Tootfinder

Morphisms and comorphisms of sites II - Distributors of sites
Axel Osmond, Olivia Caramello
https://arxiv.org/abs/2507.20932 https://arxiv.org/pdf/2507.209…

Morphisms and comorphisms of sites II - Distributors of sites
We introduce a notion of distributor of sites, involving suited analogs of flatness and cover-preservation, and show that this notion jointly generalizes those of morphism and comorphism of sites. Given two sites, we exhibit an adjunction between the category of distributors of sites between them and the category of geometric morphisms between the associated sheaf topoi; this adjunction restricts to an equivalence between geometric morphisms and continuous distributors of sites. We finally disc…

A $\sigma$-morphic convex protoset
Aleksa D\v{z}uklevski
https://arxiv.org/abs/2507.20867 https://arxiv.org/pdf/2507.20867…

A $σ$-morphic convex protoset
We say that a tile is $σ$-morphic if it tiles the plane in exactly $\aleph_0$ many noncongruent ways (up to an isometry). It is an unsolved problem of whether a $σ$-morphic tile exist in the plane. In this note we present a construction of a set of convex tiles that is $σ$-morphic. The result is interesting since all the constructions of $σ$-morphic sets of tiles that arise in the literature make use of bumps and nicks, which necessarily make the tiles non-convex. We construct our set by cl…

Human-AI Collaborative Bot Detection in MMORPGs
Jaeman Son, Hyunsoo Kim
https://arxiv.org/abs/2508.20578 https://arxiv.org/pdf/2508.20578

Human-AI Collaborative Bot Detection in MMORPGs
In Massively Multiplayer Online Role-Playing Games (MMORPGs), auto-leveling bots exploit automated programs to level up characters at scale, undermining gameplay balance and fairness. Detecting such bots is challenging, not only because they mimic human behavior, but also because punitive actions require explainable justification to avoid legal and user experience issues. In this paper, we present a novel framework for detecting auto-leveling bots by leveraging contrastive representation learni…

Universal Characteristic-free Resolution of Singularities, I
Yi Hu
https://arxiv.org/abs/2507.21400 https://arxiv.org/pdf/2507.21400

Universal Characteristic-free Resolution of Singularities, I
We prove that for any singular integral affine variety $X$ of finite presentation over a perfect field defined over $\mathbb Z$, there exists a smooth morphism from $Y$ onto $X$ such that $Y$ admits a resolution. That is, there exists a smooth scheme $\widetilde{Y}$ and a projective birational morphism from $\widetilde{Y}$ onto $Y$, followed by a smooth morphism from $Y$ onto $X$. Our approach differs fundamentally from existing methods, as we neither restrict to any specific singular variety…

FrankenBot: Brain-Morphic Modular Orchestration for Robotic Manipulation with Vision-Language Models
Shiyi Wang, Wenbo Li, Yiteng Chen, Qingyao Wu, Huiping Zhuang
https://arxiv.org/abs/2506.21627

FrankenBot: Brain-Morphic Modular Orchestration for Robotic Manipulation with Vision-Language Models
Developing a general robot manipulation system capable of performing a wide range of tasks in complex, dynamic, and unstructured real-world environments has long been a challenging task. It is widely recognized that achieving human-like efficiency and robustness manipulation requires the robotic brain to integrate a comprehensive set of functions, such as task planning, policy generation, anomaly monitoring and handling, and long-term memory, achieving high-efficiency operation across all funct…

On growth and morphogenesis in mechanobiology
Angelo Rosario Carotenuto, Stefania Palumbo, Arsenio Cutolo, Massimiliano Fraldi
https://arxiv.org/abs/2507.20345 https://

On growth and morphogenesis in mechanobiology
Morphoelasticity represents a foundational theory for tracing back growth, remodelling, and morphogenesis, yet crucial challenges persist. A unified growth law, -independent of a priori assumptions about constitutive relations or specified structures of the growth tensor- remains in fact elusive, as does an intimate connection between local anisotropic growth, morphogenesis dynamics, diffusion phenomena and mechanics. When anisotropy of growth is not prescribed arbitrarily, current frameworks m…

Jupitersonde: NASA hat kaputte JunoCam mehrfach durch Erhitzen repariert
Die NASA-Sonde Juno erforscht seit neun Jahren den Jupiter. Die Bedingungen sind extrem, vor allem die Kamera leidet. Hitze hat sie aber immer wieder repariert.

On the Irreducible Morphisms for Skew group algebras
Shantanu Sardar, Alfredo Gonzalez Chaio, Sonia Trepode
https://arxiv.org/abs/2507.20103 https://arxiv.…

On the Irreducible Morphisms for Skew group algebras
For an algebraically closed field K, let G be a finite abelian group of K-linear automorphisms of a finite-dimensional path algebra KQ of a quiver Q. Under certain assumptions on the action of G, we show the existence of a certain kind of covering that we call a Galois semi-covering functor, which becomes a Galois covering when the group action is free. We study the module category of its skew group algebra under this functor. As an application, we obtain a complete description of the irreducib…

A look at MrBeast's entertainment company, which has ~$450M in annual sales but faced three years of losses due to high production costs of $3M-$4M per video (Lucas Shaw/Bloomberg)
https://www.bloomberg.com/news/features/2025-09…

YouTube Star MrBeast Is Building an Entertainment Empire
The master of viral videos now has a CEO to rein in spending on Lambos—and give his “banger content” an even wider reach.

When is the diagonal contractible?
Xi Chen, Frank Gounelas
https://arxiv.org/abs/2507.21889 https://arxiv.org/pdf/2507.21889…

When is the diagonal contractible?
For a smooth projective complex variety $X$, we prove that there exists a birational morphism $X\times X\to Y$ to a projective variety $Y$ contracting the diagonal $Δ_X\subset X\times X$ to a point if and only if $X$ has maximal Albanese dimension and irregularity $q\geq 2\dim X$. We also give necessary and sufficient conditions for arbitrary contractions of the diagonal and for the existence of a birational morphism which is an isomorphism outside the diagonal.