Tootfinder

Night Shift
There’s light
at the end of the tunnel,
the weekend is here.
No need to sleep now,
you’ll sleep tonight,
like a normal human being.
Coffee — your best friend,
your favorite drug,
that liquid
you shoot multiple times a day.
That’s the only way
to survive the day.
#writing

Word Chain Generators for Prefix Normal Words
Duncan Adamson, Moritz Dudey, Pamela Fleischmann, Annika Huch
https://arxiv.org/abs/2508.19619 https://arxiv.…

Word Chain Generators for Prefix Normal Words
In 2011, Fici and Lipták introduced prefix normal words. A binary word is prefix normal if it has no factor (substring) that contains more occurrences of the letter 1 than the prefix of the same length. Among the open problems regarding this topic are the enumeration of prefix normal words and efficient testing methods. We show a range of characteristics of prefix normal words. These include properties of factors that are responsible for a word not being prefix normal. With word chains and gen…

I stopped at the grocery store on the way to work... another thing I thought I would never do on a bike.
Loaded the panniers up so they could barely close. (I meant to put the milk crate on the rack but I forgot.)
There's actually case of seltzer in one of the bags. I would have got more chips but I was afraid of them being crushed.
I basically got everything I'd get on a normal Aldi "car" run except for more chips.

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…

Nonlinearities of Schwarzschild Black Hole Head-on Collisions
Alex Kehagias, Davide Perrone, Antonio Riotto
https://arxiv.org/abs/2508.17993 https://arxiv.…

Nonlinearities of Schwarzschild Black Hole Head-on Collisions
We derive analytically the amplitude of the quadratic quasi-normal mode generated in the ringdown stage of the gravitational waveform produced by the ultra-relativistic head-on collision of two non-spinning Schwarzschild black holes. Although being a highly nonlinear event, second-order perturbation theory suffices and that nonlinearities may be derived by a simple bootstrapping procedure.

Finite-temperature transport in the gapped spin-1/2 XXZ chain and one-dimensional lattice spinless fermion model
J. M. P. Carmelo, P. D. Sacramento
https://arxiv.org/abs/2509.08741

Finite-temperature transport in the gapped spin-1/2 XXZ chain and one-dimensional lattice spinless fermion model
Here we consider a class of energy eigenstates of the spin-1/2 XXZ chain that exist both for anisotropies 1 and larger than 1. We show that at the isotropic point their contributions are behind the diffusion constant being infinite, spin transport being anomalous superdiffusive for temperatures T>0. That for anisotropy larger than 1 such states do not contribute to the diffusion constant is shown to imply it is finite, spin transport being normal diffusive for T>0. By combining the connection t…

Now, anyone can quote. I went into preferences and posting defaults.
This is a great feature. I think a "normal Mastodon" should have quote posts.
Abnormality comes with the lack of it!
I love it! It's beautiful!
Btw, you can edit your post and then the interface tells me I can add a quote post to my post but it didn't work in the end.
Now time to fix all the bugs that arrived due to this new feature being introduced...
Poor programmers, …

Exactness of the normal-ordered two-body truncation of three-nucleon forces
Maxwell Rothman, Ben Johnson-Toth, Francesca Bonaiti, Gaute Hagen, Matthias Heinz, Thomas Papenbrock
https://arxiv.org/abs/2508.01507

Exactness of the normal-ordered two-body truncation of three-nucleon forces
Reference-state based many-body methods start from Hamiltonians that are normal-ordered with respect to the reference state. In low-energy nuclear physics applications normal-ordered Hamiltonians consisting of two- and three-nucleon forces are usually truncated at the two-body rank with residual three-nucleon operators being discarded. Benchmark computations have showed that this truncation is accurate, but we lack an understanding about why it works. We show that the normal-ordered two-body tr…

Good Morning #Canada
I've been a bachelor since Thursday as my wife is in Toronto helping my daughter with her latest chemo session. She's back late Monday when life, for me, returns to normal. According to #StatsCan, being married at our age (late 60s) is the most prevalent relationship. But Canadians in younger age brackets are more likely these days to be living common-law and getting married later in life, if at all. Canada has one of the highest rates of common-law relationships worldwide and the highest in the G7. Between 1981 and 2021, common-law couples increased 447% while the number of married couples grew by only 26%. Common-law unions are most prevalent in Nunavut (52%), Quebec (43%), and the Northwest Territories (36%). It's no surprise that more than half of Canadians believe that marriage is not necessary, and even less surprising that this opinion is stronger with young men versus young women.
#CanadaIsAwesome #Relationship
https://madeinca.ca/marriage-statistics-canada/

On the $IC$-$\Pi$-property of subgroups of finite groups
Zhengtian Qiu, Shouhong Qiao
https://arxiv.org/abs/2510.08426 https://arxiv.org/pdf/2510.08426

On the $IC$-$Π$-property of subgroups of finite groups
Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the $ Π$-property in $ G $ if $ | G/K : N_{G/K}((H \cap L)K/K)| $ is a $ π(( H \cap L)K/K ) $-number for any chief factor $ L/K $ of $ G $; and we call that $ H $ satisfies the $ IC $-$ Π$-property in $ G $ if $ H\cap [H, G] $ satisfies the $ Π$-property in $ G $. In this paper, we obtain a criterion of a normal subgroup being contained in the $ p\mathfrak{U} $-hypercenter of a finite group by the $IC$-$ …