Tootfinder

Kind of amazing that you can dot a couple of messages like this around the internet https://post.lurk.org/@yaxu/114188134015638878
and then end up with ~40 lovely people hanging out with their computers in the middle of nowhere, what a great thing

Apple says ChatGPT image generation is now available in Image Playground with new ChatGPT styles, releases an API, adds Genmoji text descriptions, and more (Hartley Charlton/MacRumors)
https://www.macrumors.com/2025/06/09/chatgpt-integration-co…

ChatGPT Integration Coming to Apple's Image Playground
Apple today revealed a number of updates for Image Playground and Genmoji. ChatGPT image generation is now available directly in Image Playground,...

Extending the Affirmative Action Problem: mixing numbers and integrated colorings of graphs
Charles Burnette, Broden Caton, Olivia Coward, Julian Davis, Austin Teter
https://arxiv.org/abs/2506.07192

Extending the Affirmative Action Problem: mixing numbers and integrated colorings of graphs
Consider a graph whose vertices are colored in one of two colors, say black or white. A white vertex is called integrated if it has at least as many black neighbors as white neighbors, and similarly for a black vertex. The coloring as a whole is integrated if every vertex is integrated. A classic exercise in graph theory, known as the Affirmative Action Problem, is to prove that every finite simple graph admits an integrated coloring. The solution can be neatly summarized with the one-liner: "m…

Putting a crypto insider in charge of the Commodity Futures Trading Commission is like putting a drug lord in charge of the DEA.
Industry insiders shouldn’t be regulators, but this is even worse.
Crypto isn’t even a legitimate industry, just one good at playing the catch-me-if-you-can game with the regulators it’s about to own.
-- Kristen Simplicio

The Blockchain Association Just Bought the CFTC
The revolving door isn’t just corrupting the CFTC—it may end the pretense of a Commission altogether.

Evaluating Learned Indexes in LSM-tree Systems: Benchmarks,Insights and Design Choices
Junfeng Liu, Jiarui Ye, Mengshi Chen, Meng Li, Siqiang Luo
https://arxiv.org/abs/2506.08671 …

Evaluating Learned Indexes in LSM-tree Systems: Benchmarks,Insights and Design Choices
LSM-tree-based data stores are widely used in industry due to their exceptional performance. However, as data volumes grow, efficiently querying large-scale databases becomes increasingly challenging. To address this, recent studies attempted to integrate learned indexes into LSM-trees to enhance lookup performance, which has demonstrated promising improvements. Despite this, only a limited range of learned index types has been considered, and the strengths and weaknesses of different learned i…

Communicating Through Avatars in Industry 5.0: A Focus Group Study on Human-Robot Collaboration
Stina Klein, Pooja Prajod, Katharina Weitz, Matteo Lavit Nicora, Dimitra Tsovaltzi, Elisabeth Andr\'e
https://arxiv.org/abs/2506.08805

Communicating Through Avatars in Industry 5.0: A Focus Group Study on Human-Robot Collaboration
The integration of collaborative robots (cobots) in industrial settings raises concerns about worker well-being, particularly due to reduced social interactions. Avatars - designed to facilitate worker interactions and engagement - are promising solutions to enhance the human-robot collaboration (HRC) experience. However, real-world perspectives on avatar-supported HRC remain unexplored. To address this gap, we conducted a focus group study with employees from a German manufacturing company tha…

Coulomb Branch and Integrability
Frank Coronado, Shota Komatsu, Konstantin Zarembo
https://arxiv.org/abs/2506.07222 https://arxiv.org…

Coulomb Branch and Integrability
We study one-point functions of non-BPS single-trace operators on the Coulomb branch of planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory. Holography relates them to overlaps between on-shell closed string states and a boundary state describing a probe D3-brane in $AdS_5\times S^{5}$. Assuming that the D-brane preserves integrability, we formulate and solve integrable bootstrap equations satisfied by the boundary state at finite 't Hooft coupling. This leads to a closed-form determinant e…

Galois groups of random integer matrices
Theresa C. Anderson, Evan M. O'Dorney
https://arxiv.org/abs/2506.06463 https://arxiv.org…

Galois groups of random integer matrices
We study the number $M_n(T)$ be the number of integer $n\times n$ matrices $A$ with entries bounded in absolute value by $T$ such that the Galois group of characteristic polynomial of $A$ is not the full symmetric group $S_n$. One knows $M_n(T) \gg T^{n^2 - n + 1} \log T$, which we conjecture is sharp. We first use the large sieve to get $M_n(T) \ll T^{n^2 - 1/2}\log T$. Using Fourier analysis and the geometric sieve, as in Bhargava's proof of van der Waerden's conjecture, we improve this bound…

The return of web rings.
https://serverless.industries/2025/05/27/webring.en.html

Skew monoidal structures on actegories
Pavla Proch\'azkov\'a
https://arxiv.org/abs/2506.06847 https://arxiv.org/pdf/2506.0684…

Skew monoidal structures on actegories
We present a construction of skew monoidal structures from strong actions. We prove that the existence of a certain adjoint allows one to equip the actegory with a skew monoidal structure and that this adjunction becomes monoidal. This construction provides a unifying framework for the description of several examples of skew monoidal categories. We also demonstrate how braidings on the original monoidal category of a given action induce braidings on the resulting skew monoidal structure on the …