Tootfinder

Metric criteria for fixed price of countable groups
Erin Bevilacqua, Lewis Bowen
https://arxiv.org/abs/2510.05459 https://arxiv.org/pdf/2510.05459

Metric criteria for fixed price of countable groups
We establish general criteria for a countable group $Γ$ to have fixed price 1 depending on a choice of left-invariant proper metric on $Γ$. We apply this criterion to show that if $Γ_1,Γ_2$ are two countable groups satisfying a certain growth condition then $Γ_1\times Γ_2$ has fixed price 1. For example, $Γ\times Γ$ has fixed price 1 for any countable group $Γ$.

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…

Cut-and-choose games in topological spaces
Lucas Chiozini, Tam\'as Csern\'ak, Lajos Soukup
https://arxiv.org/abs/2510.05754 https://arxiv.org/pdf/2…

Cut-and-choose games in topological spaces
We study transfinite cut-and-choose games on $T_0$ spaces, introducing the {\em point-separating number} $ps(X)$ and the {\em set membership number} ${sm}(X)$ as ordinal-valued invariants measuring the minimal length of a game in which a Seeker can determine a hidden point or subset. A central motivating question is which countable ordinals can occur as the value of $ps(X)$, in particular whether any countable ordinal can arise. These invariants generalize Scott's $T_0$-pseudoweight $ψw_0$. We…

Gifford Fire
Highway 166 west of the Gifford Trailhead, East of Santa Maria
San Luis Obispo & Santa Barbara Counties
5,000 ACRES
Zero CONTAINMENT
Updated 4 minutes ago
https://m.ai6yr.org/@MiBaWi/114956180526023960
Watchduty

MiBaWi - Michael Barthel (@MiBaWi@m.ai6yr.org)
Attached: 4 images #GiffordFire > Highway 166 west of the Gifford Trailhead, San Luis Obispo & Santa Barbara Counties / CA 820 acres, 0% contained SR 166 East is CLOSED from US 101 near Santa Maria to Perkins Rd near New Cuyama Watch Duty > https://app.watchduty.org/i/58187 Cam > https://ops.alertcalifornia.org/cam-console/16438 Santa Barbara County OEM > https://www.countyofsb.org/4726/Gifford-Fire---August-1-2025 San Luis Obispo OEM > https://www.emergencyslo.org/en/incident-informatio…

ok so it turns out that using "your own" anycast infra (renting a shared /32, since a /24 costs waaaay too much) is actually quite straightforward? *shuffles five hours lost to baroque BGP software and stupid fucking TCP MD5 option under the desk*
if i knew this i'd not have bothered with IaaS providers (primary occupuation: billing. secondary occupation: pro-AI extremist rants on the blog full of contept for their customers)

Renormalization of Chern-Simons Wilson Loops via Flux Quantization in Cohomotopy
Hisham Sati, Urs Schreiber
https://arxiv.org/abs/2509.25336 https://arxiv.…

Renormalization of Chern-Simons Wilson Loops via Flux Quantization in Cohomotopy
In the practice of physics model building, the process of renormalization, resummation, and anomaly cancellation is to incrementally repair initially ill-defined Lagrangian quantum field theories. Impressive as this is, one would rather have concisely defined complete theories to begin with, and understand these choices as emergent from fundamental principles. As an instructive example, we recall renormalization choices for Wilson loop observables in abelian Chern-Simons theory. Then we show th…

Decidability of some complicated structures definable in $\mathbb{C}(t)$
Thomas Scanlon
https://arxiv.org/abs/2508.17485 https://arxiv.org/pdf/2508.17485…

Decidability of some complicated structures definable in $\mathbb{C}(t)$
Several properly countable unions of algebraic sets in $\mathbb{C}^n$ are definable in $\mathbb{C}(t)$ including the set CM of $j$-invariants of complex elliptic curves with complex multiplication. It has been suggested that one could prove the undecidability of $\operatorname{Th}(\mathbb{C}(t))$ by showing that the theory of the structure $\mathsf{CM} := (\mathbb{C},+,\cdot,0,1,CM)$ of the field of complex numbers considered with a unary predicate picking out CM is undecidable. We show using a…

Studying the variability of the He triplet to understand the detection limits of evaporating exoplanet atmospheres
Samson J. Mercier, Xavier Dumusque, Vincent Bourrier, Khaled Al Moulla, Michael Cretignier, William Dethier, Gaspare Lo Curto, Pedro Figueira, Christophe Lovis, Francesco Pepe, Nuno C. Santos, St\'ephane Udry, Fran\c{c}ois Wildi, Romain Allart, Fr\'ed\'erique Baron, Fran\c{c}ois Bouchy, Andres Carmona, Marion Cointepas, Ren\'e Doyon, Yolanda Frensch, Nolan …

Studying the variability of the He triplet to understand the detection limits of evaporating exoplanet atmospheres
With more than a dozen significant detections, the helium triplet has emerged as a key tracer of evaporating exoplanet atmospheres. This near-infrared feature can be observed from the ground and holds great promise, especially with upcoming observations provided by new-generation instruments such as the Near Infrared Planet Searcher (NIRPS). However, as the helium triplet is also present in stellar spectra, careful removal of the average stellar contribution is necessary to accurately character…

ChemDFM-R: An Chemical Reasoner LLM Enhanced with Atomized Chemical Knowledge
Zihan Zhao, Bo Chen, Ziping Wan, Lu Chen, Xuanze Lin, Shiyang Yu, Situo Zhang, Da Ma, Zichen Zhu, Danyang Zhang, Huayang Wang, Zhongyang Dai, Liyang Wen, Xin Chen, Kai Yu
https://arxiv.org/abs/2507.21990

ChemDFM-R: An Chemical Reasoner LLM Enhanced with Atomized Chemical Knowledge
While large language models (LLMs) have achieved impressive progress, their application in scientific domains such as chemistry remains hindered by shallow domain understanding and limited reasoning capabilities. In this work, we focus on the specific field of chemistry and develop a Chemical Reasoner LLM, ChemDFM-R. We first construct a comprehensive dataset of atomized knowledge points to enhance the model's understanding of the fundamental principles and logical structure of chemistry. Then,…

Beyond Slater's Condition in Online CMDPs with Stochastic and Adversarial Constraints
Francesco Emanuele Stradi, Eleonora Fidelia Chiefari, Matteo Castiglioni, Alberto Marchesi, Nicola Gatti
https://arxiv.org/abs/2509.20114

Beyond Slater's Condition in Online CMDPs with Stochastic and Adversarial Constraints
We study \emph{online episodic Constrained Markov Decision Processes} (CMDPs) under both stochastic and adversarial constraints. We provide a novel algorithm whose guarantees greatly improve those of the state-of-the-art best-of-both-worlds algorithm introduced by Stradi et al. (2025). In the stochastic regime, \emph{i.e.}, when the constraints are sampled from fixed but unknown distributions, our method achieves $\widetilde{\mathcal{O}}(\sqrt{T})$ regret and constraint violation without relyin…