Tootfinder

Here’s a mind-blowing experiment that you can try at home:
Gather some children’s blocks and place them on a table.
Take one block and slowly push it over the table’s edge, inch by inch, until it’s on the brink of falling.
If you possess patience and a steady hand, you should be able to balance it so that exactly half of it hangs off the edge.
Nudge it any farther, and gravity wins.
Now take two blocks and start over.
Stacking one on top of the other, how…

This Block-Stacking Math Problem Has a Preposterous Solution You Need to See to Believe — Scientific American
In principle, this impossible math allows for a glue-free bridge of stacked blocks that can stretch across the Grand Canyon—and into infinity Amanda Montañez Math Here’s a mind-blowing experiment that you can try at home: Gather some children’s blocks and place them on a table. Take one block and slowly push it over the table’s edge, inch by inch, until it’s on the brink of falling. If you possess patience and a steady hand, you should be able to balance it so that exactly half of it…

Disorder-induced suppression of superconductivity in infinite-layer nickelates
Abhishek Ranna, Romain Grasset, Martin Gonzalez, Kyuho Lee, Bai Yang Wang, Edgar Abarca Morales, Florian Theuss, Zuzanna H. Filipiak, Michal Moravec, Marcin Konczykowski, Harold Y. Hwang, Andrew P. Mackenzie, Berit H. Goodge
https://arxiv.org/abs/2506…

Disorder-induced suppression of superconductivity in infinite-layer nickelates
The pairing symmetry of superconducting infinite-layer nickelates is a fundamental yet experimentally challenging question. We employ high-energy electron irradiation to induce disorder in superconducting Nd$_{0.825}$Sr$_{0.175}$NiO$_2$ thin films and examine the impact of pair-breaking defects on superconductivity and elucidate the nature of the superconducting gap. Our measurements reveal a complete suppression of superconductivity with increasing disorder, suggesting an unconventional, sign-…

Infinitesimal Torelli problems for special Gushel-Mukai and related Fano threefolds: Hodge theoretical and categorical perspectives
Xun Lin, Shizhuo Zhang, Zheng Zhang
https://arxiv.org/abs/2507.06995

Infinitesimal Torelli problems for special Gushel-Mukai and related Fano threefolds: Hodge theoretical and categorical perspectives
We investigate infinitesimal Torelli problems for some of the Fano threefolds of the following two types: (a) those which can be described as zero loci of sections of vector bundles on Grassmannians (for instance, ordinary Gushel-Mukai threefolds), and (b) double covers of rigid Fano threefolds branched along a $K3$ surface (such as, special Gushel-Mukai threefolds). The differential of the period map for ordinary Gushel-Mukai threefolds has been studied by Debarre, Iliev and Manivel; in partic…

A good news story about the great gender preference divide.
After years of declining sex ratios that saw increases in female infanticide and missing girls, it seems there's a change.
'Globally, among babies born in 2000, a staggering 1.6m girls were missing from the number you would expect, given the natural sex ratio at birth. This year that number is likely to be 200,000—and it is still falling.'
Beautiful hope.

The stunning decline of the preference for having boys
Millions of girls were aborted for being girls. Now parents often lean towards them

If you set limits for a scale (e.g. x-axis) in ggplot, how would you like data outside of that range be handled? There is the oob parameter for that and a set of functions to use with it: https://scales.r-lib.org/reference/oob.html

Hausdorff Dimension of non-conical and Myrberg limit sets
Mahan Mj, Wenyuan Yang
https://arxiv.org/abs/2506.04955 https://arxiv.org/p…

Hausdorff Dimension of non-conical and Myrberg limit sets
In this paper, we develop techniques to study the Hausdorff dimensions of non-conical and Myrberg limit sets for groups acting on negatively curved spaces. We establish maximality of the Hausdorff dimension of the non-conical limit set of $G$ in the following cases. 1. $M$ is a finite volume complete Riemannian manifold of pinched negative curvature and $G$ is an infinite normal subgroups of infinite index in $π_1(M)$. 2. $G$ acts on a regular tree $X$ with $X/G$ infinite and amenable (dimensi…

Finslerian lightconvex boundaries: applications to causal simplicity and the space of cone geodesics $\mathcal{N}$
J\'onatan Herrera, Miguel S\'anchez
https://arxiv.org/abs/2506.09032

Finslerian lightconvex boundaries: applications to causal simplicity and the space of cone geodesics $\mathcal{N}$
Our outcome is structured in the following sequence: (1) a general result for indefinite Finslerian manifolds with boundary $(M,L)$ showing the equivalence between local and infinitesimal (time, light or space) convexities for the boundary $\partial M$, (2) for any cone structure $(M,\mathcal{C})$ which is globally hyperbolic with timelike boundary, the equivalence among: (a) the boundary $\partial M$ is lightconvex, (b) the interior $\mathring{M}$ is causally simple and (c) the space of the co…

The problem of infinite Spin for parabolic and collision solutions in the planar $n$-body problem
Zhe Wang, Guowei Yu
https://arxiv.org/abs/2507.05801 http…

The problem of infinite Spin for parabolic and collision solutions in the planar $n$-body problem
In the planar $n$-body problem, the problem of infinite spin occurs for both parabolic and collision solutions. Recently Moeckel and Montgomery \cite{MM25} showed that there is no infinite spin for total collision solutions. Following their approach, we show it can not happen for both complete and partially parabolic solutions. Our approach also allows us to generalize Moeckel and Montgomery's result to partial collision solutions.

Best approximation of a three-variable function by sum of one-variable coordinate functions
Rashid A. Aliev, Vugar A. Guliyev, Amil F. Jabiyev
https://arxiv.org/abs/2507.04747

Best approximation of a three-variable function by sum of one-variable coordinate functions
Consider the following approximation problem of a continuous function of three variables by the sum of three continuous functions of one variable: \[ E(f,Ω)=\inf||f(x,y,z)-ϕ(x)-ψ(y)-ω(z)||_{\infty}=? \] where $f(x,y,z)$ is a given continuous function defined on $Ω=[0,1]^3$ and the infimum runs over all triplets of continuous functions $ϕ(x),ψ(y),ω(z)$ defined on the unit interval $[0,1]$. In this paper, we will prove a formula to calculate the error $E(f,Ω)$ und…

Cardinalities of the total number of independent sets
Benedek Kov\'acs, Zolt\'an L\'or\'ant Nagy
https://arxiv.org/abs/2505.24794 https://

Cardinalities of the total number of independent sets
We study the set of numbers the total number of independent sets can admit in $n$-vertex graphs. In this paper, we prove that the cardinality of this set $\mathcal{N}i(n)$ is very close to $2^n$ in the following sense: $\mathcal{N}i(n)/2^n = O(n^{-1/5})$ while for infinitely many $n$, we have $\log_2(\mathcal{N}i(n)/2^n)\ge -2^{(1+o(1)\sqrt{\log_2 n}}$. This set is also precisely the set of possible values of the independence polynomial $I_G(x)$ at $x=1$ for $n$-vertex graphs $G$. As an applica…