Tootfinder

Simple field test of ChatGPT 5. "Produce a table of Bolivia's largest 15 cities by population in the latest census. Provide a link to the source."
It offered the 2012 Census data, and provided a link. But each of the top nine cities has a population that doesn't match the source.
#ChatGPT #GPT5

K-theoretic Hikita conjecture for quiver gauge theories
Ilya Dumanski, Vasily Krylov
https://arxiv.org/abs/2509.06226 https://arxiv.org/pdf/2509.06226

K-theoretic Hikita conjecture for quiver gauge theories
We study variants of Hikita conjecture for Nakajima quiver varieties and corresponding Coulomb branches. First, we derive the equivariant version of the conjecture from the non-equivariant one for a set of gauge theories. Second, we suggest a variant of the conjecture, with K-theoretic Coulomb branches involved. We show that this version follows from the usual (homological) one for a set of theories. We apply this result to prove the conjecture in finite ADE types. In the course of the proof, w…

Artificial Intelligence as an Opportunity for the Science of Consciousness: A Dual-Resolution Framework
Shahar Dror, Dafna Bergerbest, Moti Salti
https://arxiv.org/abs/2509.07001

Artificial Intelligence as an Opportunity for the Science of Consciousness: A Dual-Resolution Framework
The encounter of artificial intelligence with consciousness research is often framed as a challenge: could this science determine whether such systems are conscious? We suggest it is equally an opportunity to expand and test the scope of existing theories of consciousness. Current approaches remain polarized. Computational functionalism emphasizes abstract organization, often realized through neural correlates of consciousness, while biological naturalism insists that consciousness is tied to l…

A graph energy conjecture through the lenses of semidefinite programming
Aida Abiad, Gabriel Coutinho, Emanuel Juliano, Luuk Reijnders
https://arxiv.org/abs/2509.05814 https://

A graph energy conjecture through the lenses of semidefinite programming
Let $G$ be a graph on $n$ vertices with independence number $α(G)$. Let $\mathcal{E}(G)$ be the energy of a graph, defined as the sum of the absolute values of the adjacency eigenvalues of $G$. Using Graffiti, Fajtlowicz conjectured in the 1980s that $$\frac{1}{2}\mathcal{E}(G) \geq n - α(G).$$ In this paper we derive a semidefinite program formulation of the graph energy, and we use it to obtain several results that constitute a first step towards proving this conjecture. In particular, we s…

Despite having beencriticized by civil rights groups for using
"cell site simulators" (Stingrays) during the last Trump administration,
ICE continues to use the technology.
Earlier this year, new media publication Straight Arrow News said it had
“mobile network anomalies” around a Washington state protest against ICE raids that were consistent with Stingray use.
Forbes found contract records showing ICE purchased nearly
$1 million worth of “cell s…

How ICE Is Using Fake Cell Towers To Spy On People’s Phones
ICE is using a controversial spy tool to locate smartphones, court records show.

Consistent Four-derivative Heterotic Truncations and the Kerr-Sen Solution
Liang Ma, Yi Pang, Robert J. Saskowski, Minghao Xia
https://arxiv.org/abs/2509.07069 https://

Consistent Four-derivative Heterotic Truncations and the Kerr-Sen Solution
Four-derivative heterotic supergravity (without gauge fields) reduced on a $p$-dimensional torus leads to half-maximal supergravity coupled to $p$ vector multiplets, and it is known that removing the vector multiplets is a consistent truncation of the theory. We find a new consistent truncation of four-derivative heterotic supergravity on a torus that keeps the vector multiplets and precisely reproduces the bosonic action of heterotic supergravity (with heterotic gauge fields). We show that bot…

On the integral cohomology of real toric manifolds
Feifei Fan
https://arxiv.org/abs/2509.06059 https://arxiv.org/pdf/2509.06059

On the integral cohomology of real toric manifolds
Real toric manifolds are the real loci of nonsingular complete toric varieties. In this paper, we calculate the integral cohomology groups of real toric manifolds in terms of the combinatorial data contained in the underlying simplicial fans, generalizing a formula due to Cai and Choi. We also present a combinatorial formula to describe the ring structure, modulo the ideal consisting of elements of order $2$. As an application, a combinatorial-algebraic criterion is established for when a real …

How to Be Accountable to Yourself and Why It Matters
#integrity #MentalHealth

How to Be Accountable to Yourself and Why It Matters
What if the promises you make to yourself mattered just as much as the ones you make to others? Self-accountability starts with knowing your line and following through.

"The Marshall Plan did help rebuild Europe. The Civil Rights Movement did end Jim Crow. Smallpox was eradicated through an international coordination effort. The Montreal Protocol did address the ozone hole. Are these perfect success stories? No, they all happened through a series of shitty compromises, through flawed execution and with unintended consequences." <-- Thanks Joan!

Ramsey numbers of trees
Richard Montgomery, Mat\'ias Pavez-Sign\'e, Jun Yan
https://arxiv.org/abs/2509.07934 https://arxiv.org/pdf/2509.07934

Ramsey numbers of trees
We show that there exists a constant $c>0$ such that every $n$-vertex tree $T$ with $Δ(T)\le cn$ has Ramsey number $R(T)=\max\{t_1+2t_2,2t_1\}-1$, where $t_1\ge t_2$ are the sizes of the bipartition classes of $T$. This improves an asymptotic result of Haxell, Łuczak, and Tingley from 2002, and shows that, though Burr's 1974 conjecture on the Ramsey numbers of trees has long been known to be false for certain `double stars', it is true for trees with up to small linear maximum degree.