Tootfinder

It's June, so I've got my Javastation off the shelf for the first time in a couple of decades. This is a Javastation Krups, with 100MHz sparc, sold as a diskless workstation. I never realised it had a PPP ROM boot in! Anyway, I should get on and set up networking and a boot server.
(Note: the plastic on the clips on the doors is fragile, 2 just pinged off on me)
#retrocomputing

AWS = Amazon = Jeff Bezos, auf dem Schoß von Trump.
Corporate Presence.
European sovereign cloud.
Merkste selbst.
Souverän? Wer ist da souverän? Was bedeutet dieses sinnentleerte Wort? Nichts.
AWS establishes new German corporate presence to advance European sovereign cloud | TechCrunch

This https://arxiv.org/abs/2406.13240 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

$ω$-weak equivalences between weak $ω$-categories
We study $ω$-weak equivalences between weak $ω$-categories in the sense of Batanin-Leinster. Our $ω$-weak equivalences are strict $ω$-functors satisfying essential surjectivity in every dimension, and when restricted to those between strict $ω$-categories, they coincide with the weak equivalences in the model category of strict $ω$-categories defined by Lafont, Métayer, and Worytkiewicz. We show that the class of $ω$-weak equivalences has the 2-out-of-3 property. We also consider a gene…

Algebraic approximations to linear combinations of S-units
Parvathi S Nair, Veekesh Kumar, S. S. Rout
https://arxiv.org/abs/2506.02898 https://

Algebraic approximations to linear combinations of S-units
Let $Γ\subset \bar{\mathbb{Q}}^{\times}$ be a finitely generated multiplicative group of algebraic numbers, let $α_1,\ldots,α_m\in K$ be given algebraic numbers and not all zero, and let $\varepsilon >0$ be fixed. In this paper, we prove that there exist only finitely many tuples $(u_1, \ldots, u_m, q, p)\in Γ^m\times\mathbb{Z}^2$ with $d = [\mathbb{Q}(u_1, \ldots, u_m):\mathbb{Q}]$ such that $\max\{|α_1 qu_1|, \ldots, |α_m qu_m|\}>1$, the tuple $(α_1qu_1, \ldots, α_…

Indeed says CEO Chris Hyams is stepping down, replaced by parent Recruit Holdings CEO Hisayuki "Deko" Idekoba, who is returning to the role after six years (Chester Dawson/Bloomberg)
https://www.bloomberg.com/news/articles/20

Asymptotic Plateau problem for $2$-convex hypersurface in $\mathbb{H}^4$
Defa Chen, Zhenan Sui, Letao Sun
https://arxiv.org/abs/2506.00565 https://

Asymptotic Plateau problem for $2$-convex hypersurface in $\mathbb{H}^4$
We prove the existence of smooth complete $2$-convex hypersurface which satisfies prescribed curvature equation $(κ_1 + κ_2)(κ_1 + κ_3)(κ_2 + κ_3) = (2 σ)^3$ and has prescribed asymptotic boundary at infinity of hyperbolic space of dimension 4, where $σ\in (0, 1)$ is a constant. We also prove the existence for $σ_k (κ_2 + \cdots + κ_n, \cdots, κ_1 + \cdots + κ_{n - 1}) = C_n^k (n - 1)^k σ^k$ with $k < n$ in $\mathbb{H}^{n + 1}$.

This https://arxiv.org/abs/2407.08881 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Newspaces with Nebentypus: An Explicit Dimension Formula and Classification of Trivial Newspaces
Consider $N \geq 1$, $k \geq 2$, and $χ$ a Dirichlet character modulo $N$ such that $χ(-1) = (-1)^k$. For any bound $B$, one can show that $\dim S_k(Γ_0(N),χ) \le B$ for only finitely many triples $(N,k,χ)$. It turns out that this property does not extend to the newspace; there exists an infinite family of triples $(N,k,χ)$ for which $\dim S_k^{\text{new}}(Γ_0(N),χ) = 0$. However, we classify this case entirely. We also show that excluding the infinite family for which $\dim S_k^{\text{…

This https://arxiv.org/abs/2501.17769 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Colimits of internal categories
We show that for an extensive $1$-category $\mathcal{E}$ with pullbacks and pullback stable coequalisers in which the forgetful functor $\mathcal{U}: \mathbf{Cat}(\mathcal{E})_1 \to \mathbf{Gph}(\mathcal{E})$ has left adjoint, the $2$-category $\mathbf{Cat}(\mathcal{E})$ of internal categories, functors and natural transformations has finite $2$-colimits. In addition, $\mathbf{Cat}(\mathcal{E})$ is extensive, has pullbacks and codescent coequalisers are stable under pullback along discrete Cond…

This https://arxiv.org/abs/2411.09063 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The typical elasticity of a quadratic order
For an atomic domain $D$, the $elasticity$ $ρ(D)$ of $D$ is defined as $\sup\{r/s: π_1\cdots π_r = ρ_1 \cdots ρ_s,~ \text{where each $π_i, ρ_j$ is irreducible}\}$; the elasticity provides a concrete measure of the failure of unique factorization in $D$. Fix a quadratic number field $K$ with discriminant $Δ_K$, and for each positive integer $f$, let $\mathcal{O}_f = \mathbb{Z} + f\mathcal{O}_K$ denote the order of conductor $f$ in $K$. Results of Halter-Koch imply that $\mathcal{O}_f$ ha…

Projective and anomalous representations of categories and their linearizations
Domenico Fiorenza, Chetan Vuppulury
https://arxiv.org/abs/2506.01521 https:…

Projective and anomalous representations of categories and their linearizations
We invesigate the relation between projective and anomalous representations of categories, and show how to any anomaly $J\colon \mathcal{C}\to 2\mathrm{Vect}$ one can associate an extension $\mathcal{C}^J$ of $\mathcal{C}$ and a subcategory $\mathcal{C}^J_{\mathrm{ST}}$ of $\mathcal{C}^J$ with the property that: (i) anomalous representations of $\mathcal{C}$ with anomaly $J$ are equivalent to $\mathrm{Vect}$-linear functors $E\colon \mathcal{C}^J\to \mathrm{Vect}$, and (ii) these are in turn eq…