that the derived $\infty$-category of permutation modules is equivalent to the category of modules over the Eilenberg-MacLane spectrum associated to a constant Mackey functor in the $\infty$-category of equivariant spectra. On such module categories we define a modular fixed point functor using geometric fixed points followed by an extension of scalars and identify it with the modular fixed point functor on derived permutation modules introduced by Balmer-Gallauer. As an application, we…

Design and Mechanical Integration of Scintillation Modules for SUB-Millicharge ExperimenT (SUBMET)
Claudio Campagnari, Sungwoong Cho, Suyong Choi, Seokju Chung, Matthew Citron, Albert De Roeck, Martin Gastal, Seungkyu Ha, Andy Haas, Christopher Scott Hill, Byeong Jin Hong, Haeyun Hwang, Insung Hwang, Hoyong Jeong, Hyunki Moon, Jayashri Padmanaban, Ryan Schmitz, Changhyun Seo, David Stuart, Eunil Won, Jae Hyeok Yoo, Jinseok Yoo, Ayman Youssef, Ahmad Zaraket, Haitham Zaraket

Design and Mechanical Integration of Scintillation Modules for SUB-Millicharge ExperimenT (SUBMET)
We present a detailed description of the detector design for the SUB-Millicharge ExperimenT (SUBMET), developed to search for millicharged particles. The experiment probes a largely unexplored region of the charge-mass parameter space, focusing on particles with mass $m_χ< 1.6~\textrm{GeV}/c^2$ and electric charge $Q < 10^{-3}e$. The detector has been optimized to achieve high sensitivity to interactions of such particles while maintaining effective discrimination against background events. We…

Ukraine's F-16 have a new trick to avoid Russian ballistic missiles: https://benborges.xyz/2025/07/26/ukraines-f-have-a-new.html

On sequentially Cohen-Macaulay modules and sequentially generalized Cohen-Macaulay modules
Nguyen Xuan Linh, Le Thanh Nhan
https://arxiv.org/abs/2506.17717

On sequentially Cohen-Macaulay modules and sequentially generalized Cohen-Macaulay modules
We introduce the notions of sequential sequence and sequential f-sequence in order to characterize sequentially Cohen-Macaulay modules and sequentially generalized Cohen-Macaulay modules. Let R be a Noetherian local ring and M a finitely generated R-module. We show that M is sequentially Cohen-Macaulay (resp. sequentially generalized Cohen-Macaulay) if and only if there exists a system of parameters of M that is an M- sequential sequence (resp. each generalized regular sequence s.o.p of M is an…

On Automating Proofs of Multiplier Adder Trees using the RTL Books
Mayank Manjrekar (Arm Inc.)
https://arxiv.org/abs/2507.19010 https://arxiv.org/pdf/2507.…

On Automating Proofs of Multiplier Adder Trees using the RTL Books
We present an experimental, verified clause processor ctv-cp that fits into the framework used at Arm for formal verification of arithmetic hardware designs. This largely automates the ACL2 proof development effort for integer multiplier modules that exist in designs ranging from floating-point division to matrix multiplication.

Day 13
version 0.6.0 released
Scoped access is now enforced across all core modules. Each repository operation is tenant-aware via a shared ScopedRepository base class.
Key facts:
12 modules refactored
96 updated tests
1 shared base class (ScopedRepository) used across the board
subscriberId is automatically applied in all find, findOne, save, remove operations
1 very long workday
Commit, tag, release — done

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

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

A Concurrent Modular Agent: Framework for Autonomous LLM Agents
Norihiro Maruyama, Takahide Yoshida, Hiroki Sato, Atsushi Masumori, Johnsmith, Takashi Ikegami
https://arxiv.org/abs/2508.19042

A Concurrent Modular Agent: Framework for Autonomous LLM Agents
We introduce the Concurrent Modular Agent (CMA), a framework that orchestrates multiple Large-Language-Model (LLM)-based modules that operate fully asynchronously yet maintain a coherent and fault-tolerant behavioral loop. This framework addresses long-standing difficulties in agent architectures by letting intention emerge from language-mediated interactions among autonomous processes. This approach enables flexible, adaptive, and context-dependent behavior through the combination of concurren…

What do you think?
https://drupal.community/@ifrik/115060791646810935

Rethinking HSM and TPM Security in the Cloud: Real-World Attacks and Next-Gen Defenses
Shams Shaikh, Trima P. Fernandes e Fizardo
https://arxiv.org/abs/2507.17655 https://

Rethinking HSM and TPM Security in the Cloud: Real-World Attacks and Next-Gen Defenses
As organizations rapidly migrate to the cloud, the security of cryptographic key management has become a growing concern. Hardware Security Modules (HSMs) and Trusted Platform Modules (TPMs), traditionally seen as the gold standard for securing encryption keys and digital trust, are increasingly challenged by cloud-native threats. Real-world breaches have exposed weaknesses in cloud deployments, including misconfigurations, API abuse, and privilege escalations, allowing attackers to access sens…

Algebraic conformal nets, investigation of the locally constant case -- M1 internship supervised by Domenico Fiorenza
Quentin Moreau
https://arxiv.org/abs/2508.18275 https://

Algebraic conformal nets, investigation of the locally constant case -- M1 internship supervised by Domenico Fiorenza
We define the tricategory of algebraic conformal nets, defects, sectors and intertwiners where algebraic refers to the absence of a topology on the relevant algebras and modules. We aim at making these definitions satisfying from a categorical point of view, and in a few cases, e.g., for defects, we propose more general definitions than what can be found in the literature. This allows us in particular to propose an implementation of solitons as defects. Then we focus on the locally constant cas…

SelfRACG: Enabling LLMs to Self-Express and Retrieve for Code Generation
Qian Dong, Jia Chen, Qingyao Ai, Hongning Wang, Haitao Li, Yi Wu, Yao Hu, Yiqun Liu, Shaoping Ma
https://arxiv.org/abs/2507.19033

SelfRACG: Enabling LLMs to Self-Express and Retrieve for Code Generation
Existing retrieval-augmented code generation (RACG) methods typically use an external retrieval module to fetch semantically similar code snippets used for generating subsequent fragments. However, even for consecutive code fragments, the content often diverges due to logical progression, resulting in a content gap. This gap undermines the performance of current RACG methods, as \textit{external} retrieval modules based on content matching fail to infer the specific information need of LLMs to …

OmniSim: Simulating Hardware with C Speed and RTL Accuracy for High-Level Synthesis Designs
Rishov Sarkar, Cong Hao
https://arxiv.org/abs/2508.19299 https://

OmniSim: Simulating Hardware with C Speed and RTL Accuracy for High-Level Synthesis Designs
High-Level Synthesis (HLS) is increasingly popular for hardware design using C/C++ instead of Register-Transfer Level (RTL). To express concurrent hardware behavior in a sequential language like C/C++, HLS tools introduce constructs such as infinite loops and dataflow modules connected by FIFOs. However, efficiently and accurately simulating these constructs at C level remains challenging. First, without hardware timing information, functional verification typically requires slow RTL synthesis …

Humanoid Occupancy: Enabling A Generalized Multimodal Occupancy Perception System on Humanoid Robots
Wei Cui, Haoyu Wang, Wenkang Qin, Yijie Guo, Gang Han, Wen Zhao, Jiahang Cao, Zhang Zhang, Jiaru Zhong, Jingkai Sun, Pihai Sun, Shuai Shi, Botuo Jiang, Jiahao Ma, Jiaxu Wang, Hao Cheng, Zhichao Liu, Yang Wang, Zheng Zhu, Guan Huang, Jian Tang, Qiang Zhang
https:…

Humanoid Occupancy: Enabling A Generalized Multimodal Occupancy Perception System on Humanoid Robots
Humanoid robot technology is advancing rapidly, with manufacturers introducing diverse heterogeneous visual perception modules tailored to specific scenarios. Among various perception paradigms, occupancy-based representation has become widely recognized as particularly suitable for humanoid robots, as it provides both rich semantic and 3D geometric information essential for comprehensive environmental understanding. In this work, we present Humanoid Occupancy, a generalized multimodal occupanc…

LLM coding is the opposite of DRY
An important principle in software engineering is DRY: Don't Repeat Yourself. We recognize that having the same code copied in more than one place is bad for several reasons:
1. It makes the entire codebase harder to read.
2. It increases maintenance burden, since any problems in the duplicated code need to be solved in more than one place.
3. Because it becomes possible for the copies to drift apart if changes to one aren't transferred to the other (maybe the person making the change has forgotten there was a copy) it makes the code more error-prone and harder to debug.
All modern programming languages make it almost entirely unnecessary to repeat code: we can move the repeated code into a "function" or "module" and then reference it from all the different places it's needed. At a larger scale, someone might write an open-source "library" of such functions or modules and instead of re-implementing that functionality ourselves, we can use their code, with an acknowledgement. Using another person's library this way is complicated, because now you're dependent on them: if they stop maintaining it or introduce bugs, you've inherited a problem, but still, you could always copy their project and maintain your own version, and it would be not much more work than if you had implemented stuff yourself from the start. It's a little more complicated than this, but the basic principle holds, and it's a foundational one for software development in general and the open-source movement in particular. The network of "citations" as open-source software builds on other open-source software and people contribute patches to each others' projects is a lot of what makes the movement into a community, and it can lead to collaborations that drive further development. So the DRY principle is important at both small and large scales.
Unfortunately, the current crop of hyped-up LLM coding systems from the big players are antithetical to DRY at all scales:
- At the library scale, they train on open source software but then (with some unknown frequency) replicate parts of it line-for-line *without* any citation [1]. The person who was using the LLM has no way of knowing that this happened, or even any way to check for it. In theory the LLM company could build a system for this, but it's not likely to be profitable unless the courts actually start punishing these license violations, which doesn't seem likely based on results so far and the difficulty of finding out that the violations are happening. By creating these copies (and also mash-ups, along with lots of less-problematic stuff), the LLM users (enabled and encouraged by the LLM-peddlers) are directly undermining the DRY principle. If we see what the big AI companies claim to want, which is a massive shift towards machine-authored code, DRY at the library scale will effectively be dead, with each new project simply re-implementing the functionality it needs instead of every using a library. This might seem to have some upside, since dependency hell is a thing, but the downside in terms of comprehensibility and therefore maintainability, correctness, and security will be massive. The eventual lack of new high-quality DRY-respecting code to train the models on will only make this problem worse.
- At the module & function level, AI is probably prone to re-writing rather than re-using the functions or needs, especially with a workflow where a human prompts it for many independent completions. This part I don't have direct evidence for, since I don't use LLM coding models myself except in very specific circumstances because it's not generally ethical to do so. I do know that when it tries to call existing functions, it often guesses incorrectly about the parameters they need, which I'm sure is a headache and source of bugs for the vibe coders out there. An AI could be designed to take more context into account and use existing lookup tools to get accurate function signatures and use them when generating function calls, but even though that would probably significantly improve output quality, I suspect it's the kind of thing that would be seen as too-baroque and thus not a priority. Would love to hear I'm wrong about any of this, but I suspect the consequences are that any medium-or-larger sized codebase written with LLM tools will have significant bloat from duplicate functionality, and will have places where better use of existing libraries would have made the code simpler. At a fundamental level, a principle like DRY is not something that current LLM training techniques are able to learn, and while they can imitate it from their training sets to some degree when asked for large amounts of code, when prompted for many smaller chunks, they're asymptotically likely to violate it.
I think this is an important critique in part because it cuts against the argument that "LLMs are the modern compliers, if you reject them you're just like the people who wanted to keep hand-writing assembly code, and you'll be just as obsolete." Compilers actually represented a great win for abstraction, encapsulation, and DRY in general, and they supported and are integral to open source development, whereas LLMs are set to do the opposite.
[1] to see what this looks like in action in prose, see the example on page 30 of the NYTimes copyright complaint against OpenAI (#AI #GenAI #LLMs #VibeCoding

Constructible Subcategories and Unbounded Representation Type (with an appendix by Andres Fernandez Herrero)
Kevin Schlegel, Andres Fernandez Herrero
https://arxiv.org/abs/2507.22192

Constructible Subcategories and Unbounded Representation Type (with an appendix by Andres Fernandez Herrero)
We show that bounded type implies finite type for a constructible subcategory of the module category of a finitely generated algebra over a field, which is a variant of the first Brauer-Thrall conjecture. A full subcategory is constructible if it consists of all modules that vanish on a finitely presented functor. Our approach makes use of the Ziegler spectrum of a ring and a connection, established in this work, with the scheme of finite dimensional modules. We also discuss a variant of the se…

On Tor-vanishing of local rings
Shrikant Shekhar, Anjan Gupta
https://arxiv.org/abs/2506.21764 https://arxiv.org/pdf/2506.21764

On Tor-vanishing of local rings
Let $R$ be a local ring with residue field $k$ and $M$, $N$ be finitely generated modules over $R$. It is well known that $Tor^R_i(M, N) = 0$ for $i \gg 0$ if $pd_R(M) < \infty$ or $pd_R(N) < \infty$. The ring $R$ is said to satisfy the Tor-vanishing property if the converse holds, that is, $Tor^R_i(M, N) = 0$ for $i \gg 0$ implies $pd_R(M) < \infty$ or $pd_R(N) < \infty$. Interest in the Tor-vanishing property stems from the fact that Cohen-Macaulay local rings satisfying this property also sa…

Congruences modulo $23$ to $y^2=x^3-23$ are trivial
Elie Studnia
https://arxiv.org/abs/2507.20801 https://arxiv.org/pdf/2507.20801

Congruences modulo $23$ to $y^2=x^3-23$ are trivial
We say that two elliptic curves $E$ and $F$ over $\mathbb{Q}$ are congruent modulo a prime $p$ if their $p$-torsion Galois modules (over the algebraic closure of $\mathbb{Q}$) are isomorphic. Such a congruence is called trivial if there is a rational isogeny between $E$ and $F$ with degree prime to $p$. A version of the Frey-Mazur conjecture states that any congruence modulo any prime $p \geq 19$ is trivial. Given an elliptic curve $E/\mathbb{Q}$ and a prime $p$, it is well-known that there is …

Secure Multi-LLM Agentic AI and Agentification for Edge General Intelligence by Zero-Trust: A Survey
Yinqiu Liu, Ruichen Zhang, Haoxiang Luo, Yijing Lin, Geng Sun, Dusit Niyato, Hongyang Du, Zehui Xiong, Yonggang Wen, Abbas Jamalipour, Dong In Kim, Ping Zhang
https://arxiv.org/abs/2508.19870

Secure Multi-LLM Agentic AI and Agentification for Edge General Intelligence by Zero-Trust: A Survey
Agentification serves as a critical enabler of Edge General Intelligence (EGI), transforming massive edge devices into cognitive agents through integrating Large Language Models (LLMs) and perception, reasoning, and acting modules. These agents collaborate across heterogeneous edge infrastructures, forming multi-LLM agentic AI systems that leverage collective intelligence and specialized capabilities to tackle complex, multi-step tasks. However, the collaborative nature of multi-LLM systems int…

Walk the Robot: Exploring Soft Robotic Morphological Communication driven by Spiking Neural Networks
Matthew Meek, Guy Tallent, Thomas Breimer, James Gaskell, Abhay Kashyap, Atharv Tekurkar, Jonathan Fischman, Luodi Wang, Viet-Dung Nguyen, John Rieffel
https://arxiv.org/abs/2508.19920

Walk the Robot: Exploring Soft Robotic Morphological Communication driven by Spiking Neural Networks
Recently, researchers have explored control methods that embrace nonlinear dynamic coupling instead of suppressing it. Such designs leverage dynamical coupling for communication between different parts of the robot. Morphological communication refers to when those dynamics can be used as an emergent data bus to facilitate coordination among independent controller modules within the same robot. Previous research with tensegrity-based robot designs has shown that evolutionary learning models that…

Simulating Human Behavior with the Psychological-mechanism Agent: Integrating Feeling, Thought, and Action
Qing Dong, Pengyuan Liu, Dong Yu, Chen Kang
https://arxiv.org/abs/2507.19495

Simulating Human Behavior with the Psychological-mechanism Agent: Integrating Feeling, Thought, and Action
Generative agents have made significant progress in simulating human behavior, but existing frameworks often simplify emotional modeling and focus primarily on specific tasks, limiting the authenticity of the simulation. Our work proposes the Psychological-mechanism Agent (PSYA) framework, based on the Cognitive Triangle (Feeling-Thought-Action), designed to more accurately simulate human behavior. The PSYA consists of three core modules: the Feeling module (using a layer model of affect to sim…

Distributed fault-tolerant quantum memories over a 2xL array of qubit modules
Edwin Tham, Min Ye, Ilia Khait, John Gamble, Nicolas Delfosse
https://arxiv.org/abs/2508.01879 http…

Distributed fault-tolerant quantum memories over a 2xL array of qubit modules
We propose an architecture for a quantum memory distributed over a $2 \times L$ array of modules equipped with a cyclic shift implemented via flying qubits. The logical information is distributed across the first row of $L$ modules and quantum error correction is executed using ancilla modules on the second row equipped with a cyclic shift. This work proves that quantum LDPC codes such as BB codes can maintain their performance in a distributed setting while using solely one simple connector: a…

What Makes the Best Decomposition? Investigating Binary Decomposition Under FCG Variance
Ang Jia, He Jiang, Zhilei Ren, Xiaochen Li, Ming Fan, Ting Liu
https://arxiv.org/abs/2506.19425

What Makes the Best Decomposition? Investigating Binary Decomposition Under FCG Variance
Binary decomposition, which decomposes binary files into modules, plays a critical role in binary reuse detection. Existing binary decomposition works either apply anchor-based methods by extending anchor functions to generate modules, or apply clustering-based methods by using clustering algorithms to group binary functions, which all rely on that reused code shares similar function call relationships. However, we find that function call graphs (FCGs) vary a lot when using different compilatio…

Nondegenerate actions on Hilbert C*-modules
Elias Katsoulis, Christopher Ramsey
https://arxiv.org/abs/2507.17104 https://arxiv.org/pd…

Nondegenerate actions on Hilbert C*-modules
Let X be a (right) Hilbert C*-module and let B be a C*-algebra acting on X from the left via adjointable operators. In this note we establish the equivalence of two notions of nondegeneracy for such an action of B on X. Furthermore, we explain how techniques from an earlier paper of Kim can be used to give a short proof of a recent result of Dessi, Kakariadis and Paraskevas.

Comparing four definitions of cotilting modules
Kamran Divaani-Aazar, Ali Mahin Fallah, Massoud Tousi
https://arxiv.org/abs/2507.18860 https://arxiv.org/pd…

Comparing four definitions of cotilting modules
In contrast to the theory of tilting modules, in the dual theory, there is not a unified definition. However, there are several definitions proposed for cotilting modules. In this paper, we compare four of the main definitions for cotilting modules that have been put forward.

Another building facade, another #AbstractAug -- I'll try to get you some pics of vendors at the Ithaca Farmer's Market next where I had the bad judgement of telling a lady that she only wanted to me to take pictures of her flowers that I had 15,000 photos of flowers I hadn't developed
#photo

Fourier-Sato transform for monodromic mixed Hodge modules
R. Virk
https://arxiv.org/abs/2507.16170 https://arxiv.org/pdf/2507.16170…

Fourier-Sato transform for monodromic mixed Hodge modules
We discuss a construction of the Fourier-Sato transform for monodromic mixed Hodge modules.

Govorov--Lazard and finite deconstructibility for Gorenstein and restricted homological dimensions
Souvik Dey, Michal Hrbek, Giovanna Le Gros
https://arxiv.org/abs/2508.20281 ht…

Govorov--Lazard and finite deconstructibility for Gorenstein and restricted homological dimensions
Over Cohen--Macaulay rings admitting a pointwise dualizing module, we show that the class of modules of restricted projective dimension bounded by any integer is finitely deconstructible and that the class of modules of restricted flat dimension bounded by any integer satisfies the Govorov-Lazard property. Along the way, we prove the corresponding result for Gorenstein projective and flat dimensions over (locally) Gorenstein rings. Outside of Cohen--Macaulay rings, we consider analogous propert…

Retrieving biparameter persistence modules from monoparameter ones: a characterization of hook-decomposable persistence modules
Isabella Mastroianni, Marco Guerra, Ulderico Fugacci, Emanuela De Negri
https://arxiv.org/abs/2506.14678

Retrieving biparameter persistence modules from monoparameter ones: a characterization of hook-decomposable persistence modules
Motivated by the need to relate the biparameter persistence module induced by a pair of scalar functions with the monoparameter persistence modules induced by each function separately, we introduce a construction that defines a kind of product between two monoparameter persistence modules. While originally conceived to serve this comparative purpose, our construction unexpectedly reveals a deeper structural property: it also characterizes a class of biparameter modules known as hook-decomposabl…

The category of propositional deductive systems
Ciro Russo
https://arxiv.org/abs/2508.19426 https://arxiv.org/pdf/2508.19426…

The category of propositional deductive systems
We define the category $\mathcal{QM}$ of quantales and their modules and prove the existence of coproducts, and the one of pushout and amalgamated coproducts under certain conditions. Then we define the non-full subcategory $\mathcal{DS}_0$, of propositional deductive systems, show that it is equivalent to the one of ``real'' propositional logics whose morphisms are interpretations (modulo a language translation, when needed), and prove that the coproduct in $\mathcal{DS}_0$ is precisely the de…

Large-Scale LiDAR-Inertial Dataset for Degradation-Robust High-Precision Mapping
Xiaofeng Jin, Ningbo Bu, Shijie Wang, Jianfei Ge, Jiangjian Xiao, Matteo Matteucci
https://arxiv.org/abs/2507.20516

Large-Scale LiDAR-Inertial Dataset for Degradation-Robust High-Precision Mapping
This paper introduces a large-scale, high-precision LiDAR-Inertial Odometry (LIO) dataset, aiming to address the insufficient validation of LIO systems in complex real-world scenarios in existing research. The dataset covers four diverse real-world environments spanning 60,000 to 750,000 square meters, collected using a custom backpack-mounted platform equipped with multi-beam LiDAR, an industrial-grade IMU, and RTK-GNSS modules. The dataset includes long trajectories, complex scenes, and high-…

Weil representations associated to isocrystals over function fields
Maxim Mornev, Richard Pink
https://arxiv.org/abs/2507.20807 https://arxiv.org/pdf/2507.…

Weil representations associated to isocrystals over function fields
Every Anderson $A$-motive $M$ over a field determines a compatible system of Galois representations on its Tate modules at almost all primes of $A$. This adapts easily to $F$-isocrystals, which are rational analogues of $A$-motives for the global function field $F:=\operatorname{Quot}(A)$. We extend this compatible system by constructing a Weil group representation associated to $M$ for every place of $F$. To this end we generalize the Tate module construction to a tensor functor on $F_{\mathfr…

Lightweight Multi-Frame Integration for Robust YOLO Object Detection in Videos
Yitong Quan, Benjamin Kiefer, Martin Messmer, Andreas Zell
https://arxiv.org/abs/2506.20550

Lightweight Multi-Frame Integration for Robust YOLO Object Detection in Videos
Modern image-based object detection models, such as YOLOv7, primarily process individual frames independently, thus ignoring valuable temporal context naturally present in videos. Meanwhile, existing video-based detection methods often introduce complex temporal modules, significantly increasing model size and computational complexity. In practical applications such as surveillance and autonomous driving, transient challenges including motion blur, occlusions, and abrupt appearance changes can …

Structure of modules stably annihilated by a fixed ideal
Yuki Mifune
https://arxiv.org/abs/2508.16137 https://arxiv.org/pdf/2508.16137

Structure of modules stably annihilated by a fixed ideal
Let $R$ be a commutative noetherian ring, and denote by $\operatorname{mod} R$ the category of finitely generated $R$-modules. In this paper, for an ideal $I$ of $R$, we introduce the full subcategory $\operatorname{mod}_{I}(R)$ of $\operatorname{mod} R$ consisting of modules whose stable annihilators contain $I$, and we investigate its structure. As an application, we explore the syzygy category of maximal Cohen--Macaulay $R$-modules, extending a theorem of Dey and Liu from the Gorenstein case…

Extended thermal cycling of ATLAS ITk strip modules with and without stress mitigating interposers
Nikolai Fomin, Bart Hommels, Thomas Ivison, Kosala Kariyapperuma, Jesse Liu
https://arxiv.org/abs/2507.12586

Extended thermal cycling of ATLAS ITk strip modules with and without stress mitigating interposers
This paper investigates critical mechanical failures during stand-alone thermocycling of ATLAS Inner Tracker strip pre-production modules. Five modules undergo extended thermocycling after adequately levelling thermal chucks and introducing interlocks for unattended operation. Module bow evolution is tracked via regular sensor metrology. All five modules exhibit bow increases with a mean of $146\pm 27~μ$m when raising maximum cycling temperatures from $20^\circ$C to $40^\circ$C. Four such modu…

SuperMag: Vision-based Tactile Data Guided High-resolution Tactile Shape Reconstruction for Magnetic Tactile Sensors
Peiyao Hou, Danning Sun, Meng Wang, Yuzhe Huang, Zeyu Zhang, Hangxin Liu, Wanlin Li, Ziyuan Jiao
https://arxiv.org/abs/2507.20002

SuperMag: Vision-based Tactile Data Guided High-resolution Tactile Shape Reconstruction for Magnetic Tactile Sensors
Magnetic-based tactile sensors (MBTS) combine the advantages of compact design and high-frequency operation but suffer from limited spatial resolution due to their sparse taxel arrays. This paper proposes SuperMag, a tactile shape reconstruction method that addresses this limitation by leveraging high-resolution vision-based tactile sensor (VBTS) data to supervise MBTS super-resolution. Co-designed, open-source VBTS and MBTS with identical contact modules enable synchronized data collection of …

GLARE: Agentic Reasoning for Legal Judgment Prediction
Xinyu Yang, Chenlong Deng, Zhicheng Dou
https://arxiv.org/abs/2508.16383 https://arxiv.org/pdf/2508.…

GLARE: Agentic Reasoning for Legal Judgment Prediction
Legal judgment prediction (LJP) has become increasingly important in the legal field. In this paper, we identify that existing large language models (LLMs) have significant problems of insufficient reasoning due to a lack of legal knowledge. Therefore, we introduce GLARE, an agentic legal reasoning framework that dynamically acquires key legal knowledge by invoking different modules, thereby improving the breadth and depth of reasoning. Experiments conducted on the real-world dataset verify the…

De Rham-Higgs comparison for mixed Hodge modules in positive characteristic
Zhang Zebao
https://arxiv.org/abs/2507.15175 https://arxi…

De Rham-Higgs comparison for mixed Hodge modules in positive characteristic
Building on the nonabelian Hodge theory in positive characteristic developed by Ogus, Vologodsky, and Schepler, we propose a generalization of the decomposition theorem of Deligne and Illusie from the perspective of mixed Hodge modules. This generalization is verified in certain special cases by extending the method of Sheng and the author, leading to several interesting byproducts.

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.

A chromatic approach to homological stability
Oscar Randal-Williams
https://arxiv.org/abs/2508.20629 https://arxiv.org/pdf/2508.20629

A chromatic approach to homological stability
We propose a way to organise the subject of ``higher-order homological stability'', in the context of a graded $E_2$-algebra $\mathbf{R}$, along the same lines that the chromatic perspective organises stable homotopy theory. From this point of view proving a (higher-order) homological stability theorem corresponds to producing Smith--Toda complexes in the category of $\mathbf{R}$-modules: using this perspective we prove that whenever $\mathbf{R}$ is defined over a field of positive characteri…

Detecting Hardware Trojans in Microprocessors via Hardware Error Correction Code-based Modules
Alessandro Palumbo, Ruben Salvador
https://arxiv.org/abs/2506.15417

Detecting Hardware Trojans in Microprocessors via Hardware Error Correction Code-based Modules
Software-exploitable Hardware Trojans (HTs) enable attackers to execute unauthorized software or gain illicit access to privileged operations. This manuscript introduces a hardware-based methodology for detecting runtime HT activations using Error Correction Codes (ECCs) on a RISC-V microprocessor. Specifically, it focuses on HTs that inject malicious instructions, disrupting the normal execution flow by triggering unauthorized programs. To counter this threat, the manuscript introduces a Hardw…

All-in-One Slider for Attribute Manipulation in Diffusion Models
Weixin Ye, Hongguang Zhu, Wei Wang, Yahui Liu, Mengyu Wang
https://arxiv.org/abs/2508.19195 https://

All-in-One Slider for Attribute Manipulation in Diffusion Models
Text-to-image (T2I) diffusion models have made significant strides in generating high-quality images. However, progressively manipulating certain attributes of generated images to meet the desired user expectations remains challenging, particularly for content with rich details, such as human faces. Some studies have attempted to address this by training slider modules. However, they follow a One-for-One manner, where an independent slider is trained for each attribute, requiring additional tra…

Relative braid group symmetries on modified $\mathrm{i}$quantum groups and their modules
Weiqiang Wang, Weinan Zhang
https://arxiv.org/abs/2508.12041 https://

Relative braid group symmetries on modified $\mathrm{i}$quantum groups and their modules
We present a comprehensive generalization of Lusztig's braid group symmetries for quasi-split iquantum groups. Specifically, we give 3 explicit rank one formulas for symmetries acting on integrable modules over a quasi-split iquantum group of arbitrary Kac-Moody type with general parameters. These symmetries are formulated in terms of idivided powers and iweights of the vectors being acted upon. We show that these symmetries are consistent with the relative braid group symmetries on iquantum gr…

Simple smooth modules over the Lie algebras of polynomial vector fields
Zhiqiang Li, Cunguang Cheng, Shiyuan Liu, Rencai Lu, Kaiming Zhao, Yueqiang Zhao
https://arxiv.org/abs/2506.18262

Simple smooth modules over the Lie algebras of polynomial vector fields
Let $\mathfrak{g}:={\rm Der}(\mathbb{C}[t_1, t_2,\cdots, t_n])$ and $\mathcal{L}:={\rm Der}(\mathbb{C}[[t_1, t_2,\cdots, t_n]])$ be the Witt Lie algebras. Clearly, $\mathfrak{g}$ is a proper subalegbra of $\mathcal{L}$. Surprisingly, we prove that simple smooth modules over $\mathfrak{g}$ are exactly the simple modules over $\mathcal{L}$ studied by Rodakov (no need to take completion). Then we find an easy and elementary way to classify all simple smooth modules over $\mathfrak{g}$. When the …

Finiteness of associated primes for local cohomology modules of excellent locally unramified regular rings of finite Krull dimension
Takumi Murayama
https://arxiv.org/abs/2506.17875

Finiteness of associated primes for local cohomology modules of excellent locally unramified regular rings of finite Krull dimension
Thirty years ago, Huneke (for local rings) and Lyubeznik (in general) conjectured that for all regular rings $R$, the local cohomology modules $H^i_I(R)$ have finitely many associated prime ideals. We prove substantial new cases of their conjecture by proving that the local cohomology modules $H^i_I(R)$ have finitely many associated prime ideals whenever $R$ is an excellent regular ring of finite Krull dimension such that $R/pR$ is regular and $F$-finite for every prime number $p$. Our result i…

Reconstruction theorems for coadmissible D-cap-modules
Finn Wiersig
https://arxiv.org/abs/2506.12601 https://arxiv.org/pdf/2506.12601…

Reconstruction theorems for coadmissible D-cap-modules
We prove a Riemann-Hilbert correspondence for Ardakov-Wadsley's coadmissible D-cap-modules and, more generally, for Bode's $\mathcal{C}$-complexes. More precisely, we show that any given $\mathcal{C}$-complex can be reconstructed out of its solutions. As a corollary, we find that slight modifications of the solution and de Rham functors introduced by the author are fully faithful on $\mathcal{C}$-complexes and, in particular, on coadmissible D-cap-modules. One of the many steps of our proof is …

Parallels Between VLA Model Post-Training and Human Motor Learning: Progress, Challenges, and Trends
Tian-Yu Xiang, Ao-Qun Jin, Xiao-Hu Zhou, Mei-Jiang Gui, Xiao-Liang Xie, Shi-Qi Liu, Shuang-Yi Wang, Sheng-Bin Duan, Fu-Chao Xie, Wen-Kai Wang, Si-Cheng Wang, Ling-Yun Li, Tian Tu, Zeng-Guang Hou
https://arxiv.org/abs/2506.20966…

Parallels Between VLA Model Post-Training and Human Motor Learning: Progress, Challenges, and Trends
Vision-language-action (VLA) models extend vision-language models (VLM) by integrating action generation modules for robotic manipulation. Leveraging strengths of VLM in vision perception and instruction understanding, VLA models exhibit promising generalization across diverse manipulation tasks. However, applications demanding high precision and accuracy reveal performance gaps without further adaptation. Evidence from multiple domains highlights the critical role of post-training to align fou…

GLARE: Agentic Reasoning for Legal Judgment Prediction
Xinyu Yang, Chenlong Deng, Zhicheng Dou
https://arxiv.org/abs/2508.16383 https://arxiv.org/pdf/2508.…

GLARE: Agentic Reasoning for Legal Judgment Prediction
Legal judgment prediction (LJP) has become increasingly important in the legal field. In this paper, we identify that existing large language models (LLMs) have significant problems of insufficient reasoning due to a lack of legal knowledge. Therefore, we introduce GLARE, an agentic legal reasoning framework that dynamically acquires key legal knowledge by invoking different modules, thereby improving the breadth and depth of reasoning. Experiments conducted on the real-world dataset verify the…

The spectrum of global representations for families of bounded rank and VI-modules
Miguel Barrero, Tobias Barthel, Luca Pol, Neil Strickland, Jordan Williamson
https://arxiv.org/abs/2506.21525

The spectrum of global representations for families of bounded rank and VI-modules
A global representation is a compatible collection of representations of the outer automorphism groups of the finite groups belonging to a family $\mathscr{U}$. These arise in classical representation theory, in the study of representation stability, as well as in global homotopy theory. In this paper we begin a systematic study of the derived category $\mathsf{D}(\mathscr{U};k)$ of global representations over fields $k$ of characteristic zero, from the point-of-view of tensor-triangular geomet…

Replaced article(s) found for math.AT. https://arxiv.org/list/math.AT/new
[1/1]:
- Interval Decomposition of Persistence Modules over a Principal Ideal Domain
Jiajie Luo, Gregory Henselman-Petrusek

Coherent six-functor formalisms: Pro vs Solid
Fei Ren
https://arxiv.org/abs/2506.21082 https://arxiv.org/pdf/2506.21082

Coherent six-functor formalisms: Pro vs Solid
In the classical theory for coherent sheaves, the only missing piece in the Grothendieck six-functor formalism picture is $j_!$ for an open immersion $j$. Towards fixing this gap,classically Deligne proposed a construction of $j_!$ by extending the sheaf class to pro sheaves, while Clausen-Scholze provided another solution by extending the sheaf class to solid modules. In this work, we prove that Deligne's construction coincides with the Clausen-Scholze construction via a natural functor, whose…

Group valued moment maps for even and odd simple $G$-modules
Anton Alekseev, Andrey Krutov
https://arxiv.org/abs/2507.19434 https://arxiv.org/pdf/2507.1943…

Group valued moment maps for even and odd simple $G$-modules
Let $G$ be a simple Lie group, and $\mathfrak{g}$ its Lie algebra. It is well known that a $G$-module $V$ carrying an invariant symplectic form or an invariant scalar product gives rise to a Hamiltonian Poisson space with a quadratic moment maps $μ$. We show that under condition ${\rm Hom}_{\mathfrak{g}}(\wedge^3 V, S^3V)=0$ this space can be viewed as a quasi-Poisson space with the same bivector, and with the group valued moment map $Φ= \exp \circ μ$. Furthermore, we show that by modifying …

Finiteness of the set of associated primes for local cohomology modules of ideals via properties of almost factorial rings
Ryotaro Hanyu
https://arxiv.org/abs/2506.17586

Finiteness of the set of associated primes for local cohomology modules of ideals via properties of almost factorial rings
We investigate the finiteness of the set of associated primes for local cohomology modules $H_I^{i}(J)$ of an ideal $J$ generated by an $R$-sequence, through the comparison of $H_I^{d+1}(J)$ and $H_I^d(R/J)$, where $d = \mathrm{depth}_I(R)$. The properties of almost factorial rings play a key role in enabling this comparison. Under suitable conditions, we prove that the finiteness of $\mathrm{Ass} H_I^{d+1}(J)$ is equivalent to that of $\mathrm{Ass} H_I^d(R/J)$. Moreover, we give a few conditio…

APT*: Asymptotically Optimal Motion Planning via Adaptively Prolated Elliptical R-Nearest Neighbors
Liding Zhang, Sicheng Wang, Kuanqi Cai, Zhenshan Bing, Fan Wu, Chaoqun Wang, Sami Haddadin, Alois Knoll
https://arxiv.org/abs/2508.19790

APT*: Asymptotically Optimal Motion Planning via Adaptively Prolated Elliptical R-Nearest Neighbors
Optimal path planning aims to determine a sequence of states from a start to a goal while accounting for planning objectives. Popular methods often integrate fixed batch sizes and neglect information on obstacles, which is not problem-specific. This study introduces Adaptively Prolated Trees (APT*), a novel sampling-based motion planner that extends based on Force Direction Informed Trees (FDIT*), integrating adaptive batch-sizing and elliptical $r$-nearest neighbor modules to dynamically modul…

Banach modules, almost mathematics and condensed mathematics
Dimitri Dine
https://arxiv.org/abs/2508.11268 https://arxiv.org/pdf/2508.11268

Banach modules, almost mathematics and condensed mathematics
We study the relationship between almost mathematics, condensed mathematics and the categories of seminormed and Banach modules over a Banach ring $A$, with submetric (norm-decreasing) $A$-module homomorphisms for morphisms. If $A$ is a Banach ring with a norm-multiplicative topologically nilpotent unit $\varpi$ contained in the closed unit ball $A_{\leq1}$ such that $\varpi$ admits a compatible system of $p$-power roots $\varpi^{1/p^{n}}$ with \begin{equation*}\lVert\varpi^{1/p^{n}}\rVert=\lVe…

Linkage of sheaves of modules
Farhad Rahmati, Khadijeh Sayyari
https://arxiv.org/abs/2507.00200 https://arxiv.org/pdf/2507.00200

Linkage of sheaves of modules
Inspired by the works in linkage theory of modules, we define the concept of linkage of sheaves of modules as a generalization of linkage of modules. Thus, we expressed it in geometry algebraic language. We show that the linkedness of sheaves is a locally property. As an important result, we have shown that the sheaf of modules made of Glueing schemes and Glueing linked sheaves of modules is a linked sheaf. Also, it has been shown that for every sheaf of modules on non-domain, it is possible to…

On preservation of relative resolutions for poset representations
Toshitaka Aoki, Shunsuke Tada
https://arxiv.org/abs/2506.21227 https://

On preservation of relative resolutions for poset representations
The concept of Galois connections (i.e., adjoint pairs between posets) is ubiquitous in mathematics. In representation theory, it is interesting because it naturally induces the adjoint quadruple between the categories of persistence modules (representations) of the posets via Kan extensions. One of central subjects in multiparameter persistent homology analysis is to understand structures of persistence modules. In this paper, we mainly study a class of Galois connections whose left adjoint is…

Comparing the face rings of a boolean complex and its barycentric subdivision
Ben Blum-Smith, Sophie Marques
https://arxiv.org/abs/2507.20037 https://arxiv…

Comparing the face rings of a boolean complex and its barycentric subdivision
We consider the relationship between the Stanley-Reisner ring (a.k.a. face ring) of a simplicial or boolean complex $Δ$ and that of its barycentric subdivision. These rings share a distinguished parameter subring. S. Murai asked if they are isomorphic, equivariantly with respect to the automorphism group $\operatorname{Aut}(Δ)$, as modules over this parameter subring. We show that, in general, the answer is no, but for Cohen-Macaulay complexes in characteristic coprime to $|\operatorname…

The Moduli Stack of Breuil-Kisin Modules with Descent Data for Reductive Groups
Eivind Otto Hjelle
https://arxiv.org/abs/2506.11910 https://

The Moduli Stack of Breuil-Kisin Modules with Descent Data for Reductive Groups
We introduce and study the moduli stack $\mathcal{Y}$ of Breuil-Kisin modules with $\hat{G}$-structure and descent data, or Breuil-Kisin $(Γ,\hat{G})$-torsors for short. Specifically, for a dominant cocharacter $μ$, we define the moduli stack $\mathcal{Y}^{\leq μ}$ of Breuil-Kisin $(Γ,\hat{G})$-torsors with Hodge-Tate weights bounded by $μ$. We prove that $\mathcal{Y}^{\leq μ}$ is a $p$-adic formal algebraic stack, and show that it is smoothly equivalent to (the $p$-adic completion of) a …

An isometry theorem induced by the Radon transform between the convolution and interleaving distances
Michiaki Takiwaki
https://arxiv.org/abs/2506.12046 ht…

An isometry theorem induced by the Radon transform between the convolution and interleaving distances
One-parameter persistence modules are applied to various subjects as tools in data analysis. On the other hand, since the theoretical study of multi-parameter persistence modules is not enough and in progress, they have few applications. The sheaf theory is expected to elucidate detailed properties of persistence modules and give features of multi-parameter ones for applications. However, the categories of sheaves on two or more dimensional Euclidean spaces have more complicated structures than…

Constructing and transforming standard resolutions of local modules
Xingbang Hao
https://arxiv.org/abs/2508.11306 https://arxiv.org/pdf/2508.11306

Constructing and transforming standard resolutions of local modules
We construct standard resolutions for analytic local modules on complex hypersurfaces using standard basis methods, with extensions to complete intersections. The algebraic version over arbitrary infinite fields is also suggested. Applications include derived category formula of local hypersurface blow-ups, revealing new connections between standard bases and categorical geometry.

Construction of Young modules and filtration multiplicities for Brauer algebras of type $C$
Sulakhana Chowdhury, Geetha Thangavelu
https://arxiv.org/abs/2507.14078

Construction of Young modules and filtration multiplicities for Brauer algebras of type $C$
In this paper, we construct the permutation modules and Young modules for Brauer algebras of type $C$ by extending the representation theory of the group algebra of hyperoctahedral groups. Additionally, we develop a stratifying system for Brauer algebras of type $C$, thereby extending the work of Hemmer-Nakano in \cite{HN} on Hecke algebras. This framework allows us to determine when the multiplicities of cell modules in any filtration are well-defined. As a result, we prove that if the charact…

On Projective modules over graded $R$-subalgebras of $R[X,1/X]$
Diksha Garg, Anjan Gupta
https://arxiv.org/abs/2506.18826 https://arx…

On Projective modules over graded $R$-subalgebras of $R[X,1/X]$
Let $R$ be a Noetherian ring of dimension $d$ and $A$ be a graded $R$-subalgebra of $R[X,1/X]$. Let $P$ be a projective module over $A$ of rank $r \geq \max\{d+1,2\}$ and $\v=(a,p)$ be a unimodular element of $A \oplus P$. We find an elementary automorphism $τ$ such that $τ(\v) = (1, 0)$. Consequently, we obtain the cancellative property of $P$. We show that $P$ splits off a free summand of rank one. When $A = R[X]$ or $R[X, 1/ X]$, the results are well-known due to the contributions by vario…

Replaced article(s) found for math.RT. https://arxiv.org/list/math.RT/new
[1/1]:
- A weight-formula for all highest weight modules, and a higher order parabolic category $\mathcal{O}$
Apoorva Khare, G. Krishna Teja

The second Hilbert coefficient of modules with almost maximal depth
Van Duc Trung
https://arxiv.org/abs/2506.17591 https://arxiv.org/…

The second Hilbert coefficient of modules with almost maximal depth
Let $\mathbb{M} = \{ M_n \}$ be a good $\mathfrak{q}$-filtration of a finitely generated $R$-module $M$ of dimension $d$, where $(R,\mathfrak{m})$ is a local ring and $\mathfrak{q}$ is an $\mathfrak{m}$-primary ideal of $R$. In case $depth(M) \geq d-1$, we give an upper bound for the second Hilbert coefficient $e_2(\mathbb{M})$ generalizing results by Huckaba-Marley and Rossi-Valla proved assuming that $M$ is Cohen-Macaulay. We also give a condition for the equality, which relates to the depth …

Radical property of the traces of the canonical modules of Cohen-Macaulay rings
Mitsuhiro Miyazaki
https://arxiv.org/abs/2506.17987 https://

Radical property of the traces of the canonical modules of Cohen-Macaulay rings
In this paper, we define a new concept of Noetherian commutative rings which stands between Gorenstein and Cohen-Macaulay properties. We show that this new property keep hold under common operations of commutative rings such as localization, polynomial extension and under mild assumptions, flat extension, tensor product, Segre product and so on. We show that for Schubert cycles, the Ehrhart rings of cycle graphs and perfect graphs, this new concept is close to Gorenstein property.

More ghost modules I
Kiyoshi Igusa
https://arxiv.org/abs/2506.12904 https://arxiv.org/pdf/2506.12904…

More ghost modules I
Ghost modules were introduced in [I3] without definitions or proofs. We also introduced stability diagrams or "relative pictures" for torsion classes and torsion-free classes for representations of Dynkin quivers. Modules which were not in the chosen class reappeared as "ghosts", in fact one missing module produced two ghosts. In this short paper, we give a precise definition of ghost modules. We give several examples and prove basis properties of ghosts and pictures for torsion and torsion-fre…

Bigraded components of F-finite F-modules
Sayed Sadiqul Islam, Tony J. Puthenpurakal
https://arxiv.org/abs/2508.15742 https://arxiv.org/pdf/2508.15742

Bigraded components of F-finite F-modules
Let $A$ be a regular ring containing a field of characteristic $p>0$ and let $R=A[x_1,\ldots,x_m,y_1,\ldots,y_n]$ be standard bigraded over $A$, i.e., $\operatorname{bideg}(A)=(0,0)$, $\operatorname{bideg}(x_i)=(1,0)$ and $\operatorname{bideg}(y_j)=(0,1)$ for all $i$ and $j$. Assume that $M=\bigoplus_{i,j} M_{(i,j)}$ is a bigraded $F_R$-finite, $F_R$-module. We use Lyubeznik's theory of $F$-finite, $F$-modules from \cite{Lyu-Fmod} to study the bigraded components of $M$. The properties we study…

An explicit construction of the Weyl module as a quotient of symmetric tensors by dual Garnir relations
Eoghan McDowell
https://arxiv.org/abs/2508.14788 https://

An explicit construction of the Weyl module as a quotient of symmetric tensors by dual Garnir relations
The Weyl modules are the standard modules for the Schur algebra. Their duals (the costandard modules) have well-known constructions as quotients of exterior powers and as submodules of symmetric powers. This paper presents analogous constructions for the Weyl modules themselves, introducing relations that are a non-trivial dualisation of the Garnir relations. More generally, our constructions describe endofunctors on the category of representations of any group.

Quasi-Whittaker modules
Cunguang Cheng, Wenting Gao, Shiyuan Liu, Kaiming Zhao, Yueqiang Zhao
https://arxiv.org/abs/2508.05917 https://arxiv.org/pdf/2508.0…

Quasi-Whittaker modules
In this paper, a general setting is proposed to define a class of modules over nonsemisimple Lie algebras $\mathfrak{g}$ induced by a nonperfect ideal $\mathfrak{p}$. This class of Lie algebras includes many well-known Lie algebras, and some of this class of modules are Whittaker modules and others are not. We call these modules quasi-Whittaker modules. By introducing a new concept: the Whittaker annihilator for universal quasi-Whittaker modules, we are able to determine the necessary and suffi…

Ascent and descent of Artinian module structures under flat base changes
Tran Do Minh Chau, Le Thanh Nhan
https://arxiv.org/abs/2507.19019 https://arxiv.or…

Ascent and descent of Artinian module structures under flat base changes
Let $φ: R\rightarrow S$ be a flat local homomorphism between commutative Noetherian local rings. In this paper, the ascent and descent of Artinian module structures between $R$ and $S$ are investigated. For an Artinian $R$-module $A$, the structure of $A\otimes_RS$ is described. As an application, the Artinianess of certain local cohomology modules is clarified.

A note on D-modules on the projective spaces of a class of G-representations
Philibert Nang
https://arxiv.org/abs/2507.17970 https://arxiv.org/pdf/2507.179…

A note on D-modules on the projective spaces of a class of G-representations
Consider $(G, V)$ a finite-dimensional representation of a connected reductive complex Lie group $G$ and $\mathbb{P}\left( V\right) $ the projective space of $V$. Denote by $G'$ the derived subgroup of $G$ and assume that the categorical quotient is one dimensional. In the case where the representation $(G, V)$ is also multiplicity-free, it is known from Howe-Umeda [4] that the algebra of $G$-invariant differential operators $Γ\left(V, \mathcal{D}_V\right)^G$ is a commutative polynomial ring. …

New simple modules for the $W$-algebra $W(2,2)$
Hongjia Chen, Dashu Xu
https://arxiv.org/abs/2506.08794 https://arxiv.org/pdf/2506.08…

New simple modules for the $W$-algebra $W(2,2)$
In this paper, we construct a novel class of simple modules for the $W$-algebra $W(2,2)$. Our approach involves taking tensor products of finitely many non-weight simple modules $Ω(λ,α,h)$ with an arbitrary simple restricted module. We provide a necessary and sufficient condition for these modules to be simple, and subsequently determine their isomorphism classes. Through a comparative analysis with other known simple modules in the literature, we establish that these constructed modules are…

Tilting theoretic approach to quasi-hereditary structures
Takahide Adachi, Aaron Chan, Yuta Kimura, Mayu Tsukamoto
https://arxiv.org/abs/2507.16575 https:/…

Tilting theoretic approach to quasi-hereditary structures
A quasi-hereditary algebra is an algebra equipped with a certain partial order $\unlhd$ on its simple modules. Such a partial order -- called a quasi-hereditary structure -- gives rise to a characteristic tilting module $T_{\unlhd}$ by a classical result due to Ringel. A fundamental question is to determine which tilting modules can be realised as characteristic tilting modules. We answer this question by using the notion of IS-tilting module, which is a pair $(T,\unlhd)$ of a tilting module $T…

Joint reductions and mixed Buchsbaum-Rim multiplicities of modules and a joint-reduction-number-zero theorem
Daniel Katz, Vijay Kodiyalam, J. K. Verma
https://arxiv.org/abs/2508.07437

Joint reductions and mixed Buchsbaum-Rim multiplicities of modules and a joint-reduction-number-zero theorem
We offer new definitions of joint reductions and mixed Buchsbaum-Rim multiplicity for certain collections of modules over a Noetherian local ring and illustrate their application to give two different proofs of a joint-reduction-number-zero theorem for integrally closed modules over two-dimensional regular local rings. We also relate the mixed Buchsbaum-Rim multiplicity of modules to the Euler-Poincaré characteristic of a natural Koszul complex and relate it to the mixed Buchsbaum-Rim multipli…

Homological Bounds of Gentle algebras
Yu-Zhe Liu, Xin Ma, Jiacheng Xu, Chao Zhang
https://arxiv.org/abs/2508.19763 https://arxiv.org/pdf/2508.19763

Homological Bounds of Gentle algebras
This paper studies the homological bounds of gentle algebras, i.e., the upper bounds for the sum of the projective and injective dimensions of indecomposable modules over gentle algebras. We provide conditions under which this sum is strictly less than twice the global dimension, and as an application, we give a characterization of quasi-tilted gentle algebras.

Representations of the N=1 Heisenberg-Virasoro superalgebra
Ziqi Hong, Haibo Chen, Yucai Su
https://arxiv.org/abs/2508.08738 https://arxiv.org/pdf/2508.087…

Representations of the N=1 Heisenberg-Virasoro superalgebra
We first define a class of non-weight modules over the N=1 Heisenberg-Virasoro superalgebra $\mathfrak{g}$, which are reducible modules. Then we give all submodules of such modules, and present the corresponding irreducible quotient modules which were exactly studied in \cite{DL}. Also, we prove that those modules constitute a complete classification of $U(\mathfrak{h})$-free modules of rank $2$ over $\mathfrak{g}$, where $\mathfrak{h}=\C L_{0}\oplus\C H_{0}$ is the degree-0 part of $\mathfra…

Replaced article(s) found for math.RT. https://arxiv.org/list/math.RT/new
[1/1]:
- Generic modules for the category of filtered by standard modules
Raymundo Bautista Ramos, Jes\'us Efr\'en P\'erez Terrazas, Leonardo Salmer\'on Castro

A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories
Zhenxing Di, Liping Li, Li Liang
https://arxiv.org/abs/2506.08685

A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories
We prove that every Grothendieck topology induces a hereditary torsion pair in the category of presheaves of modules on a ringed site, and obtain a homological characterization of sheaves of modules: a presheaf of modules is a sheaf of modules if and only if it is saturated with respect to torsion presheaves, or equivalently, it is right perpendicular to torsion presheaves in the sense of Geigle and Lenzing. We also study Grothendieck topologies on directed categories $\mathscr{C}$, and show th…

Classification of irreducible Harish-Chandra modules over map full toroidal Lie algebras
Sudipta Mukherjee
https://arxiv.org/abs/2508.11448 https://arxiv.o…

Classification of irreducible Harish-Chandra modules over map full toroidal Lie algebras
A natural higher dimensional analogue of the affine-Virasoro algebra is the full toroidal Lie algebra. In this paper, we classify irreducible Harish-Chandra modules for map full toroidal Lie algebras. We show that every such module is either a cuspidal or a highest weight module. Furthermore, we prove that they turn out to be single point evaluation modules.

Simple restricted modules of non-zero level over a deformed Heisenberg-Virasoro algebra
Shun Liu, Dashu Xu
https://arxiv.org/abs/2506.10830 https://…

Simple restricted modules of non-zero level over a deformed Heisenberg-Virasoro algebra
We study representations of a deformed Heisenberg-Virasoro algebra that does not admit a triangular decomposition. Despite this, its $\mathbb{Z}$-gradation allows the classification of simple restricted modules. We show that all such modules of non-zero level arise via induction from simple modules of finite-dimensional solvable Lie algebras.