Tootfinder

Q&A with Notion CEO Ivan Zhao on Notion's evolution into an "AI workspace", being profitable, B2B vs. B2C, usage-based pricing for AI, and more (Casey Newton/The Verge)
https://www.theverge.com/decoder-podcast-w

Notion CEO Ivan Zhao wants you to demand better from your tools
Notion’s Ivan Zhao on AI, productivity, and the future of work.

Interesting observation by Langdon Winner regarding technological transformation: “by the time the issue of ‘use’ comes up for consideration at all, many of the most interesting questions involved in how technologies are constituted and how they affect what we do are settled or sub-merged.”
This is happening right now with #GenAI .

Generalized splitting of algebras with application to a bialgebra structure of Leibniz algebras induced from averaging Lie bialgebras
Chengming Bai, Li Guo, Guilai Liu, Quan Zhao
https://arxiv.org/abs/2509.14137

Generalized splitting of algebras with application to a bialgebra structure of Leibniz algebras induced from averaging Lie bialgebras
The classical notion of splitting a binary quadratic operad $\mathcal{P}$ gives the notion of pre-$\mathcal{P}$-algebras characterized by $\mathcal{O}$-operators, with pre-Lie algebras as a well-known example. Pre-$\mathcal{P}$-algebras give a refinement of the structure of $\mathcal{P}$-algebras and is critical in the Manin triple approach to bialgebras for $\mathcal{P}$-algebras. Motivated by the new types of splitting appeared in recent studies, this paper aims to extend the classical notion…

On Strong and Weak Admissibility in Non-Flat Assumption-Based Argumentation
Matti Berthold, Lydia Bl\"umel, Anna Rapberger
https://arxiv.org/abs/2508.11182 https://

On Strong and Weak Admissibility in Non-Flat Assumption-Based Argumentation
In this work, we broaden the investigation of admissibility notions in the context of assumption-based argumentation (ABA). More specifically, we study two prominent alternatives to the standard notion of admissibility from abstract argumentation, namely strong and weak admissibility, and introduce the respective preferred, complete and grounded semantics for general (sometimes called non-flat) ABA. To do so, we use abstract bipolar set-based argumentation frameworks (BSAFs) as formal playgroun…

A note on disjointness and discrete elements in partially ordered vector spaces
Jani Jokela
https://arxiv.org/abs/2509.11212 https://arxiv.org/pdf/2509.112…

A note on disjointness and discrete elements in partially ordered vector spaces
The notions of disjointness and discrete elements play a prominent role in the classical theory of vector lattices. There are at least three different generalizations of the notion of disjointness to a larger class of partially ordered vector spaces. In recent years, one of these generalizations has been widely studied in the context of pre-Riesz spaces. The notion of $D$-disjointness is the most general of the three disjointness concepts. In this paper we study $D$-disjointness and the related…

Towards Universal Quantum Tamper Detection
Anne Broadbent, Upendra Kapshikar, Denis Rochette
https://arxiv.org/abs/2509.12986 https://arxiv.org/pdf/2509.12…

Towards Universal Quantum Tamper Detection
Tamper-resilient cryptography studies how to protect data against adversaries who can physically manipulate codewords before they are decoded. The notion of tamper detection codes formalizes this goal, requiring that any unauthorized modification be detected with high probability. Classical results, starting from Jafargholi and Wichs (TCC 2015), established the existence of such codes against very large families of tampering functions, subject to structural restrictions ruling out identity and …

Super Covering Maps
Beat Nairz
https://arxiv.org/abs/2509.12302 https://arxiv.org/pdf/2509.12302

Super Covering Maps
We define analytic maps between super Riemann surfaces which extend the notion of branched covering maps to a supersymmetric setting. We show that these super covering maps appear naturally both in symmetric product orbifolds of superconformal field theories, as well as in the hybrid formalism for tensionless string theory on $\text{AdS}_3\times S^3\times\mathbb{T}^4$. In the former, they can be used to calculate correlators in a manifestly supersymmetric way, while in the latter they solve War…

Balloon Animal Maps with Applications to the Cohomology of Hypertoric Hitchin Systems
Evan Sundbo
https://arxiv.org/abs/2509.12368 https://arxiv.org/pdf/25…

Balloon Animal Maps with Applications to the Cohomology of Hypertoric Hitchin Systems
In this article we introduce the notion of a balloon animal map between broken toric varieties and construct several long exact sequences in cohomology related to them. We give a new proof of the deletion-contraction relation on hypertoric Hitchin systems of Dansco-Mcbreen-Shende and present some refinements of it. The end result is a formula for the Poincaré polynomial of any hypertoric Hitchin system associated to a graph with first Betti number 2 along with a recipe to calculate the Poincar…

Remarks on proper conflict-free degree-choosability of graphs with prescribed degeneracy
Masaki Kashima, Riste \v{S}krekovski, Rongxing Xu
https://arxiv.org/abs/2509.12560 https…

Remarks on proper conflict-free degree-choosability of graphs with prescribed degeneracy
A proper coloring $ϕ$ of $G$ is called a proper conflict-free coloring of $G$ if for every non-isolated vertex $v$ of $G$, there is a color $c$ such that $|ϕ^{-1}(c)\cap N_G(v)|=1$. As an analogy of degree-choosability of graphs, we introduced the notion of proper conflict-free $({\rm degree}+k)$-choosability of graphs. For a non-negative integer $k$, a graph $G$ is proper conflict-free $({\rm degree}+k)$-choosable if for any list assignment $L$ of $G$ with $|L(v)|\geq d_G…

Limit Theorems for Verbose Persistence Diagrams
Jeong-hwi Joe, Woojin Kim, Cheolwoo Park
https://arxiv.org/abs/2509.11256 https://arxiv.org/pdf/2509.11256

Limit Theorems for Verbose Persistence Diagrams
The persistence diagram is a central object in the study of persistent homology and has also been investigated in the context of random topology. The more recent notion of the verbose diagram (a.k.a. verbose barcode) is a refinement of the persistence diagram that is obtained by incorporating ephemeral persistence features as extra points along the diagonal. In this work, we initiate the study of random verbose diagrams. We establish a strong law of large numbers for verbose diagrams as a rando…

Transforming Football Data into Object-centric Event Logs with Spatial Context Information
Vito Chan, Lennart Ebert, Paul-Julius Hillmann, Christoffer Rubensson, Stephan A. Fahrenkrog-Petersen, Jan Mendling
https://arxiv.org/abs/2507.12504

Transforming Football Data into Object-centric Event Logs with Spatial Context Information
Object-centric event logs expand the conventional single-case notion event log by considering multiple objects, allowing for the analysis of more complex and realistic process behavior. However, the number of real-world object-centric event logs remains limited, and further studies are needed to test their usefulness. The increasing availability of data from team sports can facilitate object-centric process mining, leveraging both real-world data and suitable use cases. In this paper, we presen…

Partial Dirac Structures and Dynamical Systems
Fernand Pelletier, Patrick Cabau
https://arxiv.org/abs/2508.10799 https://arxiv.org/pdf/2508.10799

Partial Dirac Structures and Dynamical Systems
In a previous paper (PeCa24), the notion of Dirac structure in finite dimension was extended to the convenient setting. In particular, we introduce the notion of \emph{partial Dirac structure on a convenient manifold} and look for which all geometrical results in finite dimension which are still true in this infinite dimensional framework. Note that this context is justified by many mechanical infinite dimensional examples which recover all the classical ones, such as Hilbert, Banach, Fréchet …

On the fate of spacetime singularities
Federico Piazza
https://arxiv.org/abs/2509.12314 https://arxiv.org/pdf/2509.12314

On the fate of spacetime singularities
I investigate spacetime singularities from the point of view of the wavefunction of the universe. In order to extend the classical notion of geodesic incompleteness one has to include the proper time of an observer as a degree of freedom in the Wheeler DeWitt equation. This leads to a Schrödinger equation along the observer worldline. Near the singularity, as in the classical BLK treatment, I ignore spatial gradients and effectively describe the spacetime around the worldline in the mini-super…

ein noch relativ frischer Aufsatz zum italienischen Sonderweg in Sachen freier Zugang zu gemeinfreiem Kulturgut: Sappa, C., Bossi, L. Postcards from Italy – The Art of Controlling Images of Cultural Goods Better Than Copyright Could. IIC 56, 320–368 (2025). https://doi.org/10.1007/s40319-025-01565-w

Identifying Imperfect Clones in Elections
Piotr Faliszewski, Lukasz Janeczko, Grzegorz Lisowski, Kristyna Pekarkova, Ildiko Schlotter
https://arxiv.org/abs/2509.11261 https://…

Identifying Imperfect Clones in Elections
A perfect clone in an ordinal election (i.e., an election where the voters rank the candidates in a strict linear order) is a set of candidates that each voter ranks consecutively. We consider different relaxations of this notion: independent or subelection clones are sets of candidates that only some of the voters recognize as a perfect clone, whereas approximate clones are sets of candidates such that every voter ranks their members close to each other, but not necessarily consecutively. We e…

A Tight Lower Bound for Doubling Spanners
An La, Hung Le, Shay Solomon, Cuong Than, Vinayak, Shuang Yang, Tianyi Zhang
https://arxiv.org/abs/2508.11555 https://

A Tight Lower Bound for Doubling Spanners
Any $n$-point set in the $d$-dimensional Euclidean space $\mathbb{R}^d$, for $d = O(1)$, admits a $(1+ε)$-spanner with $\tilde{O}(n \cdot ε^{-d+1})$ edges and lightness $\tilde{O}(ε^{-d})$, for any $ε> 0$. (The {lightness} is a normalized notion of weight, where we divide the spanner weight by the MST weight. The $\tilde{O}$ and $\tildeΩ$ notations hide $\texttt{polylog}(ε^{-1})$ terms.) Moreover, this result is tight: For any $2 \le d = O(1)$, there exists an $n$-point set in $\mathbb{R}…

Effects of the Strict-Tolerant Approach on Intuitionistic and Minimal Logic
Victor Barroso-Nascimento, German Mejia
https://arxiv.org/abs/2509.10322 https://

Effects of the Strict-Tolerant Approach on Intuitionistic and Minimal Logic
This paper extends the literature on the strict-tolerant logical approach by applying its methods to intuitionistic and minimal logic. In short, the strict-tolerant approach modifies the usual notion of logical consequence by stipulating that, in order for an inference to be valid, from the truth of the premises must follow the non-falsity of the conclusion. This notion can also be generalized to define strict-tolerant metainferences, metametainferences and so on, which may or may not generate …

Opinion Clustering under the Friedkin-Johnsen Model: Agreement in Disagreement
Aashi Shrinate, Twinkle Tripathy
https://arxiv.org/abs/2509.11045 https://ar…

Opinion Clustering under the Friedkin-Johnsen Model: Agreement in Disagreement
The convergence of opinions in the Friedkin-Johnsen (FJ) framework is well studied, but the topological conditions leading to opinion clustering remain less explored. To bridge this gap, we examine the role of topology in the emergence of opinion clusters within the network. The key contribution of the paper lies in the introduction of the notion of topologically prominent agents, referred to as Locally Topologically Persuasive (LTP) agents. Interestingly, each LTP agent is associated with a un…

#Notion #ai is working just fine

Every criticism of Israel,
any sympathy for the Palestinians,
any pressure to end the war,
is seen today as a form of antisemitism
– even endorsement of Hamas.
Over 60% of Israelis, according to recent polls, believe “nobody in Gaza is innocent.”
Along with Israel’s sense of impunity, this popular notion explains how this war has turned into a genocide.
The core of Palestinian identity, most Israelis believe, is the physical destruction of their stat…

Robust, sub-Gaussian mean estimators in metric spaces
Daniel Bartl, Gabor Lugosi, Roberto Imbuzeiro Oliveira, Zoraida F. Rico
https://arxiv.org/abs/2509.13606 https://

Robust, sub-Gaussian mean estimators in metric spaces
Estimating the mean of a random vector from i.i.d. data has received considerable attention, and the optimal accuracy one may achieve with a given confidence is fairly well understood by now. When the data take values in more general metric spaces, an appropriate extension of the notion of the mean is the Fréchet mean. While asymptotic properties of the most natural Fréchet mean estimator (the empirical Fréchet mean) have been thoroughly researched, non-asymptotic performance bounds have onl…

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…

Szeg\H{o}'s theorem for Jordan arcs
Benedikt Buchecker
https://arxiv.org/abs/2509.12445 https://arxiv.org/pdf/2509.12445…

Szegő's theorem for Jordan arcs
The $n$-th Christoffel function for a point $z_0\in\mathbb C$ and a finite measure $μ$ supported on a Jordan arc $Γ$ is \[ λ_n(μ,z_0)=\inf\left\{\int_Γ|P|^2dμ\mid P\text{ is a polynomial of degree at most }n\text{ and } P(z_0)=1\right\}. \] It is natural to extend this notion to $z_0=\infty$ and define $λ_n(μ,\infty)$ to be the infimum of the squared $L^2(μ)$-norm over monic polynomials of degree $n$. The classical Szegő theorem provides an asymptotic description of $λ_n(μ…

dbpedia_all: DBpedia network (v3.6)
A network among all entries in DBpedia, a project that extracts structured information from Wikipedia. Nodes represent entities in DBpedia and an edge connects two entities based on DBpedia's notion of their relatedness. The data is extracted from the version 3.6 of the database.
This network has 3966924 nodes and 13820853 edges.
Tags: Informational, Relatedness, Unweighted, Multigraph

Mo' Memory, Mo' Problems: Stream-Native Machine Unlearning
Kennon Stewart
https://arxiv.org/abs/2508.10193 https://arxiv.org/pdf/2508.10193

Mo' Memory, Mo' Problems: Stream-Native Machine Unlearning
Machine unlearning work assumes a static, i.i.d training environment that doesn't truly exist. Modern ML pipelines need to learn, unlearn, and predict continuously on production streams of data. We translate the notion of the batch unlearning scenario to the online setting using notions of regret, sample complexity, and deletion capacity. We further tighten regret bounds to a logarithmic $\mathcal{O}(\ln{T})$, a first for a machine unlearning algorithm. And we swap out an expensive Hessian inve…

Generalized Whittaker models beyond $\mathfrak{sl}_{2}$-triples
Gyujin Oh
https://arxiv.org/abs/2508.08523 https://arxiv.org/pdf/2508.08523

Generalized Whittaker models beyond $\mathfrak{sl}_{2}$-triples
We extend the notion of generalized Whittaker models by allowing them to be built upon smooth irreducible representations of unipotent subgroups of a $p$-adic reductive group that are not necessarily characters, nor induced from Weil representations. This notion generalizes the usual notion of generalized Whittaker models, which include the Bessel and Fourier--Jacobi models. Using Kirillov's orbit method for unipotent groups, we define and prove basic properties of the corresponding Jacquet fun…

Regular sequences for triangulated categories
Antonia Kekkou, Janina C. Letz, Marc Stephan
https://arxiv.org/abs/2509.09941 https://arxiv.org/pdf/2509.0994…

Regular sequences for triangulated categories
This paper systematically develops a notion of regular sequences in the context of $R$-linear triangulated categories for a graded-commutative ring $R$. The notion has equivalent characterizations involving Koszul objects and local cohomology. The main examples are in the context of the Hochschild cohomology ring or the group cohomology ring acting on derived or stable categories. As applications, lengths of regular sequences provide lower bounds for level and Rouquier dimension.

Gravitational Entropy
Sangmin Choi, Malcolm J. Perry
https://arxiv.org/abs/2509.10921 https://arxiv.org/pdf/2509.10921

Gravitational Entropy
We formulate the classical gravitational entropy of a horizon as a Noether charge that does not require the notion of a temperature, and which is applicable to horizons that are not necessarily associated with black holes. This introduces a correction to the covariant phase space formalism that accounts for the configuration-dependence of the generating vector field conjugate to the charge. The vector field is related to the proposal of Bousso that the gravitational entropy of a region is deter…

On the Local-to-Global Principle for Zero-Cycles on Self Products of Elliptic Curves with CM
Michael Wills
https://arxiv.org/abs/2509.13641 https://arxiv.o…

On the Local-to-Global Principle for Zero-Cycles on Self Products of Elliptic Curves with CM
For a smooth projective variety $X$ defined over a global field $K$, one can form a notion of Weak Approximation for the Chow group of zero-cycles of $X$. There exists a Brauer-Manin obstruction to Weak Approximation here akin to that for rational points. However, unlike for rational points, it is conjectured that this obstruction is the only one; early versions of this conjecture date back to work of Colliot-Thélène and Sansuc (1981) and of Kato and Saito (1986). In this paper, we provide ev…

KI-Update kompakt: KI-Brillen von Meta, LinkedIn, Notion 3.0, DSA-Beschwerde
Das "KI-Update" liefert drei mal pro Woche eine Zusammenfassung der wichtigsten KI-Entwicklungen.
https://www.

Partial Poisson Lie groups and groupoids. Application to Von Neumann algebras
Fernand Pelletier, Patrick Cabau
https://arxiv.org/abs/2510.12688 https://arx…

Partial Poisson Lie groups and groupoids. Application to Von Neumann algebras
The purpose of this paper is to propose a version of the notion of convenient Lie groupoid as a generalization of this concept in finite dimension. The authors point out which obstructions appear in the infinite dimensional context and how an adapted notion of "bi-algebroid " in finite dimension (cf. \cite{MaXu94}) can be, nevertheless, recovered. This paper is self-contained and recalls some important properties of "partial Poisson manifolds" (cf. \cite{CaPe23}, Chapter~7) and "Banach Poisson …

Borel distinguishing number
Onur Bilge, Burak Kaya
https://arxiv.org/abs/2508.08201 https://arxiv.org/pdf/2508.08201

Borel distinguishing number
In this paper, we study definable variants of the notion of the distinguishing number of a graph in descriptive set theoretic setting. We introduce the notion of the Borel distinguishing number of a Borel graph and provide examples that separate distinguishing number and Borel distinguishing number at various levels. More specifically, we prove that there exist Borel graphs with countable distinguishing number but uncountable Borel distinguishing number and that, for every integer $n \geq 3$, t…

Cycling Along Euler Road
Dylan Wyrzykowski
https://arxiv.org/abs/2509.10460 https://arxiv.org/pdf/2509.10460

Cycling Along Euler Road
We introduce the notion of $P_λ$ points, which canonically parametrize points on the Euler line. This allows us to show that the Euler line of any inscribed $n$-polytope in $d$-dimensional Euclidean space arises from the Euler lines of its facets, beginning from the Euler line of a point in the plane. Furthermore, we situate $P_λ$ points in the literature of modern triangle centers.

Succinct Oblivious Tensor Evaluation and Applications: Adaptively-Secure Laconic Function Evaluation and Trapdoor Hashing for All Circuits
Damiano Abram, Giulio Malavolta, Lawrence Roy
https://arxiv.org/abs/2508.09673

Succinct Oblivious Tensor Evaluation and Applications: Adaptively-Secure Laconic Function Evaluation and Trapdoor Hashing for All Circuits
We propose the notion of succinct oblivious tensor evaluation (OTE), where two parties compute an additive secret sharing of a tensor product of two vectors $\mathbf{x} \otimes \mathbf{y}$, exchanging two simultaneous messages. Crucially, the size of both messages and of the CRS is independent of the dimension of $\mathbf{x}$. We present a construction of OTE with optimal complexity from the standard learning with errors (LWE) problem. Then we show how this new technical tool enables a host o…

Generalized Lema\^itre time for rotating and charged black holes and its near-horizon properties
A. V. Toporensky, O. B. Zaslavskii
https://arxiv.org/abs/2509.12485 https://

Generalized Lemaître time for rotating and charged black holes and its near-horizon properties
We consider the behavior of the analogue of the Lemaitre time when a particle approaches the horizon of a rotating black hole. For the Kerr metric, the aforementioned time coincides with the Doran or Natario time but we consider a more general class of metrics. We scrutiny relationship between (i) its finiteness or divergence, (ii) the forward-in-time condition, (iii) the sign of a generalized momentum/energy, (iv) the validity of the principle of kinematic censorship. The latter notion means i…

Quasi Normal Modes in Dispersive Photonic Time-Crystals
Calvin M. Hooper, Ian R. Hooper, Simon A. R. Horsley
https://arxiv.org/abs/2510.12438 https://arxiv…

Quasi Normal Modes in Dispersive Photonic Time-Crystals
Quasinormal modes characterise the transient response of static optical cavities. Here, we introduce the notion of a Floquet quasinormal mode to describe transient responses in photonic time crystals. Contrasting their static counterparts, exceptional points associated with symmetry transitions are an inherent feature, as modes spontaneously and non-perturbatively lock their phase to the oscillations of the material. We further investigate the limiting behaviour of the Floquet quasinormal modes…

Monodromies of surfaces in 3-manifolds, right-veeringness, and primeness of links
Peter Feller, Lukas Lewark, Miguel Orbegozo Rodriguez
https://arxiv.org/abs/2509.09615 https://…

Monodromies of surfaces in 3-manifolds, right-veeringness, and primeness of links
Extending the notion of monodromies associated with open books of $3$-manifolds, we consider monodromies for all incompressible surfaces in $3$-manifolds as partial self-maps of the arc set of the surfaces. We use them to develop a primeness criterion for incompressible surfaces constructed as iterative Murasugi sums in irreducible $3$-manifolds. We also consider a suitable notion of right-veeringness for monodromies of incompressible surfaces. We show strongly quasipositive surfaces are righ…

TL;DR: what if nationalism, not anarchy, is futile?
Since I had the pleasure of seeing the "what would anarchists do against a warlord?" argument again in my timeline, I'll present again my extremely simple proposed solution:
Convince the followers of the warlord that they're better off joining you in freedom, then kill or exile the warlord once they're alone or vastly outnumbered.
Remember that even in our own historical moment where nothing close to large-scale free society has existed in living memory, the warlord's promise of "help me oppress others and you'll be richly rewarded" is a lie that many understand is historically a bad bet. Many, many people currently take that bet, for a variety of reasons, and they're enough to coerce through fear an even larger number of others. But although we imagine, just as the medieval peasants might have imagined of monarchy, that such a structure is both the natural order of things and much too strong to possibly fail, in reality it takes an enormous amount of energy, coordination, and luck for these structures to persist! Nations crumble every day, and none has survived more than a couple *hundred* years, compared to pre-nation societies which persisted for *tends of thousands of years* if not more. I'm this bubbling froth of hierarchies, the notion that hierarchy is inevitable is certainly popular, but since there's clearly a bit of an ulterior motive to make (and teach) that claim, I'm not sure we should trust it.
So what I believe could form the preconditions for future anarchist societies to avoid the "warlord problem" is merely: a widespread common sense belief that letting anyone else have authority over you is morally suspect. Given such a belief, a warlord will have a hard time building any following at all, and their opponents will have an easy time getting their supporters to defect. In fact, we're already partway there, relative to the situation a couple hundred years ago. At that time, someone could claim "you need to obey my orders and fight and die for me because the Queen was my mother" and that was actually a quite successful strategy. Nowadays, this strategy is only still working in a few isolated places, and the idea that one could *start a new monarchy* or even resurrect a defunct one seems absurd. So why can't that same transformation from "this is just how the world works" to "haha, how did anyone ever believe *that*? also happen to nationalism in general? I don't see an obvious reason why not.
Now I think one popular counterargument to this is: if you think non-state societies can win out with these tactics, why didn't they work for American tribes in the face of the European colonizers? (Or insert your favorite example of colonialism here.) I think I can imagine a variety of reasons, from the fact that many of those societies didn't try this tactic (and/or were hierarchical themselves), to the impacts of disease weakening those societies pre-contact, to the fact that with much-greater communication and education possibilities it might work better now, to the fact that most of those tribes are *still* around, and a future in which they persist longer than the colonist ideologies actually seems likely to me, despite the fact that so much cultural destruction has taken place. In fact, if the modern day descendants of the colonized tribes sow the seeds of a future society free of colonialism, that's the ultimate demonstration of the futility of hierarchical domination (I just read "Theory of Water" by Leanne Betasamosake Simpson).
I guess the TL;DR on this is: what if nationalism is actually as futile as monarchy, and we're just unfortunately living in the brief period during which it is ascendant?

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 …

Symmetry-Resolved Spread Complexity
Pawel Caputa, Giuseppe Di Giulio, Tran Quang Loc
https://arxiv.org/abs/2509.12992 https://arxiv.org/pdf/2509.12992

Symmetry-Resolved Spread Complexity
In this work, we investigate the impact of conserved charges on the dynamics of spread complexity of quantum states. Building on the notion of symmetry-resolved Krylov complexity [1], we extend the framework to general quantum states and analyze the relation between the total spread complexity and its decomposition into fixed-charge sectors. After exploring a range of analytical examples and using orthogonal polynomial approach, we identify conditions under which spread complexity exhibits equi…

A notion of partial order in the Choose the Leader model
Amit Einav, Yue Jiang
https://arxiv.org/abs/2508.02579 https://arxiv.org/pdf/2508.02579

A notion of partial order in the Choose the Leader model
In this work we continue the study of non-chaotic asymptotic correlations in many element systems and discuss the emergence of a new notion of asymptotic correlation -- partial order -- in the Choose the Leader (CL) system. Similarly to the newly defined notion of order, partial order refers to alignment of the elements in the system -- though it allows for deviation from total adherence. Our presented work revolves around the definition of partial order and shows its emergence in the CL model …

Type Theory with Single Substitutions
Ambrus Kaposi (E\"otv\"os Lor\'and University), Szumi Xie (E\"otv\"os Lor\'and University)
https://arxiv.org/abs/2510.12303

Type Theory with Single Substitutions
Type theory can be described as a generalised algebraic theory. This automatically gives a notion of model and the existence of the syntax as the initial model, which is a quotient inductive-inductive type. Algebraic definitions of type theory include Ehrhard's definition of model, categories with families (CwFs), contextual categories, Awodey's natural models, C-systems, B-systems. With the exception of B-systems, these notions are based on a parallel substitution calculus where substitutions …

A PCA-based Data Prediction Method
Peteris Daugulis, Vija Vagale, Emiliano Mancini, Filippo Castiglione
https://arxiv.org/abs/2510.09246 https://arxiv.org/…

A PCA-based Data Prediction Method
The problem of choosing appropriate values for missing data is often encountered in the data science. We describe a novel method containing both traditional mathematics and machine learning elements for prediction (imputation) of missing data. This method is based on the notion of distance between shifted linear subspaces representing the existing data and candidate sets. The existing data set is represented by the subspace spanned by its first principal components. Solutions for the case of th…

Isoperimetric behavior of generalized Stallings-Bieri groups
Noel Brady, Pratit Goswami, Rob Merrell
https://arxiv.org/abs/2509.09939 https://arxiv.org/pdf…

Isoperimetric behavior of generalized Stallings-Bieri groups
We introduce the notion of $n$-split for an epimorphism from a group to a finite rank free abelian group. This is used to provide bounds for the Dehn functions of certain coabelian subgroups of direct products of finitely presented groups. Such subgroups include and significantly generalize the Stallings-Bieri groups.

Detectability via observability in a nonuniform framework: dual relationship with controllability and stabilizability
Ignacio Huerta, Pablo Monz\'on
https://arxiv.org/abs/2508.09918

Detectability via observability in a nonuniform framework: dual relationship with controllability and stabilizability
In this paper we propose a new observability property for nonautonomous linear control systems in finite dimension: the nonuniform complete observability, which is more general than the uniform complete observability. A dual relationship is established between this new notion of observability and the recently defined nonuniform complete controllability property, with the aim of obtaining the main result, which proves that nonuniform complete observability guarantees the nonuniform exponential d…

Generation Space Size: Understanding and Calibrating Open-Endedness of LLM Generations
Sunny Yu, Ahmad Jabbar, Robert Hawkins, Dan Jurafsky, Myra Cheng
https://arxiv.org/abs/2510.12699

Generation Space Size: Understanding and Calibrating Open-Endedness of LLM Generations
Different open-ended generation tasks require different degrees of output diversity. However, current LLMs are often miscalibrated. They collapse to overly homogeneous outputs for creative tasks and hallucinate diverse but incorrect responses for factual tasks. We argue that these two failure modes are unified by, and can both be addressed by, the notion of effective generation space size (GSS) -- the set of semantically distinct outputs a model considers for a prompt. We present GSSBench, a ta…

I was considering using Notion with students to help keep some of their projects organized this semester, but it’s become AI-bloaty in a way that is meddlesome and annoying.
I wrote to them to see if I could turn off the AI features, and got a mildly snotty AI-generated response about how they can only be disabled for Business- and Enterprise-tier plans, but if I don’t want those features I’m “not required to use them.”
“Pay us to disable the crap you didn’t want” was…a nonstarter with me.

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…

Notion launches customizable agents that can create documents and perform other actions in the background, and says it has reached $500M in annualized revenue (Jordan Novet/CNBC)
https://www.cnbc.com/2025/09/18/notion-launches-ai-agen…

Notion rides AI boom to $500 million in annual revenue, but Microsoft competition looms
Notion, which competes with Google and Microsoft in productivity software, has seen soaring revenue growth thanks to a host of AI tools.

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…

A note on the number of non-cycle components in a pseudo 2-factor of graphs
Masaki Kashima
https://arxiv.org/abs/2510.12155 https://arxiv.org/pdf/2510.1215…

A note on the number of non-cycle components in a pseudo 2-factor of graphs
A pseudo 2-factor of a graph is a spanning subgraph such that each component is $K_1$, $K_2$, or a cycle. This notion was introduced by Bekkai and Kouider in 2009, where they showed that every graph $G$ has a pseudo 2-factor with at most $α(G)-δ(G)+1$ components that are not cycles. For a graph $G$ and a set of vertices $S$, let $δ_G(S)$ denote the minimum degree of vertices in $S$. In this note, we show that every graph $G$ has a pseudo 2-factor with at most $f(G)$ components that are not c…

Universal Analog Computation: Fra\"iss\'e limits of dynamical systems
Levin Hornischer
https://arxiv.org/abs/2510.10184 https://arxiv.org/pdf/2510…

Universal Analog Computation: Fraïssé limits of dynamical systems
Analog computation is an alternative to digital computation, that has recently re-gained prominence, since it includes neural networks. Further important examples are cellular automata and differential analyzers. While analog computers offer many advantages, they lack a notion of universality akin to universal digital computers. Since analog computers are best formalized as dynamical systems, we review scattered results on universal dynamical systems, identifying four senses of universality and…

Reweighting metric measure spaces and Onsager-Machlup
Zachary Selk
https://arxiv.org/abs/2510.10591 https://arxiv.org/pdf/2510.10591

Reweighting metric measure spaces and Onsager-Machlup
Given a metric measure space $M:=(X,d,μ)$ the Onsager-Machlup (OM) functional is a real valued function that has been seen as a generalized notion of a probability density function. The effect of reweighting the measure on OM functionals has been studied, however analogous reweightings of the metric to the best of our knowledge remain open. In this short note, we prove a transformation formula for OM functionals on geodesic metric measure spaces under reweighting of both the metric and the mea…

Challenges in designing ethical rules for Infrastructures in Internet of Vehicles
Razi Iqbal
https://arxiv.org/abs/2510.09374 https://arxiv.org/pdf/2510.09…

Challenges in designing ethical rules for Infrastructures in Internet of Vehicles
Vehicular Ad-hoc Networks (VANETs) have seen significant advancements in technology. Innovation in connectivity and communication has brought substantial capabilities to various components of VANETs such as vehicles, infrastructures, passengers, drivers and affiliated environmental sensors. Internet of Things (IoT) has brought the notion of Internet of Vehicles (IoV) to VANETs where each component of VANET is connected directly or indirectly to the Internet. Vehicles and infrastructures are key…

dbpedia_all: DBpedia network (v3.6)
A network among all entries in DBpedia, a project that extracts structured information from Wikipedia. Nodes represent entities in DBpedia and an edge connects two entities based on DBpedia's notion of their relatedness. The data is extracted from the version 3.6 of the database.
This network has 3966924 nodes and 13820853 edges.
Tags: Informational, Relatedness, Unweighted, Multigraph

Proportional and Pareto-Optimal Allocation of Chores with Subsidy
Jugal Garg, Eklavya Sharma, Xiaowei Wu
https://arxiv.org/abs/2510.10335 https://arxiv.org…

Proportional and Pareto-Optimal Allocation of Chores with Subsidy
We consider the problem of allocating $m$ indivisible chores among $n$ agents with possibly different weights, aiming for a solution that is both fair and efficient. Specifically, we focus on the classic fairness notion of proportionality and efficiency notion of Pareto-optimality. Since proportional allocations may not always exist in this setting, we allow the use of subsidies (monetary compensation to agents) to ensure agents are proportionally-satisfied, and aim to minimize the total subsid…

Near Invariance of The Dual Compressed Shift
Arup Chattopadhyay, Supratim Jana
https://arxiv.org/abs/2510.12230 https://arxiv.org/pdf/2510.12230

Near Invariance of The Dual Compressed Shift
We present the notion of the nearly dual compressed shift-invariant subspaces of the orthogonal complement of the model space and obtain their structure using Hitt's algorithm \cite{DH}.

Maximally $\psi-$epistemic models cannot explain gambling with two qubits
Sagnik Ray, Anubhav Chaturvedi, Debashis Saha
https://arxiv.org/abs/2509.10437 https://

Maximally $ψ-$epistemic models cannot explain gambling with two qubits
We investigate the minimal proof for ruling out maximally $ψ-$epistemic interpretations of quantum theory, in which the indistinguishable nature of two quantum states is fully explained by the epistemic overlap of their corresponding distributions over ontic states. To this end, we extend the standard notion of epistemic overlap by considering a penalized distinguishability game involving two states and three possible answers, named as Quantum Gambling. In this context, using only two pure sta…

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.

Triangulated Categories Admitting Linear Generators
Marina Godinho, Dave Murphy
https://arxiv.org/abs/2510.12433 https://arxiv.org/pdf/2510.12433

Triangulated Categories Admitting Linear Generators
The main result of this paper is that there is an additive equivalence between $\overline{\mathcal{C}}_n$, the Paquette-Yildirim completion of the discrete cluster categories of Dynkin type $A_{\infty}$, and the perfect derived category of a certain DG algebra. This additive equivalence preserves some of the triangulated structure: it commutes with the suspension functor and preserves triangles with at least two indecomposable terms. In the process, we introduce the notion of a linear generator…

Dominating Hadwiger's Conjecture holds for all $2K_2$-free graphs
Zi-Xia Song, Thomas Tibbetts
https://arxiv.org/abs/2510.12567 https://arxiv.org/pdf/2…

Dominating Hadwiger's Conjecture holds for all $2K_2$-free graphs
A dominating $K_t$ minor in a graph $G$ is a sequence $(T_1,\dots,T_t)$ of pairwise disjoint non-empty connected subgraphs of $G$, such that for $1 \leq i

dbpedia_all: DBpedia network (v3.6)
A network among all entries in DBpedia, a project that extracts structured information from Wikipedia. Nodes represent entities in DBpedia and an edge connects two entities based on DBpedia's notion of their relatedness. The data is extracted from the version 3.6 of the database.
This network has 3966924 nodes and 13820853 edges.
Tags: Informational, Relatedness, Unweighted, Multigraph

Kinematical Lie algebras and symplectic symmetric spaces I: Lie algebraic aspects
Pierre Bieliavsky, Nicolas Boulanger
https://arxiv.org/abs/2508.10565 https://

Kinematical Lie algebras and symplectic symmetric spaces I: Lie algebraic aspects
We generalize the notion of kinematical Lie algebra introduced in physics for the classification of the various possible relativity algebras an isotropic spacetime can accommodate. We first give an elementary proof of the fact that such a generalized kinematical Lie algebra $\mathfrak{g}$ always carries a canonical structure of symplectic involutive Lie algebra (shortly ``siLa''). In other words, if $G$ is a connected Lie group admitting $\mathfrak{g}$ as Lie algebra, there always exists a Li…

Single-Deviation Stability in Additively Separable Hedonic Games with Constrained Coalition Sizes
Martin Bullinger, Adam Dunajski, Edith Elkind, Matan Gilboa
https://arxiv.org/abs/2510.12641

Single-Deviation Stability in Additively Separable Hedonic Games with Constrained Coalition Sizes
We study stability in additively separable hedonic games when coalition sizes have to respect fixed size bounds. We consider four classic notions of stability based on single-agent deviations, namely, Nash stability, individual stability, contractual Nash stability, and contractual individual stability. For each stability notion, we consider two variants: in one, the coalition left behind by a deviator must still be of a valid size, and in the other there is no such constraint. We provide a ful…

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 …

On the semi-infinite cohomology of graded-unitary vertex algebras
Christopher Beem, Niklas Garner
https://arxiv.org/abs/2509.10364 https://arxiv.org/pdf/25…

On the semi-infinite cohomology of graded-unitary vertex algebras
Recently, the first author with A. Ardehali, M. Lemos, and L. Rastelli introduced the notion of graded unitarity for vertex algebras. This generalization of unitarity is motivated by the SCFT/VOA correspondence and introduces a novel Hilbert space structure on the state space of a large class of vertex algebras that are not unitary in the conventional sense. In this paper, we study the relative semi-infinite cohomology of graded-unitary vertex algebras that admit a chiral quantum moment map for…

Approximate DBSCAN under Differential Privacy
Yuan Qiu, Ke Yi
https://arxiv.org/abs/2508.08749 https://arxiv.org/pdf/2508.08749

Approximate DBSCAN under Differential Privacy
This paper revisits the DBSCAN problem under differential privacy (DP). Existing DP-DBSCAN algorithms aim at publishing the cluster labels of the input points. However, we show that both empirically and theoretically, this approach cannot offer any utility in the published results. We therefore propose an alternative definition of DP-DBSCAN based on the notion of spans. We argue that publishing the spans actually better serves the purposes of visualization and classification of DBSCAN. Then we …

Interference between non-overlapping waves
Alan C. Santos, Celso J. Villas-Boas
https://arxiv.org/abs/2508.10622 https://arxiv.org/pdf/2508.10622

Interference between non-overlapping waves
In classical mechanics and electromagnetism, interference occurs when two or more waves overlap at the same point in spacetime. However, the advent of quantum electrodynamics (QED) and its remarkable success in describing light-matter interactions at the microscopic level invites us to reconsider whether interference-like effects could arise even when the waves do not physically overlap. In this work, we extend the notion of wave interference to a novel and unconventional regime. Building upon …

A note on adding isomorphisms and the pseudointersection number
Corey Bacal Switzer
https://arxiv.org/abs/2510.11155 https://arxiv.org/pdf/2510.11155

A note on adding isomorphisms and the pseudointersection number
We prove that for every tower $\mathcal T$ there are $\aleph_1$-dense $A$ and $B$ so that any ``reasonable" forcing notion $\mathbb{P}$ -- an adjective that includes all known ones -- for making $A$ and $B$ isomorphic will add a pseudointersection for the tower. This shows in particular that $\mathsf{MA}_{\aleph_1}(σ{\rm -centered})$ holds in all known models of $\mathsf{BA}$, which provides intrigue to well known questions of Todorčević and Steprāns-Watson.

Instances of models of double-categorical theories
Kevin Carlson, Evan Patterson
https://arxiv.org/abs/2510.08861 https://arxiv.org/pdf/2510.08861

Instances of models of double-categorical theories
We contribute a chapter in common to categorical database theory and to the study of higher morphisms between double categories. The common thread here is the notion of instance, or right module, which we generalize from functors from a plain category into Set to the models of a (cartesian) double theory. This provides a concept of instance for such objects as a category equipped with a monad, or a (symmetric) multicategory, recovering the multifunctors into Set in the latter case. We also show…

Cocycle weighted infinitesimal bialgebras and pre-Lie algebras on rooted trees
Lo\"ic Foissy (LMPA), Yunzhou Xie (NJUST), Dawei Zhang (NJUST), Yi Zhang (NJUST)
https://arxiv.org/abs/2510.12239

Cocycle weighted infinitesimal bialgebras and pre-Lie algebras on rooted trees
The concept of weighted infinitesimal bialgebras provides an algebraic framework for understanding the non-homogeneous associative Yang-Baxter equation. In this paper, we endow the space of decorated planar rooted forests with a two-parameters family of coproducts, making it into a weighted infinitesimal bialgebra. A combinatorial characterization of the coproducts is given via the notion of forest biideals. Furthermore, by constructing a bilinear symmetric form and introducing a new grafting o…

Dual Truncated Hankel Operators: Characterization and Properties
Arup Chattopadhyay, Supratim Jana
https://arxiv.org/abs/2510.12223 https://arxiv.org/pdf/2…

Dual Truncated Hankel Operators: Characterization and Properties
We introduce the notion of the Dual Truncated Hankel Operator (DTHO) and provide several operator equation characterizations using the dual compressed shift operator. These characterizations are similar to classical results concerning Hankel operators and align with recent findings related to Truncated Hankel Operators (THO) \cite{GM}. Additionally, our work addresses comprehensive solutions to various operator equations encountered in studying THO and the classical Hankel operator. We have als…

Purity and distances between conjugates of elements over henselian valued fields
Arpan Dutta, Josnei Novacoski
https://arxiv.org/abs/2509.10839 https://arx…

Purity and distances between conjugates of elements over henselian valued fields
For a henselian valued field $(K,v)$ and a separable-algebraic element $a\in\overline{K}\setminus K$, we consider the set $S_K(a):= \{ v(a-a^\prime) \mid a^\prime\neq a \text{ is a $K$-conjugate of $a$} \}$. The central aim of this paper is to provide a bound for the cardinality of the set $S_K(a)$, and to characterize the elements $a$ for which this set is a singleton. Connections of this set with the notion of \textit{depth} of $a$ has also been explored. We show that $S_K(a)$ is a singleton …

Explaining Tournament Solutions with Minimal Supports
Cl\'ement Contet, Umberto Grandi, J\'er\^ome Mengin
https://arxiv.org/abs/2509.09312 https://…

Explaining Tournament Solutions with Minimal Supports
Tournaments are widely used models to represent pairwise dominance between candidates, alternatives, or teams. We study the problem of providing certified explanations for why a candidate appears among the winners under various tournament rules. To this end, we identify minimal supports, minimal sub-tournaments in which the candidate is guaranteed to win regardless of how the rest of the tournament is completed (that is, the candidate is a necessary winner of the sub-tournament). This notion co…

Basic interactive algorithms: Preview
Yuri Gurevich
https://arxiv.org/abs/2508.05798 https://arxiv.org/pdf/2508.05798…

Basic interactive algorithms: Preview
This dialog paper offers a preview and provides a foretaste of an upcoming work on the axiomatization of basic interactive algorithms. The modern notion of algorithm was elucidated in the 1930s--1950s. It was axiomatized a quarter of a century ago as the notion of ``sequential algorithm'' or ``classical algorithm''; we prefer to call it ``basic algorithm" now. The axiomatization was used to show that for every basic algorithm there is a behaviorally equivalent abstract state machine. It was a…

Generic special Lagrangian moduli spaces of a non-K\"ahler Calabi--Yau threefold
Benjamin Friedman
https://arxiv.org/abs/2510.12735 https://arxiv.org/…

Generic special Lagrangian moduli spaces of a non-Kähler Calabi--Yau threefold
Given a (possibly non-Kähler) Calabi--Yau threefold $(X,Ω)$, we introduce the notion of a (perturbed) special Lagrangian (SL) submanifold of $(X,ω,Ω)$, where $ω$ is a Hermitian metric on $X$. The equations defining this class of submanifolds reduce to the usual SL equations when $ω$ is a Kähler metric. Using the Sard--Smale technique, we prove the existence of a comeagre set of Hermitian metrics $ω$ on $X$ such that the moduli space of perturbed SL submanifolds in $(X,ω,Ω)$ consists o…

Asymptotically flat divisors and strongly $F$-regular type varieties
Donghyeon Kim
https://arxiv.org/abs/2510.11208 https://arxiv.org/pdf/2510.11208…

Asymptotically flat divisors and strongly $F$-regular type varieties
In this paper, we define the notion of asymptotically flat divisor on a normal variety over $\C$, and prove that if $X$ is a strongly $F$-regular type variety and $K_X$ is asymptotically flat, then $X$ is of klt type.

Viscosity CBFs: Bridging the Control Barrier Function and Hamilton-Jacobi Reachability Frameworks in Safe Control Theory
Dylan Hirsch, Jaime Fern\'andez Fisac, Sylvia Herbert
https://arxiv.org/abs/2510.09929

Viscosity CBFs: Bridging the Control Barrier Function and Hamilton-Jacobi Reachability Frameworks in Safe Control Theory
Control barrier functions (CBFs) and Hamilton-Jacobi reachability (HJR) are central frameworks in safe control. Traditionally, these frameworks have been viewed as distinct, with the former focusing on optimally safe controller design and the latter providing sufficient conditions for safety. A previous work introduced the notion of a control barrier value function (CB-VF), which is defined similarly to the other value functions studied in HJR but has certain CBF-like properties. In this work, …

Atiyah Classes in the Context of Generalized Complex Geometry
Dadi Ni
https://arxiv.org/abs/2508.10723 https://arxiv.org/pdf/2508.10723

Atiyah Classes in the Context of Generalized Complex Geometry
In analogy to the classical holomorphic setting, Lang, Jia and Liu introduced the notion of the Atiyah class for a generalized holomorphic vector bundle using three different approaches: leveraging $\rm{\check{C}}$ech cohomology, employing the first jet short exact sequence, and adopting the perspective of Lie algebroid pairs. The purpose of this note is to establish the equivalence among these diverse definitions of the Atiyah class.

Hall algebras and shifted quantum affine algebras
Pallav Goyal, Peter Samuelson
https://arxiv.org/abs/2508.09405 https://arxiv.org/pdf/2508.09405

Hall algebras and shifted quantum affine algebras
In \cite{FT19}, Finkelberg and Tsymbaliuk introduced the notion of shifted quantum affine algebras and described their role in the study of quantized Coulomb branches associated to certain 3D $N = 4$ quiver gauge theories. We describe a new geometric construction of a deformation of one of these shifted quantum affine algebras as the Hall algebra of the category of representations of a certain quiver $Q_{\textrm{Rud}}$ (modulo relations). This quiver first arose in the work of Rudakov in the st…

dbpedia_all: DBpedia network (v3.6)
A network among all entries in DBpedia, a project that extracts structured information from Wikipedia. Nodes represent entities in DBpedia and an edge connects two entities based on DBpedia's notion of their relatedness. The data is extracted from the version 3.6 of the database.
This network has 3966924 nodes and 13820853 edges.
Tags: Informational, Relatedness, Unweighted, Multigraph

On Middle Grounds for Preference Statements
Anne-Marie George, Ana Ozaki
https://arxiv.org/abs/2508.09553 https://arxiv.org/pdf/2508.09553

On Middle Grounds for Preference Statements
In group decisions or deliberations, stakeholders are often confronted with conflicting opinions. We investigate a logic-based way of expressing such opinions and a formal general notion of a middle ground between stakeholders. Inspired by the literature on preferences with hierarchical and lexicographic models, we instantiate our general framework to the case where stakeholders express their opinions using preference statements of the form I prefer 'a' to 'b', where 'a' and 'b' are alternative…

Complexity of Effective Reductions with Ordinal Turing Machines
Merlin Carl
https://arxiv.org/abs/2509.02766 https://arxiv.org/pdf/2509.02766

Complexity of Effective Reductions with Ordinal Turing Machines
In arXiv:1811.11630, we introduced a notion of effective reducibility between set-theoretical $Π_{2}$-statements; in arXiv:2411.19386, this was extended to statements of arbitrary (potentially even infinite) quantifier complexity. We also considered a corresponding notion of Weihrauch reducibility, which allows only one call to the effectivizer of $ψ$ in a reduction of $ϕ$ to $ψ$. In this paper, we refine this notion considerably by asking how many calls to an effectivizer for $ψ$ are requ…

Improved Maximin Share Guarantee for Additive Valuations
Ehsan Heidari, Alireza Kaviani, Masoud Seddighin, AmirMohammad Shahrezaei
https://arxiv.org/abs/2510.10423 https://

Improved Maximin Share Guarantee for Additive Valuations
The maximin share ($\textsf{MMS}$) is the most prominent share-based fairness notion in the fair allocation of indivisible goods. Recent years have seen significant efforts to improve the approximation guarantees for $\textsf{MMS}$ for different valuation classes, particularly for additive valuations. For the additive setting, it has been shown that for some instances, no allocation can guarantee a factor better than $1-\tfrac{1}{n^4}$ of maximin share value to all agents. However, the best cur…

Cone structures and path geometries with constant torsion
Wojciech Kry\'nski
https://arxiv.org/abs/2508.10564 https://arxiv.org/pdf/2508.10564

Cone structures and path geometries with constant torsion
We study three-dimensional path geometries with nontrivial torsion of maximal rank. We introduce the notion of constant torsion and show that such path geometries are in one-to-one correspondence with certain cone structures modeled on homogeneous ruled surfaces. We also describe these cone structures in terms of solutions to new integrable systems admitting dispersionless, non-isospectral Lax pairs.

The Role of Symmetry in Generalized Hong-Ou-Mandel Interference and Quantum Metrology
\'Eloi Descamps, Arne Keller, P\'erola Milman
https://arxiv.org/abs/2508.09887 http…

The Role of Symmetry in Generalized Hong-Ou-Mandel Interference and Quantum Metrology
The Hong-Ou-Mandel interferometer is a foundational tool in quantum optics, with both fundamental and practical significance. Earlier works identified that input-state symmetry under exchange of the two spatial modes is fundamental in the understanding of the Hong-Ou-Mandel effect. We now show that this notion of symmetry is central to generalizing this effect. In particular, this point of view enables the construction of extensions beyond the standard two single-photon case to arbitrary input …

Abelian motives and Shimura varieties in nonzero characteristic
James S. Milne
https://arxiv.org/abs/2508.09972 https://arxiv.org/pdf/2508.09972

Abelian motives and Shimura varieties in nonzero characteristic
Much of the work on Shimura varieties over the last thirty years has been devoted to constructing the theory that would follow from a good notion of motives, one incorporating the Hodge, Tate, and standard conjectures. These conjectures are believed to be beyond reach, and may not even be correct as stated. I argue in this article that there exists a theory of motives, accessible to proof, weaker than Grothendieck's, but with many of the same consequences.

Gr\"obner Bases Native to Term-ordered Commutative Algebras, with Application to the Hodge Algebra of Minors
Joshua A. Grochow, Abhiram Natarajan
https://arxiv.org/abs/2510.11212

Gröbner Bases Native to Term-ordered Commutative Algebras, with Application to the Hodge Algebra of Minors
Motivated by better understanding the bideterminant (=product of minors) basis on the polynomial ring in $n \times m$ variables, we develop theory \& algorithms for Gröbner bases in not only algebras with straightening law (ASLs or Hodge algebras), but in any commutative algebra over a field that comes equipped with a notion of "monomial" (generalizing the standard monomials of ASLs) and a suitable term order. Rather than treating such an algebra $A$ as a quotient of a polynomial ring and then…

Critical edge sets in vertex-critical graphs
Ema Skottova, Raphael Steiner
https://arxiv.org/abs/2508.08703 https://arxiv.org/pdf/2508.08703

Critical edge sets in vertex-critical graphs
Criticality is a fundamental notion in graph theory that has been studied continually since its introduction in the early 50s by Dirac. A graph is called $k$-vertex-critical ($k$-edge-critical) if it is $k$-chromatic but removing any vertex (edge) lowers the chromatic number to $k-1$. A set of edges in a graph is called critical if its removal reduces the chromatic number of the graph. In 1970, Dirac conjectured a rather strong distinction between the notions of vertex- and edge-criticality, …

An analysis of Wigner's friend in the framework of quantum mechanics based on the principle of typicality
Kohtaro Tadaki
https://arxiv.org/abs/2509.07828 https://

An analysis of Wigner's friend in the framework of quantum mechanics based on the principle of typicality
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure theory, and therefore any operational characterization of the notion of probability is still missing in quantum mechanics. In our former works [K. Tadaki, arXiv:1804.10174], based on the toolkit of algorithmic randomness, we presented a refinement of the Born ru…

Moduli of lattice-polarized K3 surfaces and boundedness of Brauer groups
Danny Bragg, Emma Brakkee, Anthony V\'arilly-Alvarado
https://arxiv.org/abs/2510.11477 https://

Moduli of lattice-polarized K3 surfaces and boundedness of Brauer groups
Inspired by constructions over the complex numbers of Dolgachev and Alexeev-Engel, we define moduli stacks $\mathcal{M}_{(L,\mathcal{A})/\mathbb{Z}}$ of lattice-polarized K3 surfaces over arbitrary bases, paying particular attention to the open locus $\mathcal{P}_{(L,\mathcal{A})/\mathbb{Z}}$ of primitive lattice polarizations. We introduce the notion of very small ample cones $\mathcal{a}$, after Alexeev and Engel's small cones, to construct smooth, separated stacks of lattice polarized K3 sur…

dbpedia_all: DBpedia network (v3.6)
A network among all entries in DBpedia, a project that extracts structured information from Wikipedia. Nodes represent entities in DBpedia and an edge connects two entities based on DBpedia's notion of their relatedness. The data is extracted from the version 3.6 of the database.
This network has 3966924 nodes and 13820853 edges.
Tags: Informational, Relatedness, Unweighted, Multigraph

The Graded Betti Numbers of the Skeletons of Simplicial Complexes
Mohammed Rafiq Namiq
https://arxiv.org/abs/2510.09969 https://arxiv.org/pdf/2510.09969

The Graded Betti Numbers of the Skeletons of Simplicial Complexes
In this paper, we study a class $C$ of squarefree monomial ideals $I$ in a polynomial ring $R=K[x_1,\dots,x_n]$ over a filed $K$ where $\dim R/I$ equals the maximum degree of the minimal generators of $I$ minus one. We show that the Stanley-Reisner ideal of any $i$-skeleton of a simplicial complex $Δ$ in the class $C$ for $-1\le i<\dimΔ$. Then, we introduce the notion of a degree resolution and prove that every ideal in the class $C$ possesses this property. Finally, we provides a formula to …

Comparison Theorems and the Intermediate Ricci Curvature Assumption
Yujie Wu
https://arxiv.org/abs/2510.11205 https://arxiv.org/pdf/2510.11205

Comparison Theorems and the Intermediate Ricci Curvature Assumption
We explore the notion of m-intermediate Ricci curvature assumption introduced by Brendle-Hirsch-Johne further. If a manifold has non-negative m-intermediate Ricci curvature and stable weighted slicing of order m-1, then the last slice has almost non-negative Ricci curvature in the spectral sense. We prove comparison theorems on the diameter and in-radius bound for stable weighted (respectively free boundary) slicing in such manifolds (respectively with mean convex boundary).

Frequencies of letters in infinite $k$-balanced sequences
Lubom\'ira Dvo\v{r}\'akov\'a, Edita Pelantov\'a
https://arxiv.org/abs/2509.05812 https://

Frequencies of letters in infinite $k$-balanced sequences
Frequency of letters in a symbolic sequence ${\bf u}$ over a finite alphabet is one of the basic characteristics of ${\bf u}$. The notion of $k$-balancedness captures the property that the number of any letter occurring in two arbitrary factors of ${\bf u}$ of equal length differs at most by $k$. For a fixed integer $k$ and alphabet size $d\in \mathbb N$, we discuss possible frequencies of letters in $k$-balanced $d$-ary sequences. For the size $d$ of the alphabet, we introduce the notion of ba…

Theta-Categories and Tannakian duality
Joost Nuiten, Bertrand Toen
https://arxiv.org/abs/2508.03145 https://arxiv.org/pdf/2508.03145

Theta-Categories and Tannakian duality
We introduce a notion of $Θ$-categories, which is a refinement of the notion of symmetric monoidal $\infty$-categories. We use this notion to prove a Tannakian duality statement, relating $Θ$-categories with fpqc-stacks by means of a certain stack of fiber functors in the context of $Θ$-categories. This provides, over a base ring of arbitrary characteristic, a strong link between Tannakian $Θ$-categories and the schematic homotopy types.

On 2-absorbing submodules and their Amalgamations
Abuzer Gunduz
https://arxiv.org/abs/2510.09863 https://arxiv.org/pdf/2510.09863

On 2-absorbing submodules and their Amalgamations
Let $R_1$ and $R_2$ be commutative rings with $1\neq 0,\;M$ and $N$ be unitary $R_1-$module and $R_2-$module, respectively. $f:R_1\rightarrow R_2$ be a ring homomorphism and $φ: M\rightarrow N$ be an $R-$module homomorphism. This article studied $2-$absorbing submodule that is a generalization of the concept of prime submodule. Firstly, some characterizations of $2-$absorbing submodule are presented. Then, we examine the notion of $2-$absorbing submodule in amalgamation module $M \bowtie^φ JN…

Mutually equi-biased bases
Seyed Javad Akhtarshenas, Saman Karimi, Mahdi Salehi
https://arxiv.org/abs/2508.08969 https://arxiv.org/pdf/2508.08969

Mutually equi-biased bases
In the framework of mutually unbiased bases (MUBs), a measurement in one basis gives \emph{no information} about the outcomes of measurements in another basis. Here, we relax the no-information condition by allowing the $d$ outcomes to be predicted according to a predefined probability distribution $q=(q_0,\cdots,q_{d-1})$. The notion of mutual unbiasedness, however, is preserved by requiring that the extracted information is the same for any preparation and any measurement; regardless of which…

\'Etude de quelques familles de $\lambda$-quiddit\'es et minoration de la taille maximale des $\lambda$-quiddit\'es irr\'eductibles sur un corps fini
Flavien Mabilat
https://arxiv.org/abs/2510.09219

Étude de quelques familles de $λ$-quiddités et minoration de la taille maximale des $λ$-quiddités irréductibles sur un corps fini
$λ$-quiddities of size $n$ are $n$-tuples of elements from a fixed set that are solutions to a matrix equation which is fundamental in the study of the combinatorics of the modular group and Coxeter's friezes. To gain further insight into these objects, we use a notion of irreducibility, which allows restricting the study to a limited number of elements that must be determined for each set. Our goal here is to define several families of $λ$-quiddities over finite fields and to study their irr…

PT symmetry-enriched non-unitary criticality
Kuang-Hung Chou, Xue-Jia Yu, Po-Yao Chang
https://arxiv.org/abs/2509.09587 https://arxiv.org/pdf/2509.09587

PT symmetry-enriched non-unitary criticality
The interplay between topology and quantum criticality gives rise to the notion of symmetry-enriched criticality, which has attracted considerable attention in recent years. However, its non-Hermitian counterpart remains largely unexplored. In this Letter, we show how parity-time (PT) symmetry enriches non-Hermitian critical points, giving rise to a topologically distinct non-unitary universality class. By analytically investigating non-Hermitian free fermion models with $PT$ symmetry, we uncov…