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A Categorical Approach to Finiteness Conditions
David Forsman
https://arxiv.org/abs/2509.10204 https://arxiv.org/pdf/2509.10204

A Categorical Approach to Finiteness Conditions
We introduce a general categorical framework for finiteness conditions that unifies classical notions such as Noetherianness, Artinianness, and various forms of topological compactness. This is achieved through the concept of \textbf{$τ$-compactness}, defined relative to a \textbf{coverage} $τ$. A coverage on a category $C$ is a specified class of covering diagrams, which are functors $F\colon I \to C/c$ of a specified variance, where the indexing category $I$ is equipped with a set of 'desig…

Computable Bases
Vasco Brattka, Emmanuel Rauzy
https://arxiv.org/abs/2510.09850 https://arxiv.org/pdf/2510.09850 …

Computable Bases
In computable analysis typically topological spaces with countable bases are considered. The Theorem of Kreitz-Weihrauch implies that the subbase representation of a second-countable $T_0$ space is admissible with respect to the topology that the subbase generates. We consider generalizations of this setting to bases that are representable, but not necessarily countable. We introduce the notions of a computable presubbase and a computable prebase. We prove a generalization of the Theorem of Kre…

Controller for Incremental Input-to-State Practical Stabilization of Partially Unknown systems with Invariance Guarantees
P Sangeerth, David Smith Sundarsingh, Bhabani Shankar Dey, Pushpak Jagtap
https://arxiv.org/abs/2510.10450

Controller for Incremental Input-to-State Practical Stabilization of Partially Unknown systems with Invariance Guarantees
Incremental stability is a property of dynamical systems that ensures the convergence of trajectories with respect to each other rather than a fixed equilibrium point or a fixed trajectory. In this paper, we introduce a related stability notion called incremental input-to-state practical stability (δ-ISpS), ensuring safety guarantees. We also present a feedback linearization based control design scheme that renders a partially unknown system incrementally input-to-state practically stable and …

Uniformly-S-pseudo-projective modules
Mohammad adarbeh, Mohammad Saleh
https://arxiv.org/abs/2510.10170 https://arxiv.org/pdf/2510.10170

Uniformly-S-pseudo-projective modules
In this paper, we introduce the notion of uniformly-S-pseudo-projective (u-S-pseudo-projective) modules as a generalization of u-S-projective modules. Let R be a ring and S a multiplicative subset of R. An R-module P is said to be u-S-pseudo-projective if for any submodule K of P, there is s\in S such that for any u-S-epimorphism f:P\to \frac{P}{K}, sf can be lifted to an endomorphism g:P\to P. Some properties of this notion are obtained. For example, we prove that an R-module M is u-S-quasi-pr…

Hey, wait a minute: on at-issue sensitivity in Language Models
Sanghee J. Kim, Kanishka Misra
https://arxiv.org/abs/2510.12740 https://arxiv.org/pdf/2510.1…

Hey, wait a minute: on at-issue sensitivity in Language Models
Evaluating the naturalness of dialogue in language models (LMs) is not trivial: notions of 'naturalness' vary, and scalable quantitative metrics remain limited. This study leverages the linguistic notion of 'at-issueness' to assess dialogue naturalness and introduces a new method: Divide, Generate, Recombine, and Compare (DGRC). DGRC (i) divides a dialogue as a prompt, (ii) generates continuations for subparts using LMs, (iii) recombines the dialogue and continuations, and (iv) compares the lik…

Multi-Copy Security in Unclonable Cryptography
Alper \c{C}akan, Vipul Goyal, Fuyuki Kitagawa, Ryo Nishimaki, Takashi Yamakawa
https://arxiv.org/abs/2510.12626 https://

Multi-Copy Security in Unclonable Cryptography
Unclonable cryptography leverages the quantum no-cloning principle to copy-protect cryptographic functionalities. While most existing works address the basic single-copy security, the stronger notion of multi-copy security remains largely unexplored. We introduce a generic compiler that upgrades collusion-resistant unclonable primitives to achieve multi-copy security, assuming only one-way functions. Using this framework, we obtain the first multi-copy secure constructions of public-key quant…

Verification of Sequential Convex Programming for Parametric Non-convex Optimization
Rajiv Sambharya, Nikolai Matni, George Pappas
https://arxiv.org/abs/2511.10622 https://arxiv.org/pdf/2511.10622 https://arxiv.org/html/2511.10622
arXiv:2511.10622v1 Announce Type: new
Abstract: We introduce a verification framework to exactly verify the worst-case performance of sequential convex programming (SCP) algorithms for parametric non-convex optimization. The verification problem is formulated as an optimization problem that maximizes a performance metric (e.g., the suboptimality after a given number of iterations) over parameters constrained to be in a parameter set and iterate sequences consistent with the SCP update rules. Our framework is general, extending the notion of SCP to include both conventional variants such as trust-region, convex-concave, and prox-linear methods, and algorithms that combine convex subproblems with rounding steps, as in relaxing and rounding schemes. Unlike existing analyses that may only provide local guarantees under limited conditions, our framework delivers global worst-case guarantees--quantifying how well an SCP algorithm performs across all problem instances in the specified family. Applications in control, signal processing, and operations research demonstrate that our framework provides, for the first time, global worst-case guarantees for SCP algorithms in the parametric setting.
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Division algebras of slice-Nash functions
Cinzia Bisi, Antonio Carbone
https://arxiv.org/abs/2510.09779 https://arxiv.org/pdf/2510.09779

Division algebras of slice-Nash functions
The purpose of this paper is to introduce the notion of Nash functions in the context of slice regular functions of one quaternionic or octonionic variable. We begin with a detailed analysis of the possible definitions of Nash slice regular functions which leads us to the definition of \textit{slice-Nash} function proposed in this paper (and which we strongly believe to be the natural generalisation of the classical real and complex Nash functions to this context). Once the `correct' definition…

On defectivity of joins, reducible secants and Fr\"oberg's conjecture
Alexander Blomenhofer, Alex Casarotti
https://arxiv.org/abs/2509.10443 https://

On defectivity of joins, reducible secants and Fröberg's conjecture
We introduce the notion of r-defectivity for a vector bundle on a quasi-projective variety. Using this tool, we prove several previously unknown cases of Fröberg's conjecture and also of the postulation problem for fat point schemes. Our techniques also allow us to study r-nondefectivity for joins and secants of reducible varieties. As a consequence, we derive results for mixture distributions and partition ranks.

The smallest $n$-pure subtopos and dimension theory
Jens Hemelaer
https://arxiv.org/abs/2510.10349 https://arxiv.org/pdf/2510.10349

The smallest $n$-pure subtopos and dimension theory
We introduce the notion of $n$-pure geometric morphism between Grothendieck toposes, over a Grothendieck base topos $\mathcal{T}$. This is a higher-dimensional analogue of the concepts of dense and pure geometric morphism. We extend the construction of the smallest dense subtopos and smallest pure subtopos by constructing a smallest $n$-pure subtopos, for each natural number $n$. Based on this, we then propose a concept of dimension for a Grothendieck topos, in this way also arriving naturally …