Tootfinder

OpenAI says GPT-5.2 Thinking hallucinates less than GPT-5.1 and has improved reliability for agentic AI needs; pre-release testers include Notion, Box, Shopify (Hayden Field/The Verge)
https://www.theverge.com/ai-artificial-intelligence/842529/open…

OpenAI calls GPT-5.2 the best model yet for professionals
OpenAI has launched GPT-5.2, which it calls its best AI model yet for professional use.

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

heise | Wissen clever organisieren: Notion, Obsidian und Anytype im Vergleich
Notion, Obsidian und Anytype ordnen das digitale Chaos und verwalten persönliches Wissen. Welche App sich für wen am besten eignet, erklärt unser Ratgeber.

@… one for the feature-requests: I'd love to see a 'jump to' hotkey with fuzzy-search, ala ⌘P in VScode / Notion, ⌘K in Discord / Beeper / Spotify / Slack,
Pictured: (annoyingly) ⌘F in my beloved @…; one of the slicker/simp…

Study: ~200 Instacart shoppers in four US cities were shown different prices for the same 20 grocery items; Instacart confirms it is running short term "tests" (Ben Casselman/New York Times)
https://www.nytimes.com/2025/12/09/business/instacart-algori…

Same Product, Same Store, but on Instacart, Prices Might Differ
The findings are the latest example of how the notion of a single price is breaking down in the digital age, a trend economists say could be pushing up some prices.

The Born rule as a natural transformation of functors
Boyu Yang, James Fullwood
https://arxiv.org/abs/2509.08323 https://arxiv.org/pdf/2509.08323

The Born rule as a natural transformation of functors
In this work, we show that the quantum mechanical notions of density operator, positive operator-valued measure (POVM), and the Born rule, are all simultaneously encoded in the categorical notion of a natural transformation of functors. In particular, we show that given a fixed quantum system, there exists an explicit bijection from the set of density operators on the associated Hilbert space to the set of natural transformations between the canonical measurement and probability functors associ…

“Meeting detected!! Let’s start transcribing AI Meeting Notes!!“
No thanks, Notion, I’m just listing to Aesop Rock via my audio interface … 😂 (Fantastic album btw! 👉 https://aesoprock.com/collections/i-heard-its-a-mess-there-too)
[Quits Notion ¯\_(ツ)_/¯]

The tensor product of p-adic Hilbert spaces
Paolo Aniello, Lorenzo Guglielmi, Stefano Mancini, Vincenzo Parisi
https://arxiv.org/abs/2510.07504 https://arx…

The tensor product of p-adic Hilbert spaces
In the framework of quantum mechanics over a quadratic extension of the ultrametric field of p-adic numbers, we introduce a notion of tensor product of p-adic Hilbert spaces. To this end, following a standard approach, we first consider the algebraic tensor product of p-adic Hilbert spaces. We next define a suitable norm on this linear space. It turns out that, in the p-adic framework, this norm is the analogue of the projective norm associated with the tensor product of real or complex normed …

On the effective YTD conjecture
Thibaut Delcroix
https://arxiv.org/abs/2509.08760 https://arxiv.org/pdf/2509.08760

On the effective YTD conjecture
We formulate an effective variant of the Yau-Tian-Donaldson conjecture, then review effective results on K-stability of spherical varieties, that is, K-stability criterions which can be effectively computed given the combinatorial data associated with the variety. We focus on the standard notion of K-stability as defined by Donaldson for constant scalar curvature Kähler metrics.

Some remarks on decay in countable groups and amalgamated free products
Srivatsav Kunnawalkam Elayavalli, Gregory Patchell, Lizzy Teryoshin
https://arxiv.org/abs/2509.08754 http…

Some remarks on decay in countable groups and amalgamated free products
In this note, we first study the notion of subexponential decay (SD) for countable groups with respect to a length function, which generalizes the well-known rapid decay (RD) property, first discovered by Haagerup in 1979. Several natural properties and examples are studied, especially including groups that have SD, but not RD. This consideration naturally has applications in $C^*$-algebras. We also consider in this setting a permanence theorem for decay in amalgamated free products (proved als…

Gravity from equilibrium thermodynamics of stretched light cones
Ana Alonso-Serrano, Luis J. Garay, Marek Li\v{s}ka, Celia L\'opez Pineros
https://arxiv.org/abs/2509.08566 h…

Gravity from equilibrium thermodynamics of stretched light cones
This work digs into the connection between gravity and thermodynamics of stretched light cones (SLC). They are associated with uniformly accelerating observers, who endow the SLC with a physical notion of temperature via the Unruh effect. We compute the expansion, shear, and vorticity of the SLC to fully study its dynamics and account for the possibility of previously predicted non-equilibrium entropy production. For consistency, we prove the equivalence of the two different geometrical methods…

Harmful structures and Killing spinors on unimodular Lie groups
Diego Conti, Federico A. Rossi, Romeo Segnan Dalmasso
https://arxiv.org/abs/2509.08507 https://

Harmful structures and Killing spinors on unimodular Lie groups
A pseudo-Riemannian Einstein manifold with a Killing spinor and Killing constant $λ$ induces on its nondegenerate hypersurfaces a pair of spinors $ϕ,ψ$ and a symmetric tensor $A$, corresponding to the second fundamental form. Viewed as an intrinsic object, $(ϕ,ψ,A,λ)$ is known as a harmful structure; this notion generalizes nearly hypo and nearly half-flat structures to arbitrary dimension and signature. We show that when $A$ is a multiple of the identity the harmful structure is determin…

Potent categorical represeentations
David Ben-Zvi, David Nadler
https://arxiv.org/abs/2510.07482 https://arxiv.org/pdf/2510.07482

Potent categorical represeentations
We introduce and motivate -- based on ongoing joint work with Germán Stefanich -- the notion of potent categorical representations of a complex reductive group $G$, specifically a conjectural Langlands correspondence identifying potent categorical representations of $G$ and its Langlands dual $\check G$. We emphasize the symplectic nature of potent categorical representations in their simultaneous dependence on parameters in maximal tori for $G$ and $\check G$, specifically how their conjectur…

Fundamental theorem of transposed Poisson $(A,H)$-Hopf modules
Yan Ning, Daowei Lu, Dingguo Wang
https://arxiv.org/abs/2509.08278 https://arxiv.org/pdf/250…

Fundamental theorem of transposed Poisson $(A,H)$-Hopf modules
Transposed Poisson algebra was introduced as a dual notion of the Poisson algebra by switching the roles played by the commutative associative operation and Lie operation in the Leibniz rule defining the Poisson algebra. Let $H$ be a Hopf algebra with a bijective antipode and $A$ an $H$-comodule transposed Poisson algebra. Assume that there exists an $H$-colinear map which is also an algebra map from $H$ to the transposed Poisson center of $A$. In this paper we generalize the fundamental theore…

Maximal regularity of Dirichlet problem for the Laplacian in Lipschitz domains
Ch\'erif Amrouche, Mohand Moussaoui
https://arxiv.org/abs/2509.08543 https://

Maximal regularity of Dirichlet problem for the Laplacian in Lipschitz domains
The focus of this work is on the homogeneous and non-homogeneous Dirichlet problem for the Laplacian in bounded Lipschitz domains (BLD). Although it has been extensively studied by many authors, we would like to return to a number of fundamental questions and known results, such as the traces and the maximal regularity of solutions. First, to treat non-homogeneous boundary conditions, we rigorously define the notion of traces for non regular functions. This approach replaces the non-tangential …

Compounding formula approach to chromatin and active polymer dynamics
Takahiro Sakaue, Enrico Carlon
https://arxiv.org/abs/2510.07949 https://arxiv.org/pdf…

Compounding formula approach to chromatin and active polymer dynamics
Active polymers are ubiquitous in nature, and often kicked by persistent noises that break detailed balance. In order to capture the out-of-equilibrium dynamics of such active polymers, we propose a simple yet reliable analytical framework based on a compounding formula. Connecting polymeric dynamics to the isolated monomeric behavior via the notion of tension propagation, the formula allows us to clarify rich scaling scenarios alongside corresponding intuitive physical pictures. We demonstrate…

Reversible computations are computations
Cl\'ement Aubert, Jean Krivine
https://arxiv.org/abs/2510.06585 https://arxiv.org/pdf/2510.06585

Reversible computations are computations
Causality serves as an abstract notion of time for concurrent systems. A computation is causal, or simply valid, if each observation of a computation event is preceded by the observation of its causes. The present work establishes that this simple requirement is equally relevant when the occurrence of an event is invertible. We propose a conservative extension of causal models for concurrency that accommodates reversible computations. We first model reversible computations using a symmetric res…

Mathematics of effective $q$-plate in polarization optics
Mohammad Umar, Paramasivam Senthilkumaran
https://arxiv.org/abs/2509.08398 https://arxiv.org/pdf/…

Mathematics of effective $q$-plate in polarization optics
The $q$-plate is a spatially inhomogeneous SU(2) birefringent optical element that has garnered significant interest due to its ability to mediate the spin-orbit interaction of light and facilitate the generation of optical vortices. The $q$-plate features a spatially varying fast axis orientation defined by two parameters: the topological charge $q$ and the offset angle $α_0$. The notion of an effective waveplate arises when multiple waveplates, whether homogeneous or inhomogeneous, are align…

Robust equilibria in continuous games: From strategic to dynamic robustness
Kyriakos Lotidis, Panayotis Mertikopoulos, Nicholas Bambos, Jose Blanchet
https://arxiv.org/abs/2512.08138 https://arxiv.org/pdf/2512.08138 https://arxiv.org/html/2512.08138
arXiv:2512.08138v1 Announce Type: new
Abstract: In this paper, we examine the robustness of Nash equilibria in continuous games, under both strategic and dynamic uncertainty. Starting with the former, we introduce the notion of a robust equilibrium as those equilibria that remain invariant to small -- but otherwise arbitrary -- perturbations to the game's payoff structure, and we provide a crisp geometric characterization thereof. Subsequently, we turn to the question of dynamic robustness, and we examine which equilibria may arise as stable limit points of the dynamics of "follow the regularized leader" (FTRL) in the presence of randomness and uncertainty. Despite their very distinct origins, we establish a structural correspondence between these two notions of robustness: strategic robustness implies dynamic robustness, and, conversely, the requirement of strategic robustness cannot be relaxed if dynamic robustness is to be maintained. Finally, we examine the rate of convergence to robust equilibria as a function of the underlying regularizer, and we show that entropically regularized learning converges at a geometric rate in games with affinely constrained action spaces.
toXiv_bot_toot

Tensorial representations of positive weakly (q,r)-dominated multilinear operators
Abdelaziz Belaada, Adel Bounabab, Athmane Ferradi, Khalil Saadi
https://arxiv.org/abs/2509.08293

Tensorial representations of positive weakly (q,r)-dominated multilinear operators
We introduce and study the class of positive weakly (q,r)-dominated multilinear operators between Banach lattices. This notion extends classical domination and summability concepts to the positive multilinear setting and generates a new positive multi-ideal. A Pietsch domination theorem and a polynomial version are established. Finally, we provide a tensorial representation that yields an isometric identification with the dual of an appropriate completed tensor product.

Inductive Learning for Possibilistic Logic Programs Under Stable Models
Hongbo Hu, Yisong Wang, Yi Huang, Kewen Wang
https://arxiv.org/abs/2510.07069 https://

Inductive Learning for Possibilistic Logic Programs Under Stable Models
Possibilistic logic programs (poss-programs) under stable models are a major variant of answer set programming (ASP). While its semantics (possibilistic stable models) and properties have been well investigated, the problem of inductive reasoning has not been investigated yet. This paper presents an approach to extracting poss-programs from a background program and examples (parts of intended possibilistic stable models). To this end, the notion of induction tasks is first formally defined, its…

When you don't know the gender of a person because he/she/they doesn't talk about it, what is the best/preferred approach in English?
1) Gender the person based on their appearance, based on the heuristic that most people are cisgender
I don't like this heuristic because it gives strength to stereotypes and the notion of "normality"
2) Use a neutral pronoun like the singular they
It feels more natural, but maybe some people will consider this som…

As somebody who’s taking a break from his working on his absurdly custom bespoke static site generator for a course, I approve the (hand waving) grand general notion here.
1/2 https://hcommons.social/@zeblarson/115500289981846435

LLMs are a fundamentally useless technology because their applications (supposedly) boil down to humans not having to think for themselves or do their own writing / drawing / filming.
But if you can do it on your own - why would you need a robot to do it? It’s, at best, a novelty.
That’s why this shit only resonates with executives and capital owners. “Get things done with fewer people and expenses” is at least an actual pitch. “Get things done faster for yourself” isn’t.
The individual angle really works for things you already were trying to avoid doing because you’re either disinterested or don’t have enough time to do things right.
“Avoid your work” as a value proposition doesn’t work when you’re dealing with intellectual labor rather than commodities. Not large scale, not long term.
Sorry for the rant, I saw some Notion ads on the subway and got irritated 😅
#AI #llm #LLMs

Rank Aggregation under Weak Stochastic Transitivity via a Maximum Score Estimator
Haoran Zhang, Yunxiao Chen
https://arxiv.org/abs/2510.06789 https://arxiv…

Rank Aggregation under Weak Stochastic Transitivity via a Maximum Score Estimator
Stochastic transitivity is central for rank aggregation based on pairwise comparison data. The existing models, including the Thurstone, Bradley-Terry (BT), and nonparametric BT models, adopt a strong notion of stochastic transitivity, known as strong stochastic transitivity (SST). This assumption imposes restrictive monotonicity constraints on the pairwise comparison probabilities, which is often unrealistic for real-world applications. This paper introduces a maximum score estimator for aggre…

Perspectives and Questions: Toward an Expansive Agenda for Particle Physics
Chris Quigg
https://arxiv.org/abs/2510.06348 https://arxiv.org/pdf/2510.06348…

Perspectives and Questions: Toward an Expansive Agenda for Particle Physics
Global celebration greeted the 2012 discovery at CERN's Large Hadron Collider of a particle that matches the textbook description of the Higgs boson. That achievement validated a remarkable chain of theoretical reasoning that combined the prescriptive notion of electroweak gauge symmetry with a simple, but \emph{ad hoc}, embodiment of spontaneous symmetry breaking. It was made possible by generational triumphs of accelerator art and experimental technique, and by human resourcefulness and colla…

(Injective) facet-complexity between simplicial complexes
Cesar A. Ipanaque Zapata, Ayse Borat
https://arxiv.org/abs/2510.03017 https://arxiv.org/pdf/2510.…

(Injective) facet-complexity between simplicial complexes
We present the notion of facet-complexity, $\text{C}(\mathsf{L};\mathsf{K})$, for two simplicial complexes $\mathsf{L}$ and $\mathsf{K}$, along with basic results for this numerical invariant. This invariant $\text{C}(\mathsf{L};\mathsf{K})$ quantifies the \aspas{complexity} of the following question: When does there exist a facet simplicial map $\mathsf{L}\to \mathsf{K}$? A facet simplicial map is a simplicial map that preserves non-unitary facets. Likewise, we introduce the notion of injectiv…

Two-scale branching functions and inhomogeneous attractors
Vilma Orgov\'anyi, Alex Rutar
https://arxiv.org/abs/2510.07013 https://arxiv.org/pdf/2510.07…

Two-scale branching functions and inhomogeneous attractors
We introduce the notion of a two-scale branching function associated with an arbitrary metric space, which encodes the lower and upper box dimensions as well as the Assouad spectrum. If the metric space is quasi-doubling, this function is approximately Lipschitz. We fully classify the attainable Lipschitz two-scale branching functions, which gives a new proof of the classification of Assouad spectra due to the second author. We then study inhomogeneous self-conformal sets satisfying standard …

Mass-to-Horizon Relation and Entropy Beyond the Bekenstein-Hawking Limit
Hussain Gohar
https://arxiv.org/abs/2510.07587 https://arxiv.org/pdf/2510.07587

Mass-to-Horizon Relation and Entropy Beyond the Bekenstein-Hawking Limit
We introduce a generalized mass-horizon relation applicable to cosmological horizons. This formulation provides a unified framework for deriving a broad class of Bekenstein entropy extensions motivated by statistical mechanics, quantum gravity, and phenomenological considerations, through the application of the Clausius relation together with the Hawking temperature. We further introduce this notion as a foundational framework for constructing generalized entropy forms that remain consistent wi…

Hopf bimodules for bialgebroids
Sophie Chemla, Niels Kowalzig
https://arxiv.org/abs/2510.06417 https://arxiv.org/pdf/2510.06417

Hopf bimodules for bialgebroids
Generalising a result for Hopf algebras, we not only define the four possible types of Hopf modules in the bialgebroid setting but also yield the notion of two-sided two-cosided Hopf modules, also known as Hopf bimodules or tetramodules, in this realm. By explicitly formulating a fundamental theorem for Hopf modules via the concept of Hopf-Galois comodules, we prove that the category of Hopf bimodules can be endowed with the structure of a (pre-)braided monoidal category in two different ways, …

On the Hardness of the One-Sided Code Sparsifier Problem
Elena Grigorescu, Alice Moayyedi
https://arxiv.org/abs/2510.03184 https://arxiv.org/pdf/2510.03184…

On the Hardness of the One-Sided Code Sparsifier Problem
The notion of code sparsification was introduced by Khanna, Putterman and Sudan (arxiv.2311.00788), as an analogue to the the more established notion of cut sparsification in graphs and hypergraphs. In particular, for $α\in (0,1)$ an (unweighted) one-sided $α$-sparsifier for a linear code $\mathcal{C} \subseteq \mathbb{F}_2^n$ is a subset $S\subseteq [n]$ such that the weight of each codeword projected onto the coordinates in $S$ is preserved up to an $α$ fraction. Recently, Gharan and Saham…

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.

Convergence of Discrete Percolation Models to the Brownian Web Distance
Craig Belair
https://arxiv.org/abs/2510.06450 https://arxiv.org/pdf/2510.06450

Convergence of Discrete Percolation Models to the Brownian Web Distance
The Brownian web is a collection of coalescing Brownian motions started from every space-time point in R2. The Brownian web can be constructed as a scaling limit of coalescing one-dimensional simple random walks started at every point in a two-dimensional space-time lattice. Veto and Virag (2023) introduced a family of discrete random distance functions defined on these sequences of rescaled lattices. It was shown that, given the appropriate notion of convergence, these discrete distance functi…

Simultaneous triangularization over max-algebras
Askar Ali M, Sachindranath Jayaraman, Himadri Mukherjee
https://arxiv.org/abs/2510.07855 https://arxiv.org…

Simultaneous triangularization over max-algebras
The purpose of this article is to investigate triangularization and simultaneous triangularization of matrices over max algebras using graph theoretic methods. We establish a connection between commutators and commutants with simultaneous triangularization over max algebras. We also define the notion of characteristic polynomial of a collection in terms of the tropical determinant and determine when it can be written as a product of linear terms.

The commutative algebra of congruence ideals and applications to number theory
Srikanth B. Iyengar, Chandrashekhar B. Khare, Jeffrey Manning
https://arxiv.org/abs/2510.05418 htt…

The commutative algebra of congruence ideals and applications to number theory
In his proof of Fermat's Last Theorem, Wiles deployed a commutative algebra technique, namely a numerical criterion for detecting isomorphisms of rings. In our recent work we pick up on Wiles' work and generalize the numerical criterion to ``higher codimension''. A critical ingredient is a notion of congruence module in higher codimension: this has turned out to be a key definition whose utility extends beyond the role it plays in the numerical criterion. In this paper we trace the origin of so…

Influence of coil geometry and coil-plasma distance on the magnetic field approximation error
Wadim Gerner
https://arxiv.org/abs/2510.06773 https://arxiv.o…

Influence of coil geometry and coil-plasma distance on the magnetic field approximation error
We investigate analytically two questions: 1) How does the coil geometry influence the effect of electric current noise on the induced magnetic field? 2) How does the coil-plasma distance influence our ability to control the pointwise magnetic field error in terms of the average magnetic field error? Regarding (1), we argue that the main geometric quantities of interest are the notion of reach and the volume of the region enclosed by the coils. Our main finding is a quantitative formula w…

Strong Dinatural Transformations and Generalised Codensity Monads
Maciej Pir\'og, Filip Sieczkowski
https://arxiv.org/abs/2510.06777 https://arxiv.org/…

Strong Dinatural Transformations and Generalised Codensity Monads
We introduce dicodensity monads: a generalisation of pointwise codensity monads generated by functors to monads generated by mixed-variant bifunctors. Our construction is based on the notion of strong dinaturality (also known as Barr dinaturality), and is inspired by denotational models of certain types in polymorphic lambda calculi - in particular, a form of continuation monads with universally quantified variables, such as the Church encoding of the list monad in System F. Extending some prev…

Needed to build something quite weird that involves NFC tags and mainly Notion DB as storage and UI
Didn’t feel like learning Notion cos I am not a fan.
Worked with ChatGPT to make a spec and prompt this was useful while doing that totally changed my mind to something better
Gave it to codex and it one-shot built it perfectly in 20 minutes without interaction, worked first time once I fixed a mistake I made in Notion.
Lots of issues with AI but it’s certainly moving…

Classification of Lipschitz unimodal function germs
Nhan Nguyen, Maria Ruas, Saurabh Trivedi
https://arxiv.org/abs/2510.06792 https://arxiv.org/pdf/2510.06…

Classification of Lipschitz unimodal function germs
In this paper, we introduce the notion of Lipschitz modality for isolated singularities $ f: (\mathbb{C}^n, 0) \to (\mathbb{C}, 0)$ and provide a complete classification of Lipschitz unimodal singularities of corank~2 with non-zero $4$-jets. As a consequence, such singularities are Lipschitz unimodal if they deform to $J_{10}$ but not to $J_{3,0}$. Furthermore, we show that singularities with vanishing $6$-jets have Lipschitz modality at least~$2$, thus establishing an upper bound for the order…

Exchange for Growth: Currency Dynamics in Emerging Markets
Shaunak Kulkarni, Rohan Ajay Dubey
https://arxiv.org/abs/2510.07039 https://arxiv.org/pdf/2510.0…

Exchange for Growth: Currency Dynamics in Emerging Markets
Currency crises are frequently discussed retrospectively as a necessary and deterministic outcome of a finite sequence of fiscal decisions, monetary manoeuvres, and limited exogenous inputs. Parallelly, the Twin Deficits Hypothesis (TDH) posits that an increase in the budget deficit leads to a direct rise in the current account deficit; although analogous to the idea of currency crises being the outcome of finite inputs (through a balance of payments crisis here), this notion runs contrary to t…

Public-Key Encryption from the MinRank Problem
Rohit Chatterjee, Changrui Mu, Prashant Nalini Vasudevan
https://arxiv.org/abs/2510.03752 https://arxiv.org/…

Public-Key Encryption from the MinRank Problem
We construct a public-key encryption scheme from the hardness of the (planted) MinRank problem over uniformly random instances. This corresponds to the hardness of decoding random linear rank-metric codes. Existing constructions of public-key encryption from such problems require hardness for structured instances arising from the masking of efficiently decodable codes. Central to our construction is the development of a new notion of duality for rank-metric codes.

📢 Looking forward to my return visit to Norwich and the @…, this time to give the Dame Janet Thornton lecture on Thursday 13th.
Register link (with reception afterwards 🍰, do come and say hello!):
➡️ #circadian clocks in #plantsci 🌿 and a bit on #OpenData infrastructure 💽, I'm re-using the notion of Arrival from Katherine Trebeck and Jeremy Williams' book, the #Economics of Arrival. Might this help us researchers to bridge the Knowledge-Action Gap (see below) ?

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.

Jets GM Darren Mougey rejects talk of 'teardown' after trade deadline deals https://www.nfl.com/news/jets-gm-darren-mougey-rejects-talk-teardown-trade-deadline-deals

Multi-dimensional chaos I: Classical and quantum mechanics
Massimo Bianchi, Maurizio Firrotta, Jacob Sonnenschein, Dorin Weissman
https://arxiv.org/abs/2510.03007 https://

Multi-dimensional chaos I: Classical and quantum mechanics
We introduce the notion of multi-dimensional chaos that applies to processes described by erratic functions of several dynamical variables. We employ this concept in the interpretation of classical and quantum scattering off a pinball system. In the former case it is illustrated by means of two-dimensional plots of the scattering angle and of the number of bounces. We draw similar patterns for the quantum differential cross section for various geometries of the disks. We find that the eigenvalu…

Oh fun find, there was actually something called Oxide in the history of #Rust already - a formalization attempt:
https://arxiv.org/abs/1903.00982 🦀
cc @…

Oxide: The Essence of Rust
Rust claims to advance industrial programming by bridging the gap between low-level systems programming and high-level application programming. At the heart of the argument that this enables programmers to build more reliable and efficient software is the borrow checker - a novel approach to ownership that aims to balance type system expressivity with usability. And yet, to date there is no core type system that captures Rust's notion of ownership and borrowing, and hence no foundation for rese…

This is wild.
EDIT:
https://castle-journal.com/sensational-claims-emerge-following-south-african-ambassadors-tragic-death-in-paris/

Abelian quotients of categories of $n$-exangles
Yutong Zhou
https://arxiv.org/abs/2510.06626 https://arxiv.org/pdf/2510.06626

Abelian quotients of categories of $n$-exangles
The notion of $n$-exangulated categories was introduced by Herschend-Liu-Nakaoka, which is a simultaneous generalization of $n$-exact categories in the sense of Jasso and $(n+2)$-angulated categories in the sense of Geiss-Kelier-Oppermann. Let $(\mathscr{C},\mathbb{E},\mathfrak{s})$ be an $n$-exangulated category with enough projectives $\mathcal{P}$ and $\mathcal{M}$ a full subcategory of $\mathscr{C}$ containing $\mathcal{P}$. In the present paper, It is proved that a certian quotient categor…

things that will not convince me to go to bed:
- lateness of the hour
- eepy
- have work tomorrow
- bed is soft and warm
things that will convince me to go to bed:
- cloudflare outage

Generalized Bogomolov Inequalities
Mihai Pavel, Julius Ross, Matei Toma
https://arxiv.org/abs/2510.04663 https://arxiv.org/pdf/2510.04663

Generalized Bogomolov Inequalities
We introduce the notion of a Hodge-Riemann pair of cohomology classes that generalizes the classical Hodge-Riemann bilinear relations, and the notion of a Bogomolov pair of cohomology classes that generalizes the Bogomolov inequality for semistable sheaves. We conjecture that every Hodge-Riemann pair is a Bogomolov pair, and prove various cases of this conjecture. As an application we get new results concerning boundedness of semistable sheaves.

Free Independence is not Definable
William Boulanger, Jakub Curda, Emma Harvey, Yizhi Li, Jennifer Pi
https://arxiv.org/abs/2510.04836 https://arxiv.org/pd…

Free Independence is not Definable
Free independence is an important tool for studying the structure of operator algebras. It is natural to ask from the model-theoretic standpoint whether free independence is captured well in first-order model theory via the notion of a definable set. We prove that pairs of freely independent elements do not form a definable set in the sense of continuous model theory, relative to the theory of both C$^*$-probability spaces and tracial von Neumann algebras.

The Computational Complexity of Almost Stable Clustering with Penalties
Kamyar Khodamoradi, Farnam Mansouri, Sandra Zilles
https://arxiv.org/abs/2510.03143 https://

The Computational Complexity of Almost Stable Clustering with Penalties
We investigate the complexity of stable (or perturbation-resilient) instances of $\mathrm{k-M\small{EANS}}$ and $\mathrm{k-M\small{EDIAN}}$ clustering problems in metrics with small doubling dimension. While these problems have been extensively studied under multiplicative perturbation resilience in low-dimensional Euclidean spaces (e.g., (Friggstad et al., 2019; Cohen-Addad and Schwiegelshohn, 2017)), we adopt a more general notion of stability, termed ``almost stable'', which is closer to the…

Statistical Signatures of Integrable and Non-Integrable Quantum Hamiltonians
Feng He, Arthur Hutsalyuk, Giuseppe Mussardo, Andrea Stampiggi
https://arxiv.org/abs/2510.02440 http…

Statistical Signatures of Integrable and Non-Integrable Quantum Hamiltonians
Integrability is a cornerstone of classical mechanics, where it has a precise meaning. Extending this notion to quantum systems, however, remains subtle and unresolved. In particular, deciding whether a quantum Hamiltonian - viewed simply as a matrix - defines an integrable system is far from obvious, yet crucial for understanding non-equilibrium dynamics, spectral correlations, and correlation functions in many-body physics. We develop a statistical framework that approaches quantum integrabil…

I do think that this framing isn't fully correct. "Open Source" often has a libertarian (and therefore explicitly non-left) bend. It can be put into left thinking and politics but it works just as well in more right-wing logics. (See Golumbia, Cyberlibertarianism)
https://mastodon.mallegolhanse…

A notion of quasi-convex subgroups in acylindrically hyperbolic groups
Ping Wan
https://arxiv.org/abs/2509.20532 https://arxiv.org/pdf/2509.20532

A notion of quasi-convex subgroups in acylindrically hyperbolic groups
In this paper, we present a notion of quasiconvexity in the setting of finitely-generated groups with hyperbolically embedded subgroups. Our main result shows that this notion yields uniform quasiconvex constants in the setting of coned-off cusped spaces. We also prove that this notion of quasiconvexity is preserved under sufficiently long Dehn filling. As an application, we generalize a theorem of Groves-Manning on groups acting on $\operatorname{CAT}(0)$ cube complexes.

Trump’s brazen approach,
publicly flaunting his corruption,
awards him perverse credit for authenticity
and takes the sting out of scandals that used to be career-ending when uncovered by muckraking journalists.
“This is a dangerous notion that,
just because a president chooses to be corrupt in public openly,
it’s OK,” said Larry Sabato,
director of the Center for Politics at the University of Virginia.
“People say, well, if it were really corru…

A Small Collusion is All You Need
Yotam Gafni
https://arxiv.org/abs/2510.05986 https://arxiv.org/pdf/2510.05986

A Small Collusion is All You Need
Transaction Fee Mechanisms (TFMs) study auction design in the Blockchain context, and emphasize robustness against miner and user collusion, moreso than traditional auction theory. \cite{chung2023foundations} introduce the notion of a mechanism being $c$-Side-Contract-Proof ($c$-SCP), i.e., robust to a collusion of the miner and $c$ users. Later work \cite{chung2024collusion,welfareIncreasingCollusion} shows a gap between the $1$-SCP and $2$-SCP classes. We show that the class of $2$-SCP mechan…

Quinnen Williams won't say it, but there's no denying his impact on the Dallas defense https://www.foxsports.com/articles/nfl/quinnen-williams-wont-say-it-but-theres-no-denying-his-impact-on-the-dallas-defense

Notions of Higher Type
Andreea C. Nicoara
https://arxiv.org/abs/2510.03168 https://arxiv.org/pdf/2510.03168

Notions of Higher Type
Notions of finite type play an important role in several complex variables. The most standard notion is D'Angelo type, which measures the order of contact of holomorphic curves with the boundary of a domain in ${\mathbb C}^n$. For the $\bar \partial$-Neumann problem, however, the order of contact of the boundary of the domain with $q$-dimensional complex varieties controls its behavior on $(p,q)$ forms. There are two different ways of measuring this order of contact, one due to John D'Angelo an…

Stable coresets: Unleashing the power of uniform sampling
Amir Carmel, Robert Krauthgamer
https://arxiv.org/abs/2509.22189 https://arxiv.org/pdf/2509.22189…

Stable coresets: Unleashing the power of uniform sampling
Uniform sampling is a highly efficient method for data summarization. However, its effectiveness in producing coresets for clustering problems is not yet well understood, primarily because it generally does not yield a strong coreset, which is the prevailing notion in the literature. We formulate \emph{stable coresets}, a notion that is intermediate between the standard notions of weak and strong coresets, and effectively combines the broad applicability of strong coresets with highly efficient…

Generalized $(C, \lambda)$-structure for nonlinear diffeomorphisms of Banach spaces
Sergey Tikhomirov
https://arxiv.org/abs/2510.05499 https://arxiv.org/pd…

Generalized $(C, λ)$-structure for nonlinear diffeomorphisms of Banach spaces
We introduce a notion of generalized $(C, λ)$-structure for nonlinear diffeomorphisms in Banach spaces. It combines generalized hyperbolicity for linear operators in Banach spaces with $(C, λ)$-structure for diffeomorphisms on compact manifolds. The main differencies are that we allow the hyperbolic splitting to be discontinuous and in invariance condition assume only inclusions instead of equalities for both stable and unstable subspace, which allows us to cover Morse-Smale systems and gener…

Bilinear spherical maximal function with fractal dilations
Surjeet Singh Choudhary, Chun-Yen Shen, Saurabh Shrivastava
https://arxiv.org/abs/2510.03094 https://

Bilinear spherical maximal function with fractal dilations
In this paper, we investigate $L^p-$boundedness of the bilinear spherical maximal function associated with a general dilation set $E\subset\R_+$. We quantify the range of $L^p-$boundedness in terms of a dilation-invariant notion of upper Minkowski dimension of the set $E$. A particular case of this study settles an open question of $L^p-$boundedness of the lacunary bilinear spherical maximal function at borderline cases $p_1=1$ or $p_2=1$ in dimension $d\geq4$.

A Concept of Possibility for Real-World Events
Daniel G. Schwartz
https://arxiv.org/abs/2510.02655 https://arxiv.org/pdf/2510.02655

A Concept of Possibility for Real-World Events
This paper offers a new concept of {\it possibility} as an alternative to the now-a-days standard concept originally introduced by L.A. Zadeh in 1978. This new version was inspired by the original but, formally, has nothing in common with it other than that they both adopt the Łukasiewicz multivalent interpretation of the logical connectives. Moreover, rather than seeking to provide a general notion of possibility, this focuses specifically on the possibility of a real-world event. An event is…

An Annotation Scheme for Factuality and its Application to Parliamentary Proceedings
Gili Goldin, Shira Wigderson, Ella Rabinovich, Shuly Wintner
https://arxiv.org/abs/2509.26406

An Annotation Scheme for Factuality and its Application to Parliamentary Proceedings
Factuality assesses the extent to which a language utterance relates to real-world information; it determines whether utterances correspond to facts, possibilities, or imaginary situations, and as such, it is instrumental for fact checking. Factuality is a complex notion that relies on multiple linguistic signals, and has been studied in various disciplines. We present a complex, multi-faceted annotation scheme of factuality that combines concepts from a variety of previous works. We develope…

Generalized Clifford algebras, weighted polynomial laws, and adjunction
Nguyen Xuan Bach
https://arxiv.org/abs/2510.06560 https://arxiv.org/pdf/2510.06560

Generalized Clifford algebras, weighted polynomial laws, and adjunction
In this paper, we study Clifford algebra construction from the perspective of adjunctions motivated by the general framework of Krashen and Lieblich. We introduce a category of weighted polynomial laws whose associated Clifford algebra functor is a left adjoint on this category. We give a notion of lifting weighted polynomial laws that generalize Krashen and Lieblich's explicit constructions. As another application, we give the construction of derived Clifford algebras for derived homogeneous p…

Characteristic polynomials of tensors via Grassmann integrals and distributions of roots for random Gaussian tensors
Nicolas Delporte, Giacomo La Scala, Naoki Sasakura, Reiko Toriumi
https://arxiv.org/abs/2510.04068

Characteristic polynomials of tensors via Grassmann integrals and distributions of roots for random Gaussian tensors
We propose a new definition of characteristic polynomials of tensors based on a partition function of Grassmann variables. This new notion of characteristic polynomial addresses general tensors including totally antisymmetric ones, but not totally symmetric ones. Drawing an analogy with matrix eigenvalues obtained from the roots of their characteristic polynomials, we study the roots of our tensor characteristic polynomial. Unlike standard definitions of eigenvalues of tensors of dimension $N$ …

Testing Quantum Mechanics with Quantum Computers: Qubit Information Capacity
Tim Palmer
https://arxiv.org/abs/2510.02877 https://arxiv.org/pdf/2510.02877…

Testing Quantum Mechanics with Quantum Computers: Qubit Information Capacity
Motivated by John Wheeler's assertion that the continuum nature of Hilbert Space conceals the information-theoretic nature of the quantum wavefunction, a specific discretisation of complex Hilbert Space is proposed, leading to the notion of qubit information capacity $N_{\mathrm{max}}$: for any $N \ge N_{\mathrm{max}}$-qubit state, there is insufficient information in the $N$ qubits to allocate even one bit to each of the $2^{N+1}-2$ degrees of freedom demanded by complex Hilbert Space and henc…

@… with all due respect, the notion of "five minutes" to learn vi is detached from reality.
You have no idea what it's like. No idea how frustrating.
Imagine someone being severely allergic to nuts.
cc @…

Optimization by Directional Attacks: Solving Problems with Neural Network Surrogates
Pierre-Yves Bouchet, Thibaut Vidal
https://arxiv.org/abs/2510.01461 https://

Optimization by Directional Attacks: Solving Problems with Neural Network Surrogates
This paper tackles optimization problems whose objective and constraints involve a trained Neural Network (NN), where the goal is to maximize $f(Φ(x))$ subject to $c(Φ(x)) \leq 0$, with $f$ smooth, $c$ general and non-stringent, and $Φ$ an already trained and possibly nonwhite-box NN. We address two challenges regarding this problem: identifying ascent directions for local search, and ensuring reliable convergence towards relevant local solutions. To this end, we re-purpose the notion of dir…

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 moduli spaces of left-invariant statistical structures on Lie groups
Hikozo Kobayashi, Yu Ohno, Takayuki Okuda, Hiroshi Tamaru
https://arxiv.org/abs/2510.04442 https://

The moduli spaces of left-invariant statistical structures on Lie groups
In the context of information geometry, the concept known as left-invariant statistical structure on Lie groups is defined by Furuhata--Inoguchi--Kobayashi [Inf. Geom. (2021)]. In this paper, we introduce the notion of the moduli space of left-invariant statistical structures on a Lie group. We study the moduli spaces for three particular Lie groups, each of which has a moduli space of left-invariant Riemannian metrics that is a singleton. As applications, we classify left-invariant conjugate s…

Bridging Kolmogorov Complexity and Deep Learning: Asymptotically Optimal Description Length Objectives for Transformers
Peter Shaw, James Cohan, Jacob Eisenstein, Kristina Toutanova
https://arxiv.org/abs/2509.22445

Bridging Kolmogorov Complexity and Deep Learning: Asymptotically Optimal Description Length Objectives for Transformers
The Minimum Description Length (MDL) principle offers a formal framework for applying Occam's razor in machine learning. However, its application to neural networks such as Transformers is challenging due to the lack of a principled, universal measure for model complexity. This paper introduces the theoretical notion of asymptotically optimal description length objectives, grounded in the theory of Kolmogorov complexity. We establish that a minimizer of such an objective achieves optimal compre…

Admissible set and squarefree-power-like function with applications to squarefree symbolic powers
Trung Chau, Kanoy Kumar Das, Amit Roy, Kamalesh Saha
https://arxiv.org/abs/2510.01366

Admissible set and squarefree-power-like function with applications to squarefree symbolic powers
We introduce the abstract notion of squarefree-power-like functions, which unify the sequences of squarefree ordinary and symbolic powers of squarefree monomial ideals. By employing the Tor-vanishing criteria for mixed sums of ideals, we establish sharp lower bounds for their Castelnuovo-Mumford regularity in terms of what we call the admissible set of the associated hypergraph. As an application, we derive the first general combinatorial lower bound for the regularity of squarefree symbolic po…

Extrinsic systole of Seifert surfaces and distortion of knots
Sahana Vasudevan
https://arxiv.org/abs/2510.01095 https://arxiv.org/pdf/2510.01095

Extrinsic systole of Seifert surfaces and distortion of knots
In 1983, Gromov introduced the notion of distortion of a knot, and asked if there are knots with arbitrarily large distortion. In 2011, Pardon proved that the distortion of $T_{p,q}$ is at least $\min\{p,q\}$ up to a constant factor. We prove that the distortion of $T_{p, p+1}\# K$ is at least $p$ up to a constant, independent of $K$. We also prove that any embedding of a minimal genus Seifert surface for $T_{p,p+1}\# K$ in $\mathbb{R}^3$ has small extrinsic systole, in the sense that it contai…

A TSO-DSO Coordination Framework via Analytical Representation and Monetization of PQV-Based Distribution System Flexibility
Burak Dindar, Can Berk Saner, H\"useyin Kemal \c{C}akmak, Veit Hagenmeyer
https://arxiv.org/abs/2510.01854

A TSO-DSO Coordination Framework via Analytical Representation and Monetization of PQV-Based Distribution System Flexibility
As the role of distribution system (DS) flexibility in transmission system operator (TSO) network management becomes increasingly vital, data privacy concerns hinder seamless interoperability. The notion of the feasible operating region (FOR), defined in the PQ domain, has emerged as a promising privacy-preserving approach. However, effectively leveraging FOR in TSO operations remains challenging due to three key factors: its accurate determination in large-scale, meshed DS networks; its tracta…

Weak containment of representation on topological groupoids
K. N. Sridharan, N. Shravan Kumar
https://arxiv.org/abs/2510.05898 https://arxiv.org/pdf/2510.0…

Weak containment of representation on topological groupoids
Let $G$ be a second-countable, locally compact Hausdorff groupoid equipped with a Haar system. This paper investigates the weak containment of continuous unitary representations of groupoids. We show that both induction and inner tensor product of representations preserve weak containment. Additionally, we introduce the notion of a topological invariant mean on $G/H$ and explore its connection to amenability. With that, we establish a groupoid analogue of Greenleaf's theorem. Finally, we provid…

Computing Envy-Free up to Any Good (EFX) Allocations via Local Search
Simina Br\^anzei
https://arxiv.org/abs/2510.05429 https://arxiv.org/pdf/2510.05429

Computing Envy-Free up to Any Good (EFX) Allocations via Local Search
We present a simple local search algorithm for computing EFX (envy-free up to any good) allocations of $m$ indivisible goods among $n$ agents with additive valuations. EFX is a compelling fairness notion, and whether such allocations always exist remains a major open question in fair division. Our algorithm employs simulated annealing with the total number of EFX violations as an objective function together with a single-transfer neighborhood structure to move through the space of allocations…

Artin--Mazur formal groups and Milne duality via unipotent spectra
Shubhodip Mondal, Tasos Moulinos, Lucy Yang
https://arxiv.org/abs/2510.06152 https://arx…

Artin--Mazur formal groups and Milne duality via unipotent spectra
We introduce and develop the notion of "unipotent spectra." This is defined to be the stabilization of Toën's category of affine stacks, and is related to recent work of Mondal--Reinecke. Unipotent spectra give rise to unipotent stable homotopy groups and unipotent homology, which are new invariants for schemes valued in unipotent group schemes. As applications, we recover the Artin--Mazur formal groups associated to schemes without any vanishing assumptions. Further, we show that syntomic coh…

On Information Transfer and Symmetry Breaking in Dynamical Systems
Subhrajit Sinha, Parvathi Kooloth
https://arxiv.org/abs/2510.03572 https://arxiv.org/pdf…

On Information Transfer and Symmetry Breaking in Dynamical Systems
In this work, we propose a novel approach to investigate symmetry breaking in dynamical systems. In particular, we use the notion of information transfer, which provides a measure of the entropy transfer between any pair of observables in a system, to predict symmetry breaking. We show that as a system loses symmetry, its trajectories \emph{slow down} and its Shannon entropy increases. This connection enables us to use information transfer to predict the onset of symmetry breaking. Furthermore,…

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

Hadamard ranks of algebraic varieties
Dario Antolini, Guido Mont\'ufar, Alessandro Oneto
https://arxiv.org/abs/2510.05231 https://arxiv.org/pdf/2510.05…

Hadamard ranks of algebraic varieties
Motivated by the study of decompositions of tensors as Hadamard products (i.e., coefficient-wise products) of low-rank tensors, we introduce the notion of Hadamard rank of a given point with respect to a projective variety: if it exists, it is the smallest number of points in the variety such that the given point is equal to their Hadamard product. We prove that if the variety $X$ is not contained in a coordinate hyperplane or a binomial hypersurface, then the generic point has a finite $X$-Had…

Replaced article(s) found for math.GR. https://arxiv.org/list/math.GR/new
[1/1]:
- A notion of quasiconvex subgroups in acylindrically hyperbolic groups
Ping Wan

Slant sums of quiver gauge theories
Hunter Dinkins, Vasily Krylov, Reese Lance
https://arxiv.org/abs/2510.02496 https://arxiv.org/pdf/2510.02496

Slant sums of quiver gauge theories
We define a notion of slant sum of quiver gauge theories, a type of surgery on the underlying quiver. Under some mild assumptions, we relate torus fixed points on the corresponding Higgs branches, which are Nakajima quiver varieties. Then we prove a formula relating the quasimap vertex functions before and after a slant sum, which is a type of ``branching rule" for vertex functions. Our construction is motivated by a conjecture, which we make here, for the factorization of the vertex function…

SeedPrints: Fingerprints Can Even Tell Which Seed Your Large Language Model Was Trained From
Yao Tong, Haonan Wang, Siquan Li, Kenji Kawaguchi, Tianyang Hu
https://arxiv.org/abs/2509.26404

SeedPrints: Fingerprints Can Even Tell Which Seed Your Large Language Model Was Trained From
Fingerprinting Large Language Models (LLMs) is essential for provenance verification and model attribution. Existing methods typically extract post-hoc signatures based on training dynamics, data exposure, or hyperparameters -- properties that only emerge after training begins. In contrast, we propose a stronger and more intrinsic notion of LLM fingerprinting: SeedPrints, a method that leverages random initialization biases as persistent, seed-dependent identifiers present even before training.…

Paris-based Upciti, which offers city operations software and hardware to over 150 municipalities in 17 countries, raised a $20M Series A led by Notion Capital (Tamara Djurickovic/Tech.eu)
https://tech.eu/2025/10/16/upciti-closes-20m-to-dr…

UPCITI closes $20M to drive global growth of its urban operating platform
UPCITI, a Paris-based company building an operating system for cities, has raised $20 million in a Series A funding round. The round was led by Notion Capital, with participation from Point Nine and Chalfen Ventures.UPCITI combines proprietary software with purpose-built hardware to help municipalities run critical operations, such as traffic flow, street management, and public safety, more efficiently and securely, with a clear ROI that simplifies adoption. By owning both the software an…

Why did Republicans close ranks around Donald Trump in 2016,
when they could have salvaged their old party and rebuilt after losing?
From the vantage point of today, it’s easy to dismiss the notion. “That’s just what parties do, of course, particularly Republicans in their era of hyperpartisanship.”
But the people who might say that have forgotten how unsettled Republicans were a decade ago.
The idea that they might be forced to withdraw support from Trump and accep…

MAGA Disarray And The Accumulated Debt Of Corruption
They'd bring America down rather than face accountability, but accountability is not optional.

A $q$-analogue of distance matrix of bi-block graphs
Joyentanuj Das
https://arxiv.org/abs/2509.26060 https://arxiv.org/pdf/2509.26060

A $q$-analogue of distance matrix of bi-block graphs
A $q$-analogue of the distance matrix, referred to as the \emph{$q$-distance matrix}, is obtained from the distance matrix by replacing each nonzero entry $α$ with the sum $1+q+\cdots+q^{α-1}$. This notion was introduced independently by Bapat, Lal, and Pati~\cite{Ba-Lal-Pati}, and by Yan and Yeh~\cite{Yan}. A connected graph is called a \emph{bi-block graph} if each of its blocks is a complete bipartite graph. In this paper, we derive explicit formulas for the determinant and the inverse of …

Strategyproof Tournament Rules for Teams with a Constant Degree of Selfishness
David Pennock, Daniel Schoepflin, Kangning Wang
https://arxiv.org/abs/2512.05235 https://arxiv.org/pdf/2512.05235 https://arxiv.org/html/2512.05235
arXiv:2512.05235v1 Announce Type: new
Abstract: We revisit the well-studied problem of designing fair and manipulation-resistant tournament rules. In this problem, we seek a mechanism that (probabilistically) identifies the winner of a tournament after observing round-robin play among $n$ teams in a league. Such a mechanism should satisfy the natural properties of monotonicity and Condorcet consistency. Moreover, from the league's perspective, the winner-determination tournament rule should be strategyproof, meaning that no team can do better by losing a game on purpose.
Past work considered settings in which each team is fully selfish, caring only about its own probability of winning, and settings in which each team is fully selfless, caring only about the total winning probability of itself and the team to which it deliberately loses. More recently, researchers considered a mixture of these two settings with a parameter $\lambda$. Intermediate selfishness $\lambda$ means that a team will not lose on purpose unless its pair gains at least $\lambda s$ winning probability, where $s$ is the individual team's sacrifice from its own winning probability. All of the dozens of previously known tournament rules require $\lambda = \Omega(n)$ to be strategyproof, and it has been an open problem to find such a rule with the smallest $\lambda$.
In this work, we make significant progress by designing a tournament rule that is strategyproof with $\lambda = 11$. Along the way, we propose a new notion of multiplicative pairwise non-manipulability that ensures that two teams cannot manipulate the outcome of a game to increase the sum of their winning probabilities by more than a multiplicative factor $\delta$ and provide a rule which is multiplicatively pairwise non-manipulable for $\delta = 3.5$.
toXiv_bot_toot

Monoid Structures on Indexed Containers
Michele De Pascalis, Tarmo Uustalu, Niccol\`o Veltr\`i
https://arxiv.org/abs/2509.25879 https://arxiv.org/pdf/2509.…

Monoid Structures on Indexed Containers
Containers represent a wide class of type constructions relevant for functional programming and (co)inductive reasoning. Indexed containers generalize this notion to better fit the scope of dependently typed programming. When interpreting types to be sets, a container describes an endofunctor on the category of sets while an I-indexed container describes an endofunctor on the category Set^I of I-indexed families of sets. We consider the monoidal structure on the category of I-indexed containe…

Abstract Cluster Structures
Jan E. Grabowski, Sira Gratz
https://arxiv.org/abs/2510.02959 https://arxiv.org/pdf/2510.02959…

Abstract Cluster Structures
We describe a framework for encoding cluster combinatorics using categorical methods. We give a definition of an abstract cluster structure, which captures the essence of cluster mutation at a tropical level and show that cluster algebras, cluster varieties, cluster categories and surface models all have associated abstract cluster structures. For the first two classes, we also show that they can be constructed from abstract cluster structures. By defining a suitable notion of morphism of abs…

Group Actions and Some Combinatorics on Words with $\mathbf{vtm}$
John Machacek
https://arxiv.org/abs/2509.26613 https://arxiv.org/pdf/2509.26613

Group Actions and Some Combinatorics on Words with $\mathbf{vtm}$
We introduce generalizations of powers and factor complexity via orbits of group actions. These generalizations include concepts like abelian powers and abelian complexity. It is shown that this notion of factor complexity cannot be used to recognize Sturmian words in general. Within our framework, we establish square avoidance results for the ternary squarefree Thue--Morse word $\mathbf{vtm}$. These results go beyond the usual squarefreeness of $\mathbf{vtm}$ and are proved using Walnut. Lastl…

Extension of a problem of Euler in $\mathbb{H}^2$ and in $\mathbb{S}^2$
Muhittin Evren Aydin, Antonio Bueno, Rafael L\'opez
https://arxiv.org/abs/2510.00544 https://

Extension of a problem of Euler in $\mathbb{H}^2$ and in $\mathbb{S}^2$
In this paper, we extend the notion of stationary curves with respect to the moment of inertia from a point $N$ in the Euclidean plane $\mathbb{R}^2$ to the case that the ambient space is either the hyperbolic plane $\mathbb{H}^2$ or the sphere $\mathbb{S}^2$. We characterize the critical points of this energy in terms of the curvature of the curve and the distance to $N$. In $\mathbb{H}^2$, we prove that the only closed stationary curves are circles centered at $N$. In $\mathbb{S}^2$, we estim…

Nominal Sets in Rocq
Fabr\'icio Sanches Paranhos (Nethermind - London, UK), Daniel Ventura (INF-UFG)
https://arxiv.org/abs/2509.25883 https://arxiv.org…

Nominal Sets in Rocq
Nominal techniques have been praised for their ability to formalize grammars with binding structures closer to their informal developments. At its core, there lies the definition of nominal sets, which capture the notion of name (in)dependence through a simple, and uniform, metatheory based on name permutations. We present a formal constructive development of nominal sets in Rocq (formerly known as Coq), with its main design and project decisions. Furthermore, we formalize the concepts of fresh…

Positive cones of $b$-divisor classes
Snehajit Misra, Nabanita Ray
https://arxiv.org/abs/2509.25948 https://arxiv.org/pdf/2509.25948

Positive cones of $b$-divisor classes
In this article, we define the notion of ample Cartier $b$-divisor classes by using the notion of Seshadri constants for Cartier $b$-divisor classes. In particular, we have shown that the set of all ample Cartier $b$-divisor classes forms a convex cone inside the nef cone of Cartier $b$-divisor classes. Furthermore, we have studied various properties of these Cartier ample $b$-divisor classes. We have also given an equivalent characterization of big Cartier $b$-divisor classes in terms of volum…

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

Immersions of complexes of groups
Jagerynn Ting Verano
https://arxiv.org/abs/2510.01516 https://arxiv.org/pdf/2510.01516

Immersions of complexes of groups
Given a complex of groups, we construct a new class of complex of groups that records its local data and offer a functorial perspective on the statement that complexes of groups are locally developable. We also construct a new notion of an immersion of complexes of groups and establish that a locally isometric immersion of a complex of groups into a non-positively curved complex of groups is $π_1$-injective. Furthermore, the domain complex of groups is developable and the induced map on geomet…

An Ohba-like Result for Flexible List Coloring
Michael C. Bowdoin, Yanghong Chi, Christian B. Ellington, Bella Ives, Seoju Lee, Fennec Morrissette, Jeffrey A. Mudrock
https://arxiv.org/abs/2509.24013

An Ohba-like Result for Flexible List Coloring
Chromatic-choosablility is a notion of fundamental importance in list coloring. A graph $G$ is chromatic-choosable when its chromatic number, $χ(G)$, is equal to its list chromatic number $χ_{\ell}(G)$. Flexible list coloring was introduced by Dvořák, Norin, and Postle in 2019 in order to address a situation in list coloring where we still seek a proper list coloring, but each vertex may have a preferred color assigned to it, and for those vertices we wish to color as many of them with thei…

Recognisability for generalised hierarchical patterns and pattern spaces of finite local complexity
James J. Walton
https://arxiv.org/abs/2509.21001 https://

Recognisability for generalised hierarchical patterns and pattern spaces of finite local complexity
We explore an extended notion of a tiling of translational finite local complexity (FLC) being substitutional, or hierarchical, to Euclidean `patterns' and define, more generally, a similar notion for spaces of patterns. We prove recognisability results for these, relating injectivity of substitution to aperiodicity, with no minimality requirements. More precisely, for a suitable power of the substitution map, we determine the size of fibre over any pattern to be the index of its inflated (tran…

Non-degenerate mixed maps and contact structures
In\'acio Rabelo, Jos\'e Seade
https://arxiv.org/abs/2510.03033 https://arxiv.org/pdf/2510.03033

Non-degenerate mixed maps and contact structures
We study the geometry and topology of real analytic maps $\mathbb{C}^n \to \mathbb{C}^k$, where $n > k$, regarded as mixed maps, defined below. Firstly, we give two natural families of mixed isolated complete intersection singularities, called mixed ICIS, which are interesting on their own. We consider the notion of (partial) non-degeneracy for mixed maps; we prove that these define mixed ICIS and that, under suitable conditions, admit a local Milnor fibration. Then, building on previous constr…

Virtual global generation in higher dimensions
Indranil Biswas, Manish Kumar, A. J. Parameswaran
https://arxiv.org/abs/2509.25653 https://arxiv.org/pdf/250…

Virtual global generation in higher dimensions
The notion of virtual global generation (VGG) for a vector bundle has multiple possible generalization from the case of curves to higher dimensional normal projective varieties. We study relationship between these notions. All these notions agree for curves but in higher dimension we show that this is not the case.