Tootfinder

Unter dem Label 'Europäische #DigitaleSouveränität' wird aktuell in #Brandenburg ein Desaster geplant. Das Wasser ist schon knapp, nicht zuletzt durch Tesla, aber auch wegen des Klimas.
"Derzeit gibt es laut Wirtschaftsministerium mehr als 30 Anfragen vo…

Some series connecting Fibonacci numbers to $\pi$
Zhi-Wei Sun, Yajun Zhou
https://arxiv.org/abs/2506.01865 https://arxiv.org/pdf/2506…

Some series connecting Fibonacci numbers to $π$
In this paper, we mainly deduce several series identities connecting the Fibonacci numbers to $π$. For example, we prove that \[\sum_{k=1}^{\infty}\frac{(135 k-56) F_{8 k}-2 (105 k-44) F_{8 k-1}}{k^{3}\binom{2k}{k}^3}=\frac{7π^{2}}{3}\]and\[\sum_{k=0}^\infty\frac{\binom{2k}{k}^3}{2^{12k}}\big[ 2 (90 k+13) F_{8 k}-2 (30 k-1) F_{8 k-1}\big]=\frac{64}π.\]

Laura Loomer's White House access erases the line between the fringe and mainstream (Steve Benen/MSNBC)
https://www.msnbc.com/rachel-maddow-show/maddowblog/laura-loomers-white-house-access-erases-line-fringe-mainstream-rcna210863
http://www.memeorandum.com/250604/p51#a250604p51

This https://arxiv.org/abs/2505.24100 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Halfway to induced saturation for even cycles
For graphs $G$ and $H$, we say that $G$ is $H$-free if no induced subgraph of $G$ is isomorphic to $H$, and that $G$ is $H$-induced saturated if $G$ is $H$-free but removing or adding any edge in $G$ creates an induced copy of $H$. A full characterization of graphs $H$ for which $H$-induced saturated graphs exist remains elusive. Even the case where $H$ is a path -- now settled by the collective results of Martin and Smith, Bonamy et al., and Dvoŕǎk -- was already quite challenging. What if…

Der Pak Choi blüht immer noch und hat über Seitentriebe neue Blütenstände gebildet. Aber jetzt kommen auch dauernd #Hummeln und #Bienen. War vielleicht nur eine Frage der Temperatur.
#Balkongarten

CiteEval: Principle-Driven Citation Evaluation for Source Attribution
Yumo Xu, Peng Qi, Jifan Chen, Kunlun Liu, Rujun Han, Lan Liu, Bonan Min, Vittorio Castelli, Arshit Gupta, Zhiguo Wang
https://arxiv.org/abs/2506.01829

CiteEval: Principle-Driven Citation Evaluation for Source Attribution
Citation quality is crucial in information-seeking systems, directly influencing trust and the effectiveness of information access. Current evaluation frameworks, both human and automatic, mainly rely on Natural Language Inference (NLI) to assess binary or ternary supportiveness from cited sources, which we argue is a suboptimal proxy for citation evaluation. In this work we introduce CiteEval, a citation evaluation framework driven by principles focusing on fine-grained citation assessment wit…

'There's no fraud': Steve Bannon says Elon Musk's DOGE cuts are a huge failure - Raw Story
https://www.rawstory.com/steve-bannon-elon-musk-fraud/

Bienen haben Launen
https://stohl.de/wordpress/?p=191221

Bienen haben Launen
Auch Bienen haben Launen: Bienen stechen unterschiedlich rasch zu „Aber das ist nicht so, die haben eine eigene Bremse. Sobald genug Bienen gestochen haben, hören sie auf zu stechen. Das ist …

Various irrational series involving binomial coefficients
Zhi-Wei Sun
https://arxiv.org/abs/2506.01870 https://arxiv.org/pdf/2506.018…

Various irrational series involving binomial coefficients
Motivated by Galois theory, we propose some new irrational series of Ramanujan's type or Zeilberger's type. For example, we conjecture that \begin{equation*}\sum_{k=1}^\infty\frac{\binom{2k}k^2\binom{4k}{2k}}{(84-32\sqrt6)^{4k}} \left(280k+5\sqrt6+26\right)=\frac3π(2\sqrt3+33\sqrt2) \end{equation*} and \begin{align*}&\sum_{k=1}^\infty\frac{(27(37102-15147\sqrt6))^k}{k^3\binom{2k}k^2\binom{3k}k} \left(9k(11\sqrt6+51)-2(19\sqrt6+54)\right) \\&\qquad=\frac{5625}2\left(\sqrt6 L_{-24}(2)-3G\r…

The Hasse principle for homogeneous polynomials with random coefficients over thin sets II
Daniel Flores, Kiseok Yeon
https://arxiv.org/abs/2506.01291 http…

The Hasse principle for homogeneous polynomials with random coefficients over thin sets II
Let $d$ and $n$ be natural numbers. Let $ν_{d,n}: \mathbb{R}^n\rightarrow \mathbb{R}^{N}$ denote the Veronese embedding with $N=N_{n,d}:=\binom{n+d-1}{d}$, defined by listing all the monomials of degree $d$ in $n$ variables using the lexicographical ordering. Let $\langle \boldsymbol{a}, ν_{d,n}(\boldsymbol{x})\rangle\in \mathbb{Z}[\boldsymbol{x}]$ be a homogeneous polynomial in $n$ variables of degree $d$ with integer coefficients $\boldsymbol{a}$, where $\langle\cdot,\cdot\rangle$ denotes t…