Tootfinder

Panthers bring back Renfrow, place Coker on IR https://www.espn.com/nfl/story/_/id/46112946/panthers-bring-back-hunter-renfrow-place-jalen-coker-ir

Tropical elliptic curves in 3-space
Laura Casabella, Lars Kastner, Raluca Vlad
https://arxiv.org/abs/2507.21958 https://arxiv.org/pdf/2507.21958

Tropical elliptic curves in 3-space
We classify trivalent graphs with 16 vertices and 16 edges that arise from intersecting two quadratic surfaces in tropical 3-space. There are 4,009 such graphs, representing maximally degenerate stable models of elliptic curves realized as tropical complete intersections of two quadrics. Our classification is derived from 405,246,030 regular unimodular triangulations of the 4-dimensional Cayley polytope.

Hilbert-Kunz multiplicity of quadrics via Ehrhart theory
Igor Pak, Boris Shapiro, Ilya Smirnov, Ken-ichi Yoshida
https://arxiv.org/abs/2508.17915 https://a…

Hilbert-Kunz multiplicity of quadrics via Ehrhart theory
We show that the Hilbert-Kunz multiplicity of the d-dimensional non-degenerate quadric hypersurface of characteristic p > 2 is a rational function of p composed from the Ehrhart polynomials of integer polytopes. In consequence, we explain and recover a result of Gessel and Monsky and prove that the Hilbert-Kunz multiplicity of quadrics of fixed characteristic is a decreasing function of dimension.

Simpler is Faster: Practical Distance Reporting by Sorting Along a Space-Filling Curve
Sarita de Berg, Ivor van der Hoog, Eva Rotenberg, Emil Toftegaard G{\ae}de
https://arxiv.org/abs/2508.19891

Simpler is Faster: Practical Distance Reporting by Sorting Along a Space-Filling Curve
Range reporting is a classical problem in computational geometry. A (rectangular) reporting data structure stores a point set $P$ of $n$ points, such that, given a (rectangular) query region $Δ$, it returns all points in $P \cap Δ$. A variety of data structures support such queries with differing asymptotic guarantees such as $k$-d trees, range trees, $R$-trees, and quadtrees. A common variant of range queries are distance reporting queries, where the input is a query point $q$ and a radius $…

$\mathfrak A_5$-equivariant geometry of quadric threefolds
Antoine Pinardin, Zhijia Zhang
https://arxiv.org/abs/2508.11496 https://arxiv.org/pdf/2508.11496…

$\mathfrak A_5$-equivariant geometry of quadric threefolds
We classify $G$-Mori fibre spaces equivariantly birational to smooth quadric threefolds with fixed-point free actions of the alternating group $G=\mathfrak A_5$. We deduce that such quadric threefolds are $G$-solid and the $G$-actions on them are not projectively linearizable.

❗️"There's a very good chance" – Trump on talks with Putin and resolution of the war #shorts: https://benborges.xyz/2025/08/16/quottheres-a-very-good-chancequot.html

Can LLMs Generate User Stories and Assess Their Quality?
Giovanni Quattrocchi, Liliana Pasquale, Paola Spoletini, Luciano Baresi
https://arxiv.org/abs/2507.15157

Can LLMs Generate User Stories and Assess Their Quality?
Requirements elicitation is still one of the most challenging activities of the requirements engineering process due to the difficulty requirements analysts face in understanding and translating complex needs into concrete requirements. In addition, specifying high-quality requirements is crucial, as it can directly impact the quality of the software to be developed. Although automated tools allow for assessing the syntactic quality of requirements, evaluating semantic metrics (e.g., language c…

Initial ideal of a general rational or elliptic curve on quadrics
Francesca Cioffi, Davide Franco, Giovanna Ilardi
https://arxiv.org/abs/2506.12428 https:/…

Initial ideal of a general rational or elliptic curve on quadrics
Over an algebraically closed field of characteristic zero, we prove that the generic initial ideal with respect to the degree reverse lexicographic term order of a general rational or elliptic curve on quadrics is almost revlex. Following constructive arguments, our proof combines features of a pencil of quadrics, interpolation methods and the notion of double generic initial ideal.

On the volume of K-semistable Fano manifolds
Chi Li, Minghao Miao
https://arxiv.org/abs/2506.17420 https://arxiv.org/pdf/2506.17420…

On the volume of K-semistable Fano manifolds
We prove that the volume of an $n$-dimensional K-semistable Fano manifold that is not $\mathbb{P}^n$ is at most $2n^n$. Moreover, the equality holds only if $X\cong \mathbb{P}^1\times \mathbb{P}^{n-1}$ or $X$ is a smooth quadric hypersurface $Q\subset \mathbb{P}^{n+1}$. Our proof is based on a new connection between K-semistability and minimal rational curves. More generally, we show that the volume of a K-semistable Fano manifold with a minimal rational curve of degree $d$ is bounded above by …