Tootfinder

Coderived and contraderived categories for a cotorsion pair, flat-type cotorsion pairs, and relative periodicity
Leonid Positselski
https://arxiv.org/abs/2509.07645 https://

Coderived and contraderived categories for a cotorsion pair, flat-type cotorsion pairs, and relative periodicity
Given a hereditary complete cotorsion pair $(\mathsf A,\mathsf B)$ generated by a set of objects in a Grothendieck category $\mathsf K$, we construct a natural equivalence between the Becker coderived category of the left-hand class $\mathsf A$ and the Becker contraderived category of the right-hand class $\mathsf B$. We show that a nested pair of cotorsion pairs $(\mathsf A_1,\mathsf B_1)\le(\mathsf A_2,\mathsf B_2)$ provides an adjunction between the related co/contraderived categories, which…

Sources: Paramount will stop airing five UK MTV channels at the end of 2025 but keep its flagship channel; some other non-US MTV channels are also set to close (Mark Savage/BBC)
https://www.bbc.com/news/articles/cdr612yz8p0o

MTV to axe its music TV channels in the UK
The broadcaster will stop showing music videos in December, but its main channel will remain on air.

Carajillo
The Mexican version of the carajillo cocktail combines strong coffee with Licor 43,
a buttery Spanish liqueur boasting 43 ingredients,
dominated by vanilla and citrus notes and a subtle hint of anise.
https://cooking.nytimes.com/recipes/102677…

Carajillo Recipe
Icy and bold, the Mexican version of the carajillo cocktail combines strong coffee with Licor 43, a buttery Spanish liqueur boasting 43 ingredients, dominated by vanilla and citrus notes and a subtle hint of anise. While many carajillo recipes combine equal parts strong coffee and rum or brandy, this Mexican interpretation has become a classic. Serve the cocktail after dinner to keep the evening going, or for a weekend brunch. If you’re avoiding caffeine, decaf coffee works just as well.

I do not think that Meta's Metaverse failed cause the devs weren't efficient enough. It's conceptually flawed and underbaked at best, without vision and direction. A toy Mark no longer cares too much about.
(And even getting 5% more efficiency out of LLMs is a stretch, studies show improvement of 1 or 2% at best - because you have to spend a lot of time to clean up the generated mess, especially if you are building frameworks and foundational technologies)

Meta Tells Workers Building Metaverse to Use AI to ‘Go 5x Faster’
Meta says that its coders should be working five times faster and that it expects "a 5x leap in productivity."

At the Man vs. Machine hackathon, co-hosted by AI nonprofit METR to test if AI helps people code faster and better, the top prize went to an "AI-supported" team (Kylie Robison/Wired)
https://www.wired.com/story/san-francisco-hackathon-man-vs-machine/

Inside the Man vs. Machine Hackathon
At a weekend hackathon in San Francisco, more than 100 coders gathered to test whether they could beat AI—and win a $12,500 cash prize.

Among college graduates ages 22-27, computer science and computer engineering majors face unemployment rates of 6.1% and 7.5%, respectively, over double the unemployment rate among recent biology and art history graduates, which is just 3%.
Goodbye, $165,000 Tech Jobs. Student Coders Seek Work at Chipotle
https://www.…

Computer Science Grads Struggle to Find Jobs in the A.I. Age
As companies like Amazon and Microsoft lay off workers and embrace A.I. coding tools, computer science graduates say they’re struggling to land tech jobs.

Cadres : Forfait jours et contrôle de la durée de travail. #Avocat
https://youtube.com/shorts/qbS1F7cDjFY?si=mcXgCT9k_yMUgqOv

On the exact region between Chatterjee's rank correlation and Spearman's footrule
Marcus Rockel
https://arxiv.org/abs/2509.07232 https://arxiv.org/…

On the exact region between Chatterjee's rank correlation and Spearman's footrule
Chatterjee's rank correlation \(ξ\) has emerged as a popular measure quantifying the strength of directed functional dependence between random variables $X$ and $Y$. If $X$ and $Y$ are continuous, $ξ$ equals Spearman's footrule~\(ψ\) for the Markov product of the copula induced by $(X,Y)$ and its transpose. We analyze the relationship between these two measures more in depth by studying the attainable region of possible pairs \((ξ, ψ)\) over all bivariate copulas. In particular, we show th…

Fixed Point Theorems for Kannan and Chatterjea-type Mappings in Probabilistic Cone Metric Spaces
Elvin Rada
https://arxiv.org/abs/2509.06962 https://arxiv.…

Fixed Point Theorems for Kannan and Chatterjea-type Mappings in Probabilistic Cone Metric Spaces
This paper establishes novel fixed point theorems for Kannan-type and Chatterjea-type mappings in probabilistic cone metric spaces. By integrating probabilistic distance functions with cone-valued structures, we generalize classical fixed point results to settings with inherent uncertainty. Our approach leverages the distributional properties of probabilistic metrics and the order structure of cones to develop contraction conditions ensuring the existence and uniqueness of fixed points. Applica…

Good people:
"At least 365 people have been arrested at a demonstration in London in support of proscribed group Palestine Action, police say.
"Scores of people simultaneously unveiled handwritten signs with the same message "I oppose genocide. I support Palestine Action" at the protest, organised by Defend Our Juries at Westminster's Parliament Square."
Palestine Action protesters arrested by police at London demo - BBC News

Palestine Action protesters arrested by police at London demo
Protesters simultaneously unveiled signs with the same message "I oppose genocide. I support Palestine Action" in Westminster's Parliament Square.