Tootfinder

Trump claims he and Xi Jinping approved a deal for TikTok's US operations; Chinese media's readout only says that China respects the wishes of businesses (Ben Berkowitz/Axios)
https://www.axios.com/2025/09/19/tiktok-trump-xi-deal-sale-terms

Trump suggests China approves TikTok deal, though app's fate still unclear
U.S. officials said earlier this week they had a framework deal with China on a sale.

Trump claims he and Xi Jinping approved a deal for TikTok's US operations; Chinese media's readout only says that China respects the wishes of businesses (Ben Berkowitz/Axios)
https://www.axios.com/2025/09/19/tiktok-trump-xi-deal-sale-terms

Trump suggests China approves TikTok deal, though app's fate still unclear
U.S. officials said earlier this week they had a framework deal with China on a sale.

Crikey, Facebook has removed the "disputes to be settled in courts of a jurisdiction that's not party to a regional human rights convention" and "we can change these terms without telling you" clauses from its terms of service. Is this, despite all the well-known enshittification of the content and the user-base, going to be the year I finally get a Facebook account?

WhatsApp updates its Business API terms to ban general-purpose chatbots starting January 15, 2026, affecting WhatsApp assistants of OpenAI, Perplexity, others (Ivan Mehta/TechCrunch)
https://techcrunch.com/2025/10/18/whatssapp-…

WhatssApp changes its terms to bar general purpose chatbots from its platform | TechCrunch
WhatsApp is banning general purpose chatbots from using its Business API

Trump doing Putin's work, absolutely horrifying, big respect for Zelensky, who stays "cool" , at least in public.
https://www.ft.com/content/7960c6aa-dbfa-4a55-91e8-ae44601842ec

Trump urged Zelenskyy to accept Putin’s terms or be ‘destroyed’ by Russia
US president tossed aside maps of Ukraine frontline in volatile White House meeting

Some nice examples in the 'use cases' section of AI for Humanists https://aiforhumanists.com/guides/usecases/ - from OCR to annotation to identifying voices and styles

Trump urged Zelenskyy to accept Putin's terms or be 'destroyed' by Russia (Financial Times)
https://www.ft.com/content/7960c6aa-dbfa-4a55-91e8-ae44601842ec
http://www.memeorandum.com/251019/p34#a251019p34

Wie zu erwarten war, geht #Arduino durch den Verkauf an #Qualcomm nun den Bach runter. Der neue Besitzer hat AGB und Datenschutz geändert. Die Arduino-Plattform ist somit wohl nicht mehr unter freier Lizenz. Auch erhält Qualcomm eine Nutzungsgenehmigung für alle hochgeladenen Materialien …

"PHP is the lingua franca of affordable web hosting options; or, in other terms, the Toyota Corolla of programming languages: boring, solid, easy, and affordable. You can find, almost anywhere in the world, an affordable web hosting with the saint quadrinity of LAMP: Linux, Apache, MySQL, and PHP; an OS, a web server, a database server, and a scripting language, in an inexpensive package, enabling the masses to go further. Paraphrasing George Clooney, what else?"

The Toyota Corolla Of Programming
In 1995, an otherwise unknown software developer released the first version of a new scripting language whose explicit aim was to make applications for this new platform called "The World Wide Web". After starting as a small project, and thanks to the crazy dot-com years, it grew dramatically to become one of the most widely used programming languages of all time. After some stumbling first steps, it eventually got some sort of standardization in 1997, even reluctantly including some OOP featur…

The right for companies to do this is in every web service Terms and Conditions you've ever ageed to.
https://www.theguardian.com/technology/2025/sep/20/parents-outraged-meta-uses-photos-schoolgirls-ads-man

Cowboys, Tyler Smith agree to terms on $96 million extension to become highest-paid guard in NFL https://www.nfl.com/news/cowboys-tyler-smith-agree-to-terms-on-96-million-extension

Raiders Week 7 inactives vs Chiefs: Will Jakobi Meyers play? https://raiderswire.usatoday.com/story/sports/nfl/raiders/2025/10/19/raiders-week-7-inactives-titans-wr-jakobi-meyers-status-update/86788352…

There's a trick for liberals who are still coming to terms with everything: from here on out, ask yourself "If this was a case in Putin's Russia, would I believe the evidence?"

So multinational companies will choose Europe or Asia for knowledge-intensive units with many nationalities, well played by Trump 😂
https://www.nytimes.com/2025/09/19/us/poli

Trump Says U.S. Will Institute $100,000 Fee for H-1B Visas
Administration officials said the charge would help American workers. President Trump also announced the terms of a new “gold card” program.

Distribution of integer points on determinant surfaces and a $\text{mod-}p$ analogue
Satadal Ganguly, Rachita Guria
https://arxiv.org/abs/2508.14793 https://

Distribution of integer points on determinant surfaces and a $\text{mod-}p$ analogue
We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form $xy-zw=r$, where $r$ is a non-zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables $x, y, z, w$ as well as of $r$. We also establish an asymptotic formula for counting integer solutions with smooth weights to the congruence $xy-zw \equiv 1 (\text{mod }p)$, where $p$ is a large prime, with a strong bound on the error term.

The fractal Goodstein principle
David Fern\'andez-Duque, Andreas Weiermann
https://arxiv.org/abs/2508.14768 https://arxiv.org/pdf/2508.14768

The fractal Goodstein principle
The original Goodstein process is based on writing numbers in hereditary $b$-exponential normal form: that is, each number $n$ is written in some base $b\geq 2$ as $n=b^ea+r$, with $e$ and $r$ iteratively being written in hereditary $b$-exponential normal form. We define a new process which generalises the original by writing expressions in terms of a hierarchy of bases $B$, instead of a single base $b$. In particular, the `digit' $a$ may itself be written with respect to a smaller base $b'$. W…

On Tackling High-Dimensional Nonconvex Stochastic Optimization via Stochastic First-Order Methods with Non-smooth Proximal Terms and Variance Reduction
Yue Xie, Jiawen Bi, Hongcheng Liu
https://arxiv.org/abs/2509.13992

On Tackling High-Dimensional Nonconvex Stochastic Optimization via Stochastic First-Order Methods with Non-smooth Proximal Terms and Variance Reduction
When the nonconvex problem is complicated by stochasticity, the sample complexity of stochastic first-order methods may depend linearly on the problem dimension, which is undesirable for large-scale problems. To alleviate this linear dependence, we adopt non-Euclidean settings and propose two choices of nonsmooth proximal terms when taking the stochastic gradient steps. This approach leads to stronger convergence metric, incremental computational overhead, and potentially dimension-insensitive …

First/last light, same day. Golden larches.
(From a hike on the last day of our recent roadtrip. The view in the second image is looking back at Hanauer Hütte, in front of Schneekarlespitze and (clipped) Dremelspitze)
#SilentSunday #LandscapePhotography

Global Anomalies in Sigma Models with Majorana--Weyl Fermions
Changha Choi
https://arxiv.org/abs/2508.14895 https://arxiv.org/pdf/2508.14895

Global Anomalies in Sigma Models with Majorana--Weyl Fermions
We investigate a global sigma model anomaly in two-dimensional sigma models with Majorana--Weyl fermions coupled to a sigma model field with target space~$G$. The anomaly originates from the nontrivial topology of the space of maps and manifests as a phase in the fermion path integral. Using the global anomaly formula expressed in terms of the reduced~$η$-invariant, we demonstrate that this anomaly modifies the standard quantization condition of the Wess--Zumino term on~$G$, in close analogy w…

Characterization of deterministically recognizable weighted tree languages over commutative semifields by finitely generated and cancellative scalar algebras
Zolt\'an F\"ul\"op, Heiko Vogler
https://arxiv.org/abs/2509.14914

Characterization of deterministically recognizable weighted tree languages over commutative semifields by finitely generated and cancellative scalar algebras
Due to the works of S. Bozapalidis and A. Alexandrakis, there is a well-known characterization of recognizable weighted tree languages over fields in terms of finite-dimensionality of syntactic vector spaces. Here we prove a characterization of bottom-up deterministically recognizable weighted tree languages over commutative semifields in terms of the requirement that the respective m-syntactic scalar algebras are finitely generated. The concept of scalar algebra is introduced in this paper; it…

Crypto exchange Kraken says it confidentially filed for a US IPO, without revealing any terms; Kraken said it raised $200M at a $20B valuation on November 18 (Arasu Kannagi Basil/Reuters)
https://www.reuters.com/business/crypto-exchange-kraken-…

Tyler Smith, Cowboys agree to terms on massive contract extension https://www.dallascowboys.com/news/tyler-smith-cowboys-agree-to-terms-on-massive-contract-extension

Apparent horizon and causal structure of spacetime singularities
Koushiki, Pankaj S. Joshi
https://arxiv.org/abs/2508.14663 https://arxiv.org/pdf/2508.1466…

Apparent horizon and causal structure of spacetime singularities
A major issue in general relativity and blackhole physics today is to determine the conditions when the spacetime singularities forming as end-states of gravitational collapse are visible to external observers, and when these are hidden within the event horizon of a black-hole. We show here that such a causal structure of singularity, in terms of its visibility or otherwise, is determined by the dynamics of the apparent horizon and trapped surfaces forming during collapse of massive matter clou…

Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms
Elijah Pelofske, Marek Rams, Andreas B\"artschi, Piotr Czarnik, Paolo Braccia, Lukasz Cincio, Stephan Eidenbenz
https://arxiv.org/abs/2509.13528

Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms
The emergent practical applicability of the Quantum Approximate Optimization Algorithm (QAOA) for approximate combinatorial optimization is a subject of considerable interest. One of the primary limitations of QAOA is the task of finding a set of good parameters. Parameter transfer is a phenomenon where QAOA angles trained on problem instances that are self-similar tend to perform well for other problem instances from that similar class. This suggests a potentially highly efficient and scalable…

Transforming Next-generation Network Planning assisted by Data Acquisition of Top Three Spanish MNOs
M. Umar Khan
https://arxiv.org/abs/2508.14445 https://…

Transforming Next-generation Network Planning assisted by Data Acquisition of Top Three Spanish MNOs
In this paper, we address the necessity of data related to mobile traffic of the legacy infrastructure to extract useful information and perform network dimensioning for 5G. These data can help us achieve a more efficient network planning design, especially in terms of topology and cost. To that end, a real open database of top three Spanish mobile network operators (MNOs) is used to estimate the traffic and to identify the area of highest user density for the deployment of new services. We pro…

Defining a classification system for augmentation technology in socio-technical terms
Isabel Pedersen, Ann Hill Duin
https://arxiv.org/abs/2509.13340 https://

Defining a classification system for augmentation technology in socio-technical terms
This short paper provides a means to classify augmentation technologies to reconceptualize them as sociotechnical, discursive and rhetorical phenomena, rather than only through technological classifications. It identifies a set of value systems that constitute augmentation technologies within discourses, namely, the intent to enhance, automate, and build efficiency. This short paper makes a contribution to digital literacy surrounding augmentation technology emergence, as well as the more speci…

Critical trajectories in kinetic geometry
Helge Dietert, Cl\'ement Mouhot, Lukas Niebel, Rico Zacher
https://arxiv.org/abs/2508.14868 https://arxiv.org…

Critical trajectories in kinetic geometry
We construct critical trajectories in kinetic geometry, i.e. curves in $\mathbb{R}^{1+2n}$ that are: tangential to the vector fields $\partial_t+v\cdot \nabla_x$ and $\nabla_v$, connecting any two given points, respecting the underlying kinetic scaling, and with the property, that the singularity of the $v$-tangent vector near the starting point equates the degeneracy of the dependency of the curve velocity in terms of the endpoint velocity. The construction is based on Newton's laws of motio…

Bosses are still mandating RTO: workers are going but on their own terms
https://www.cnbc.com/2025/10/06/bosses-are-still-mandating-rto-workers-are-going-but-on-their-own-terms.html

Deep BSDE Solver on Bounded Domains Part I: General Loss Rate
Maximilian W\"urschmidt (Trier University)
https://arxiv.org/abs/2508.14215 https://arxi…

Deep BSDE Solver on Bounded Domains Part I: General Loss Rate
We consider a ramification of the deep BSDE loss functional designed to apply for BSDEs on bounded domains, i.e. with random (unbounded) time horizons. We derive a general convergence rate of the loss functional; precisely for a class of (randomly) weighted modifications of the functional. The rate is expressed in terms of the underlying discrete-time stepsize and a universal approximation distance.

On definability of C*-tensor norms
Isaac Goldbring, Thomas Sinclair
https://arxiv.org/abs/2509.15086 https://arxiv.org/pdf/2509.15086

On definability of C*-tensor norms
We initiate the study of definability (in the model-theoretic sense) of C*-tensor norms. We show that neither the minimal nor maximal tensor norms are definable uniformly over all C*-algebras. The proof in the case of the minimal tensor product norm uses a deep theorem of Kirchberg characterizing exactness in terms of tensor products with matrix ultraproducts while the case of maximal tensor products uses Pisier's recent characterization of the lifting property in terms of maximal tensor produc…

Interesting, battery integrated into a heat pump system, so that energy can be stored and shifted when needed. An integrated system instead of two separate ones may also offer advantages in terms of efficiency.
https://www.corporate.carrier.com/news/new

Carrier Powering the Future of Energy

A characterization of locally ordered ternary relations in terms of digraphs
Guillermo Gamboa Quintero, Mart\'in Matamala, Juan Pablo Pe\~na
https://arxiv.org/abs/2509.11956

A characterization of locally ordered ternary relations in terms of digraphs
In 1917, Huntington and Kline, followed by Huntington in 1924, studied systems of axioms for ternary relations aiming to capture the concepts of linear order (called betwenness) and cycle order, respectively. Among many other properties, they proved there are several independent set of axioms defining either linear order or cycle order. In this work, we consider systems arising from the four common axioms of linear order and cycle order, together with a new axiom F, stating that if a tuple abc …

Numerical analysis of fluid estimation for source terms in neutral particles simulation
Zhirui Tang, Emil L{\o}vbak, Julian Koellermeier, Giovanni Samaey
https://arxiv.org/abs/2509.11883

Numerical analysis of fluid estimation for source terms in neutral particles simulation
In plasma edge simulations, kinetic Monte Carlo (MC) is often used to simulate neutral particles and estimate source terms. For large-sized reactors, like ITER and DEMO, high particle collision rates lead to a substantial computational cost for such schemes. To address this challenge, an asymptotic-preserving kinetic-diffusion Monte Carlo (KDMC) simulation method and a corresponding fluid estimation technique have been proposed in the literature. In this work, we perform numerical analysis on t…

Glossary of Technical and Green Terms - Understand key words, abbreviations and other terms used on Earth Notes. #tech #glossary #energy -

Glossary of Technical and Green Terms
Understand key words, abbreviations and other terms used on Earth Notes. #tech #glossary #energy

The Internet Archive and UMG (the music biz organization that was suing over IA making the 78s available to the world) have settled their litigation.
Terms not disclosed: https://cdn.arstechnica.net/wp-content/up…

Raiders Week 7 snap counts vs Chiefs: Wrong kind of history made https://raiderswire.usatoday.com/story/sports/nfl/raiders/2025/10/20/raiders-week-7-snap-counts-vs-chiefs-wrong-kind-of-history-made/86…

Bounds on bending in terms of the Schwartzian derivative and Teichm\"uller distance
Martin Bridgeman, Ming Hong Tee
https://arxiv.org/abs/2509.12493 https://

Bounds on bending in terms of the Schwartzian derivative and Teichmüller distance
Locally-univalent maps $f: Δ\rightarrow \hat{\mathbb{C}}$ can be parametrized by their Schwartzian derivatives $Sf$, a quadratic differential whose norm $\|Sf\|_\infty$ measures how close $f$ is to being Möbius. In particular, by Nehari, if $\|Sf\|_\infty < 1/2$ then $f$ is univalent and if $f$ is univalent then $\|Sf\|_\infty < 3/2$. Thurston gave another parametrization associating to $f$ a bending measured lamination $β_f$ which has a natural norm $\|β_…

RAG-Boost: Retrieval-Augmented Generation Enhanced LLM-based Speech Recognition
Pengcheng Wang, Sheng Li, Takahiro Shinozaki
https://arxiv.org/abs/2508.14048 https://

RAG-Boost: Retrieval-Augmented Generation Enhanced LLM-based Speech Recognition
In this paper, we propose RAG-Boost (ST-ShinozakiLab Task I system), which enhances the baseline LLM-based ASR system of the MLC-SLM Challenge (task I) with a retrieval-augmented generation (RAG) module on the fly. Each partial ASR hypothesis queries a vector store of audio-text pairs and domain terms, and the retrieved results are fused with the live ASR hypotheses to fix recognition errors. The fused hypotheses are passed to the LLM, yielding improved responses.

On the Yau-Tian-Donaldson conjecture for weighted cscK metrics
S\'ebastien Boucksom, Mattias Jonsson
https://arxiv.org/abs/2509.15016 https://arxiv.org…

On the Yau-Tian-Donaldson conjecture for weighted cscK metrics
We establish a version, formulated in terms of non-Archimedean pluripotential theory, of the Yau-Tian-Donaldson conjecture for constant scalar curvature and, more generally, weighted extremal Kähler metrics with prescribed compact symmetry group on an arbitrary polarized projective manifold. This is accomplished by extending important previous work of Chi Li to the weighted case, and by establishing general slope formulas for the relevant weighted entropy and energy functionals. Among other th…

Our mortgage renewal was quite simple this time. I have been working with the mortgage broker for a couple of years and is quite good and friendly.
Online call, go over the documents and terms. Electronic signature and download of the paperwork. From start to finish maybe 30 minutes.
Being paranoid I made a physical print of the pages.

Formation of protostars and the launching of stellar core outflows with moving-mesh radiation non-ideal magnetohydrodynamics
Alexander C. Mayer, R\"udiger Pakmor, Thorsten Naab, Oliver Zier, Alexei V. Ivlev, Tommaso Grassi, Paola Caselli, Volker Springel
https://arxiv.org/abs/2510.12620

Formation of protostars and the launching of stellar core outflows with moving-mesh radiation non-ideal magnetohydrodynamics
We present an implementation of radiative transfer with flux-limited diffusion (FLD) for the moving-mesh code {\small AREPO} and use the method in a physical model for the formation of protostars with non-ideal radiation-magnetohydrodynamics (RMHD). We follow previous work in splitting the additional terms to the hydrodynamical equations arising from the inclusion of radiation into terms to be integrated explicitly and implicitly, as the diffusion and coupling terms would impose very restrictiv…

A class of flexible and efficient partitioned Runge-Kutta-Chebyshev methods for some time-dependent partial differential equations
Xiao Tang, Junwei Huang
https://arxiv.org/abs/2509.14847

A class of flexible and efficient partitioned Runge-Kutta-Chebyshev methods for some time-dependent partial differential equations
Many time-dependent partial differential equations (PDEs) can be transformed into an ordinary differential equations (ODEs) containing moderately stiff and non-stiff terms after spatial semi-discretization. In the present paper, we construct a new class of second-order partitioned explicit stabilized methods for the above ODEs. We treat the moderately stiff term with an s-stage Runge-Kutta-Chebyshev (RKC) method and treat the non-stiff term with a 4m-stage explicit Runge-Kutta (RK) method. Diff…

Componentwise linearity of powers of edge ideals of weighted oriented graphs
Manohar Kumar, Joydip Mondal, Ramakrishna Nanduri
https://arxiv.org/abs/2509.14637 https://

Componentwise linearity of powers of edge ideals of weighted oriented graphs
In this paper, we study the componentwise linearity of powers of edge ideal of a weighted oriented graph $D$. We give a characterization for componentwise linearity of the edge ideal $I(D)$ in terms of forbidden subgraphs of $D$. If $D$ is house-free or complete $r$-partite, then the following statements are equivalent: (1) $I(D)$ is componentwise linear; (2) $I(D)$ is vertex splittable; (3) $I(D)$ has linear quotient property; (4) both $G$ and $H(I(D)_{(2)})$ are co-chordal and $D_1,D_2,D_3,D…

Decoding the string in terms of holographic quantum maps
Avik Chakraborty, Tanay Kibe, Mart\'in Molina, Ayan Mukhopadhyay, Hardik Vamshi
https://arxiv.org/abs/2509.13404 htt…

Decoding the string in terms of holographic quantum maps
It has recently been shown that the Nambu-Goto equation for a string emerges from the junction conditions in three-dimensional gravity. Holographically, gravitational junctions are dual to interfaces in conformal field theory. We demonstrate that each stringy mode of the junction corresponds to a universal $\mathcal{H}_{in}\rightarrow \mathcal{H}_{out}$ quantum map between in and out Hilbert spaces of excitations scattered at the interface, and also a universal $\mathcal{H}_{L}\rightarrow \math…

ASPI 12.11.2025
Resilient critical infrastructure is its own deterrence
"The ability to absorb disruption and keep operating isn’t just a technical virtue; it’s a signal. If an adversary believes that disruption will be temporary and costly to sustain, the incentive to strike is reduced."
ht…

On the equivalence and optimality of transformations of diffusive systems
Davide Gabrielli, Giovanni Jona-Lasinio
https://arxiv.org/abs/2509.14450 https://…

On the equivalence and optimality of transformations of diffusive systems
In this paper we introduce, inspired by Clausius and developing the ideas of \cite{pre}, the concept of equivalence of transformations in non equilibrium theory of diffusive systems within the framework of macroscopic fluctuation theory. Besides providing a new proof of a formula derived in \cite{mft,qc}, which is the basis of the equivalence, we show that equivalent quasistatic transformations can be distinguished in finite terms, by the renormalized work introduced in \cite{45,46,mft,qc}. Thi…

Cohen-Macaulay Type via Lattice Homology and the Motivic Poincar\'e Series
Alex Hof, Andr\'as N\'emethi
https://arxiv.org/abs/2509.11858 https://

Cohen-Macaulay Type via Lattice Homology and the Motivic Poincaré Series
We give results on reduced complex-analytic curve germs which relate their indecomposable maximal Cohen-Macaulay (MCM) modules to their lattice homology groups and related invariants, thereby providing a connection between the algebraic theory of MCM modules and techniques arising from low-dimensional topology. In particular, we characterize the germs $(C, o)$ of finite Cohen-Macaulay type in terms of the lattice homology $\mathbb{H}_*(C, o)$, and those of tame type in terms of the lattice homo…

"simple" in terms of superficial appearance. There's some bloody good cinematography on show here. #TOTP

Love the ambiguous acronyms *within a domain*:
- FIT may mean Firmware Interface Table or Flash Image Tool
- FPT may mean Flash Partition Table or Flash Programming Tool
Edit: All of those are terms from the wonderful world of Intel firmware.

"Labour has also won every time the Senedd has been contested, as it will be again in May. Yet, if the most recent Wales-wide poll holds good, that is set to change. Plaid will instead be the largest party, just ahead of Reform UK, with Labour third. Though still a minority, Plaid would be in government. In Welsh terms, that would be a political earthquake. Perhaps in Britain-wide terms too"
#UKPol

Robust Concept Erasure in Diffusion Models: A Theoretical Perspective on Security and Robustness
Zixuan Fu, Yan Ren, Finn Carter, Chenyue Wen, Le Ku, Daheng Yu, Emily Davis, Bo Zhang
https://arxiv.org/abs/2509.12024

Robust Concept Erasure in Diffusion Models: A Theoretical Perspective on Security and Robustness
Diffusion models have achieved unprecedented success in image generation but pose increasing risks in terms of privacy, fairness, and security. A growing demand exists to \emph{erase} sensitive or harmful concepts (e.g., NSFW content, private individuals, artistic styles) from these models while preserving their overall generative capabilities. We introduce \textbf{SCORE} (Secure and Concept-Oriented Robust Erasure), a novel framework for robust concept removal in diffusion models. SCORE formul…

Consistent causal discovery with equal error variances: a least-squares perspective
Anamitra Chaudhuri, Yang Ni, Anirban Bhattacharya
https://arxiv.org/abs/2509.15197 https://…

Consistent causal discovery with equal error variances: a least-squares perspective
We consider the problem of recovering the true causal structure among a set of variables, generated by a linear acyclic structural equation model (SEM) with the error terms being independent and having equal variances. It is well-known that the true underlying directed acyclic graph (DAG) encoding the causal structure is uniquely identifiable under this assumption. In this work, we establish that the sum of minimum expected squared errors for every variable, while predicted by the best linear c…

Crosslisted article(s) found for cond-mat.str-el. https://arxiv.org/list/cond-mat.str-el/new
[1/1]:
- Decoding the string in terms of holographic quantum maps
Avik Chakraborty, Tanay Kibe, Mart\'in Molina, Ayan Mukhopadhyay, Hardik Vamshi

Equiangular tight frames in real symplectic space: Zauner's conjecture and the skew Hadamard conjecture
Kean Fallon
https://arxiv.org/abs/2509.14463 https://

Equiangular tight frames in real symplectic space: Zauner's conjecture and the skew Hadamard conjecture
We introduce the notion of equiangular tight frames in real symplectic spaces and formulate a conjecture on their existence in terms of the dimension and number of vectors. Our main results shows the "symplectic Zauner's conjecture" is equivalent to the skew Hadamard conjecture. The proof involves counting subgraphs called "diamonds" in tournaments.

Good Morning #Canada
On this day in 1948, the longest serving political leader in the British Commonwealth retired. William Lyon Mackenzie King served 21 years and 154 days as Prime Minister of Canada, in non-consecutive terms, from 1921–1926, 1926–1930, and 1935–1948. He led Canada through the Great Depression, introduced Old Age Pensions, nationalized the Bank of Canada, passed the 1938 National Housing Act to improve housing affordability, established the Canadian Broadcasting Corporation, Trans-Canada Air Lines, and the National Film Board, and implemented Unemployment Insurance. His government was also responsible for Japanese Internment Camps, and he believed strongly in the occult.
This video from TVO is an excellent overview of King's career. It's probably a two coffee viewing this morning if you have the time, but IMO worth the investment.
#CanadaIsAwesome #CanadianHeroes
https://www.tvo.org/video/mackenzie-king-at-150

Transparent and Fair Profiling in Employment Services: Evidence from Switzerland
Tim R\"az
https://arxiv.org/abs/2509.11847 https://arxiv.org/pdf/2509…

Transparent and Fair Profiling in Employment Services: Evidence from Switzerland
Long-term unemployment (LTU) is a challenge for both jobseekers and public employment services. Statistical profiling tools are increasingly used to predict LTU risk. Some profiling tools are opaque, black-box machine learning models, which raise issues of transparency and fairness. This paper investigates whether interpretable models could serve as an alternative, using administrative data from Switzerland. Traditional statistical, interpretable, and black-box models are compared in terms of p…

https://petition.parliament.uk/petitions/727356
>Keep 5-year ILR terms to Hong Kong British National (Overseas) visas
Debate: https://www.

Cryptanalysis and design for a family of plaintext non-delayed chaotic ciphers
Qianxue Wang, Simin Yu
https://arxiv.org/abs/2509.11158 https://arxiv.org/pd…

Cryptanalysis and design for a family of plaintext non-delayed chaotic ciphers
Plaintext non-delayed chaotic cipher (PNDCC) means that in the diffusion equation, plaintext has no delay terms while ciphertext has a feedback term. In existing literature, chaotic cipher diffusions invariably take this form. Since its introduction, PNDCC has attracted attention but also doubts. Designers of chaotic ciphers usually claim PNDCC security by statistical tests, while rigorous cryptographic proofs are absent. Thus, it is necessary to re-examine its design rationale and empirical se…

Integrated subtraction terms and finite remainders for arbitrary processes with massless partons at colliders in the nested soft-collinear subtraction scheme
Federica Devoto, Kirill Melnikov, Raoul R\"ontsch, Chiara Signorile-Signorile, Davide Maria Tagliabue, Matteo Tresoldi
https://arxiv.org/abs/2509.08594

Integrated subtraction terms and finite remainders for arbitrary processes with massless partons at colliders in the nested soft-collinear subtraction scheme
We present integrated subtraction terms and finite remainders for arbitrary processes with massless partons at hadron and lepton colliders in the context of the nested soft-collinear subtraction scheme. These results provide the very last ingredients needed to make this scheme a fully local, analytic and process-independent framework for treating infrared singularities at next-to-next-to-leading order in perturbative QCD. The explicit infrared finiteness of all required contributions, as well a…

The effect of matter discreteness on gravitational wave propagation in post-geometrical optics
Sena Atli, Syksy Rasanen
https://arxiv.org/abs/2509.13884 https://

The effect of matter discreteness on gravitational wave propagation in post-geometrical optics
The gravitational wave equation of motion includes direct coupling to the Riemann tensor. The curvature terms are usually neglected, but they can be large at the location of matter particles and impact the angular diameter distance. We apply the recently introduced post-geometrical optics approximation that includes curvature to gravitational wave propagation. Assuming that particles are localised within their Compton wavelength, the curvature due to electrons leads to a large effect on the ang…

Multi-block exceptional points in open quantum systems
Aysel Shiralieva, Grigory A. Starkov, Bj\"orn Trauzettel
https://arxiv.org/abs/2509.11856 https://

Multi-block exceptional points in open quantum systems
Open quantum systems can be approximately described by non-Hermitian Hamiltonians (NHHs) and Lindbladians. The two approaches differ by quantum jump terms corresponding to a measurement of the system by its environment. We analyze the emergence of exceptional points (EPs) in NHHs and Lindbladians. In particular, we show how EPs in NHHs relate to a novel type of EPs -- multi-block EPs -- in the non-Hermitian Liouvillian, i.e. the Lindbladian in absence of quantum jump terms. We further analyze h…

A New Benchmark for Evaluating Code Translation with Third-Party Libraries
Pengyu Xue, Kunwu Zheng, Zhen Yang, Yifei Pei, Linhao Wu, Jiahui Dong, Xiapu Luo, Yan Xiao, Fei Liu, Yuxuan Zhang, Xiran Lyu, Xianhang Li, Xuanyu Zhu, Chengyi Wang
https://arxiv.org/abs/2509.12087

A New Benchmark for Evaluating Code Translation with Third-Party Libraries
In recent years, Large Language Models (LLMs) have been widely studied in the code translation field on the method, class, and even repository levels. However, most of these benchmarks are limited in terms of Third-Party Library (TPL) categories and scales, making TPL-related errors hard to expose and hindering the development of targeted solutions. Considering the high dependence (over 90%) on TPLs in practical programming, demystifying and analyzing LLMs' code translation performance involvin…

"How to Get a North Korea / Antarctica VPS (New Concept: Light Up the Globe)"
It's actually just putting fake information into WHOIS databases (which is a breach of their terms of service) and then sending "corrections" to geo-ip providers.
While I do think geo-ip as a concept is flawed, all this will achieve is forcing a switch to geo-ip providers that do more verification e.g. ping time sanity. They already exist and are common in streaming media.
…

On equivariant vector bundles on the Fargues--Fontaine curve over a finite extension
Rustam Steingart
https://arxiv.org/abs/2510.12533 https://arxiv.org/pd…

On equivariant vector bundles on the Fargues--Fontaine curve over a finite extension
Let $K/E/\mathbb{Q}_p$ be a tower of finite extensions with $E$ Galois. We relate the category of $G_K$-equivariant vector bundles on the Fargues--Fontaine curve with coefficients in $E$ with $E$-$G_K$-$B$-pairs and describe crystalline and de Rham objects in explicit terms. When $E$ is a proper extension, we give a new description of the category in terms of compatible tuples of $\mathbf{B}_e$-modules, which allows us to compute Galois cohomology in terms of an explicit Čech complex which can…

A US district judge rules Amazon violated consumer law by collecting Prime subscribers' billing info before disclosing terms, handing the FTC a partial win (Reuters)
https://www.reuters.com/sustainability/us-ftc-wins-key…

Multi-Objective Loss Balancing in Physics-Informed Neural Networks for Fluid Flow Applications
Afrah Farea, Saiful Khan, Mustafa Serdar Celebi
https://arxiv.org/abs/2509.14437 h…

Multi-Objective Loss Balancing in Physics-Informed Neural Networks for Fluid Flow Applications
Physics-Informed Neural Networks (PINNs) have emerged as a promising machine learning approach for solving partial differential equations (PDEs). However, PINNs face significant challenges in balancing multi-objective losses, as multiple competing loss terms such as physics residuals, boundary conditions, and initial conditions must be appropriately weighted. While various loss balancing schemes have been proposed, they have been implemented within neural network architectures with fixed activa…

Putin will not dictate terms of Ukraine peace, Canada's Carney cautions
https://kyivindependent.com/putin-will-not-dictate-terms-of-ukraine-peace-canadas-carney-cautions/

The Serre depth of Stanley--Reisner Rings and the depth of their symbolic powers
Yuji Muta, Naoki Terai
https://arxiv.org/abs/2509.14838 https://arxiv.org/…

The Serre depth of Stanley--Reisner Rings and the depth of their symbolic powers
We investigate an invariant, called the Serre depth, from the perspective of combinatorial commutative algebra. In this paper, we establish several properties of an analogue of the depth of Stanley--Reisner rings. In particular, we relate the Serre depth both to the minimal free resolution of a Stanley--Reisner ring and to that of its Alexander dual. Also, we establish an analogue of a known result that describes the depth of Stanley--Reisner rings in terms of skeletons. Moreover, we study the …

Luepke, Cowboys agree to terms on contract extension https://www.dallascowboys.com/news/luepke-cowboys-agree-to-terms-on-contract-extension

Generalizations of the Crossing Lemma
Geza Toth
https://arxiv.org/abs/2509.14074 https://arxiv.org/pdf/2509.14074…

Generalizations of the Crossing Lemma
The crossing number of a graph is the minimum number of crossings over all of its drawings on the plane. The Crossing Lemma, proved more than 40 years ago, is a tight lower bound on the crossing number of a graph in terms of the number of vertices and edges. It is definitely the most important inequality on crossing numbers. We review some generalizations and applications of the Crossing Lemma.

Court filings: Tesla has settled two lawsuits over deaths in two separate California crashes in 2019 involving Autopilot; the terms were not disclosed (Reuters)
https://www.reuters.com/business/autos-tra

Dissipation in Open Holography
Andreas Karch, Merna Youssef
https://arxiv.org/abs/2509.14312 https://arxiv.org/pdf/2509.14312

Dissipation in Open Holography
We exploit the holographic realization of a conformal theory coupled to an external bath realized via a double trace deformation and its gravity dual in terms of transparent boundary conditions in order to map out some basic dissipative properties of this simple open holographic system. In particular, we determine the energy transmission coefficient across the boundary, discover a novel duality relating weak and strong coupling to the external bath, and quantify the dissipation in the system by…

Sources: the MLS-Apple TV deal will end in 2029, three and a half years earlier than planned; compensation averages $250M for the three remaining full seasons (Sportico)
https://www.sportico.com/leagues/soccer/2025/apple-mls-streaming-contract-cha…

Apple TV MLS Streaming Deal Will End in 2029 Under Revised Terms
MLS and Apple's streaming rights agreement will now end three and half years early, letting the league explore new partners after the 2026 World Cup.

Actually, I do want to come back to masculinity under patriarchy and whiteness under white supremacy because I think it's worth talking more about. The "man" under patriarchy (at least "Western" patriarchy) is represented as power and independence. The man needs nothing and thus owes nothing to anyone. The man controls and is not controlled, which is intimately related to independence as dependence can make someone vulnerable to control. The image of "man" projects power and invulnerability. At the same time "man" is a bumbling fool who can't be held accountable for his inability to control his sexual urges. He must be fed and cared for, as though another child. His worst behaviors must be dismissed with phrases such as "boys will be boys" and "locker room talk." The absurdity of the concept of human "independence" is impossible to understate.
Even if you go all Ted Kaczynski, you have still been raised and taught. This is, perhaps, why it is so much more useful to think in terms of obligations than rights. Rights can be claimed and protected with violence alone, but obligations reveal the true interdependence that sustains us. A "man" may assert his rights. Yet, on some level, we all know that the "man" of patriarchy acts as a child who is not mature enough to recognize his obligations.
White violence and white fragility reflect the same dichotomy. "The master race" somehow always needs brown folks to make all their shit and do all the reproductive labor for them. For those who fully embrace whiteness, the "safe space" is a joke. DEI shows weakness. Yet, when presented with an honest history adults become children who are incapable of differentiating between criticism and simple facts. *They* become the ones who must be kept safe. The expectation to be responsible for one's own words and actions, one of the very core definitions of being an adult, is far too much to expect. Their guilt needs room, needs tending, needs caring. White people cannot simply "grow the fuck up" or, as they may say of slavery, "fucking get over it."
And again, interestingly, it is *rights* that they reference: "Mah Freeze PEACH!" I find it hard to distinguish between such and my own child's assertion that anything she doesn't like is "not fair!" No, these assertions fail to recognize the fundamental fabric of adult society: the obligations we hold to each other.
At the intersection of all privilege is the sovereign, the ultimate god-man-baby. Again, referencing the essay (https://hexmhell.writeas.com/observations-on-domination-and-trump)
> This is where it becomes important to consider the ideology behind the sovereign ritual. Participation within the sovereign ritual denotes to the participants elements of the sovereign. That is, all agents of the sovereign are, essentially, micro dictators. By carrying out the will of the sovereign, these micro dictators can, by extension, act outside of the law.
While law enforcement is the ultimate representative of sovereign violence, privileges allow a gradated approximation of the sovereign. Those who are "closer" in privilege to the sovereign may, for example, be permitted to carry out violence against those who are father away. The gradation of privilege turns the whole society, except for the least privileged, into a cult that protects the privilege system on behalf of the most privileged. (And immediately Malcolm X pops to mind as having already talked about part of this relationship in 1963 https://www.youtube.com/watch?v=jf7rsCAfQCo.)

How to simulate magic state cultivation with around $8$ Clifford terms on average
Kwok Ho Wan, Zhenghao Zhong
https://arxiv.org/abs/2509.08658 https://arxi…

How to simulate magic state cultivation with around $8$ Clifford terms on average
Building upon [arXiv:2509.01224], we present a sketch on how to simulate the non-Clifford $d=5$ magic state cultivation circuits [arXiv:2409.17595] with a sum of $\approx 8$ Clifford ZX-diagrams on average, at $0.1\%$ noise. Compared to a magic cat state stabiliser decomposition of all $53$ non-Clifford spiders ($6{,}377{,}292$ terms required), this is more than $7 \times 10^{5}$ times reduction in the number of terms. Our stabiliser decomposition has the advantage of representing the final non…

Diagrammatic bosonisation, aspects of criticality, and the Hohenberg-Mermin-Wagner Theorem in parquet approaches
Aiman Al-Eryani
https://arxiv.org/abs/2509.15094 https://…

Diagrammatic bosonisation, aspects of criticality, and the Hohenberg-Mermin-Wagner Theorem in parquet approaches
The parquet equations present a cornerstone of some of the most important diagrammatic many-body approximations and methods currently on the market for strongly correlated materials: from non-local extensions of the dynamical mean-field theory to the functional renormalization group. The recently introduced single-boson exchange decomposition of the vertex presents an alternative set of equivalent equations in terms of screened interactions, Hedin vertices, and rest functions. This formulation …

Liouville results for $(p,q)$-Laplacian elliptic equations with source terms involving gradient nonlinearities
Mousomi Bhakta, Anup Biswas, Roberta Filippucci
https://arxiv.org/abs/2510.12486

Liouville results for $(p,q)$-Laplacian elliptic equations with source terms involving gradient nonlinearities
In this paper, we present a series of Liouville-type theorems for a class of nonhomogeneous quasilinear elliptic equations featuring reactions that depend on the solution and its gradient. Specifically, we investigate equations of the form $-Δ_p u - Δ_q u = f(u,\nabla u)$ with $p > q > 1$, where the nonlinearity $f$ takes forms such as $u^s|\nabla u|^m$ or $u^s + M|\nabla u|^m$ ($s, m\geq 0$). Our approach is twofold. For cases where the reaction term satisfies $|f(u,…

Crosslisted article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- Bounds on bending in terms of the Schwartzian derivative and Teichm\"uller distance
Martin Bridgeman, Ming Hong Tee

Nonlinear evolution of the spin-2 black hole superradiant instability
Taillte May, William E. East
https://arxiv.org/abs/2509.13488 https://arxiv.org/pdf/2…

Nonlinear evolution of the spin-2 black hole superradiant instability
Massive spin-2 fields, which arise in proposed extensions of the standard model of particle physics and general relativity, give rise to a superradiant instability around spinning black holes. We study the nonlinear evolution of this instability in quadratic gravity, where quadratic curvature terms are added to the Einstein-Hilbert action. We find that as the massive spin-2 field grows, the black hole's spin increases, accelerating the growth rate, and eventually leading to a superextremal hori…

Gluon generalized transverse momentum dependent parton distributions and Wigner functions of the Proton
Dipankar Chakrabarti, Bheemsehan Gurjar, Asmita Mukherjee, Kauship Saha
https://arxiv.org/abs/2509.14208

Gluon generalized transverse momentum dependent parton distributions and Wigner functions of the Proton
We present a calculation of the leading-twist (twist-2) generalized transverse momentum distributions (GTMDs) for unpolarized and longitudinally polarized gluons in the proton, using a recently developed light-front gluon spectator model inspired by the soft-wall AdS/QCD prediction. We calculate the gluon GTMDs for non-zero skewness, using overlaps in terms of light-front wave functions. We also compute the gluon Wigner distributions for various polarization configurations of the proton target,…

Some remarks on invariants
Martin Cederwall, Jessica Hutomo, Sergei M. Kuzenko, Kurt Lechner, Dmitri P. Sorokin
https://arxiv.org/abs/2509.14350 https://ar…

Some remarks on invariants
The demand to know the structure of functionally independent invariants of tensor fields arises in many problems of theoretical and mathematical physics, for instance for the construction of interacting higher-order tensor field actions. In mathematical terms the problem can be formulated as follows. Given a semi-simple finite-dimensional Lie algebra $\mathfrak g$ and a $\mathfrak g$-module $V$, one may ask about the structure of the sub-ring of $\mathfrak g$-invariants inside the ring freely g…

Lattice polytopes and semigroup algebras: Generic Lefschetz properties and Parseval-Rayleigh identities
Karim Alexander Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou
https://arxiv.org/abs/2509.14152

Lattice polytopes and semigroup algebras: Generic Lefschetz properties and Parseval-Rayleigh identities
We study semigroup algebras associated to lattice polytopes. We begin by generalizing and refining work of Hochster, and describe the volume maps of these algebras, that is, their fundamental classes, in terms of Parseval-Rayleigh identities and differential equations, which we prove to be equivalent. We use these descriptions to establish strong Lefschetz properties. A consequence is the resolution of several conjectures concerning unimodality properties of the h*-polynomial of lattice p…

Sums of Exponential Terms, Conserved Quantities, and the Real Wave Numbers
Terence R. Smith
https://arxiv.org/abs/2510.07803 https://arxiv.org/pdf/2510.078…

Sums of Exponential Terms, Conserved Quantities, and the Real Wave Numbers
There is consensus that sums $S_n={ {Σ}_{k=1}^n R_{0k} e^{i θ_k}}$ of complex exponential terms, despite their mathematical significance, only possess closed-form representations for specific values of n and special values of their parameters and that there are no generally-accepted recursive formulae for their computation. This note is focused on recursive formulae that: (1) provide closed-form analytic representations of $S_n$ for any finite n; (2) include generalizations of the usual formu…

Google and Disney's agreement gives YouTube TV users access to ESPN's full lineup of sports, including ESPN Unlimited, at no additional cost by the end of 2026 (Todd Spangler/Variety)
https://variety.com/2025/tv/news/youtube-tv-disney-bla…

YouTube TV and Disney Reach Deal Ending Two-Week Blackout of ESPN, ABC
ESPN, ABC and other Disney TV networks are coming back to YouTube TV, after the media conglomerate and Google reached a deal on pricing and terms for a renewed carriage deal.

Purification of quantum trajectories in infinite dimensions
Federico Girotti, Alessandro Vitale
https://arxiv.org/abs/2509.13377 https://arxiv.org/pdf/2509…

Purification of quantum trajectories in infinite dimensions
In this work we exhibit a class of examples that show that the characterization of purification of quantum trajectories in terms of 'dark' subspaces that was proved for finite dimensional systems fails to hold in infinite dimensional ones. Moreover, we prove that the new phenomenon emerging in our class of models and preventing purification to happen is the only new possibility that emerges in infinite dimensional systems. Our proof strategy points out that the emergence of new phenomena in inf…

Anthropic requires users to accept new terms by September 28, including choosing whether new chats and coding sessions can be used to train AI models (Anthropic)
https://www.anthropic.com/news/updates-to-our-consumer-terms

Updates to Consumer Terms and Privacy Policy
Anthropic is an AI safety and research company that's working to build reliable, interpretable, and steerable AI systems.

Towards a holographic description of closed universes
Hong Liu
https://arxiv.org/abs/2509.14327 https://arxiv.org/pdf/2509.14327

Towards a holographic description of closed universes
We study baby closed universes in AdS, focusing on the Antonini-Sasieta-Swingle (AS$^2$) cosmology, which arises in the gravitational description of partially entangled thermal states (PETS), as well as the classical example of Maldacena-Maoz (MM). We show that the algebraic formulation of AdS/CFT--and in particular the subregion-subalgebra duality--provides a natural framework for describing such universes within the standard AdS/CFT setting, phrased in terms of an operator algebra ${\cal M}$ …

Patrick Graham: '[The Chargers] have a great system in terms of how they run the ball' https://www.raiders.com/video/defense-patrick-graham-raiders-week-2-home-opener-presser-nfl-2025

Frozen-corner enumeration of Alternating Sign Matrices
Filippo Colomo, Andrei G. Pronko
https://arxiv.org/abs/2509.14006 https://arxiv.org/pdf/2509.14006…

Frozen-corner enumeration of Alternating Sign Matrices
An Alternating Sign Matrix (ASM) is a square matrix with entries in $\{0,1,-1\}$, and such that: $i)$ in each row and columns, nonzero entries alternate in sign; $ii)$ for any given row or column, entries sum up to 1. We define the frozen-square enumeration as the enumeration of $n\times n$ ASMs under the refinement of having, located in a corner, an $s\times s$ square of entries that are all zeroes. We state a conjectural formula for such enumeration, in terms of a Fredholm type determinant of…

Formalizing contextuality in sequential scenarios
Kim Vall\'ee, Damian Markham
https://arxiv.org/abs/2509.14125 https://arxiv.org/pdf/2509.14125…

Formalizing contextuality in sequential scenarios
This paper provides a framework for characterizing sequential scenarios, allowing for the identification of contextuality given empirical data, and then provides precise operational interpretations in terms of the possible hidden variable model explanations of that data. Sequential scenarios are different in essence from non-local scenarios as each measurement instrument is allowed to change the state as it enters subsequent measurement instruments. Thus, it is necessary to formulate the possib…

Mordell--Tornheim zeta function: Kronecker limit type formulas and Special values
Sumukha Sathyanarayana, N. Guru Sharan
https://arxiv.org/abs/2510.10093 https://

Mordell--Tornheim zeta function: Kronecker limit type formulas and Special values
In this paper, we establish Kronecker limit type formulas for the generalized Mordell--Tornheim zeta function $Θ(r,s,t,x)$ as a function of the third variable, in terms of Riemann-zeta and Gamma values. We also give series evaluations of $Θ(r,s,t,x)$ in terms of Herglotz-Zagier type functions, and their derivatives. As applications of this, we derive Kronecker limit type formula in the second variable and a new infinite family of modular relations called mixed functional equations. We also st…

A universal approach to saddle-point methods in attosecond science
Anne Weber, Job Feldbrugge, Emilio Pisanty
https://arxiv.org/abs/2510.12545 https://arxi…

A universal approach to saddle-point methods in attosecond science
Light-matter interactions within the strong-field regime, where intense laser fields can ionise a target via tunnelling, give rise to fascinating phenomena such as the generation of high-order harmonic radiation (HHG). On the atomic scale, these strong-field processes are described in terms of highly-oscillatory time integrals which are often approximated using saddle-point methods. These methods simultaneously simplify the calculations and let us understand the physical processes in terms of s…

Dimensional reduction of the M-theory Chern-Simons term at order $\ell_p^6$
Mohammad R. Garousi
https://arxiv.org/abs/2509.13726 https://arxiv.org/pdf/2509…

Dimensional reduction of the M-theory Chern-Simons term at order $\ell_p^6$
The dimensional reduction of M-theory couplings at order $\ell_p^6$ is known to produce one-loop $α'^3$ corrections in type IIA string theory. In this paper, we perform the Kaluza-Klein reduction of the M-theory Chern-Simons coupling $t_8ε_{11} A R^4$ at this order. By meticulously accounting for non-gauge-invariant total derivative terms, we derive the complete set of corresponding one-loop, gauge-invariant couplings in the type IIA effective action. Our results not only reproduce the standa…

OpenAI projects that it will reduce the revenue share it pays to Microsoft from 20% this year to ~8% by 2030, potentially retaining over $50B more in revenue (The Information)
https://www.theinformation.com/articles/openai-gain-50-billi…

OpenAI to Gain $50 Billion From Cutting Revenue Share with Microsoft, Partners
As OpenAI irons out new terms of a partnership with Microsoft, it has told some shareholders that the percentage of revenue it will hand over to Microsoft will drop considerably in the coming years. As part of their original partnership agreement, Microsoft is entitled to 20% of the startup’s ...

Non-associative structures in extended geometry
Martin Cederwall, Jakob Palmkvist
https://arxiv.org/abs/2509.14215 https://arxiv.org/pdf/2509.14215

Non-associative structures in extended geometry
We consider a generalisation of vector fields on a vector space, where the vector space is generalised to a highest-weight module over a Kac-Moody algebra. The generalised vector field is an element in a non-associative superalgebra defined by the module and the Kac-Moody algebra. Also the Lie derivative of a vector field parameterised by another is generalised and expressed in a simple way in terms of this superalgebra. It reproduces the generalised Lie derivative in the general framework of e…

Sources: the FTC is investigating whether Amazon and Google misled advertisers by not properly disclosing the terms and pricing for ads on their websites (Bloomberg)
https://www.bloomberg.com/news/articles/2025-09-12/amazon-goo…

Amazon, Google Probed by FTC Over Search Ad Practices (AMZN, GOOGL)
The US Federal Trade Commission is investigating whether Amazon.com Inc. and Alphabet Inc.’s Google misled advertisers that place ads on their websites, according to people familiar with the matter.

OpenAI and Microsoft say they have signed a non-binding memorandum of understanding for the next phase of their partnership, and are working to finalize terms (Ina Fried/Axios)
https://www.axios.com/2025/09/11/open-ai-microsoft-agreement-deal

OpenAI and Microsoft reach tentative deal to revise partnership
The deal resolves a major hurdle to OpenAI's planned corporate restructuring.