Tootfinder

Approximation by uniformly distributed sequences
Gerardo Gonz\'alez Robert, Mumtaz Hussain, Nikita Shulga, Benjamin Ward
https://arxiv.org/abs/2507.06583

Approximation by uniformly distributed sequences
We consider approximation properties of real points by uniformly distributed sequences. Under some assumptions on the approximation functions, we prove a Khintchine-type $0$-$1$ dichotomy law. We establish a new connection between uniform distribution and the ubiquity property. Namely, we show that a bound on the discrepancy of the sequence implies the ubiquity property, which helps to obtain divergence results. We further obtain Hausdorff dimension results for weighted sets. The key tools in p…

De Morgan's law in toposes I
Olivia Caramello, Yorgo Chamoun
https://arxiv.org/abs/2507.01869 https://arxiv.org/pdf/2507.01869

De Morgan's law in toposes I
We study toposes satisfying De Morgan's law, in particular we give characterizations of geometric theories whose classifying topos is De Morgan, clarifying the link with the amalgamation property of the category of models of such theory. We then give several ways of turning a topos into a De Morgan topos.

The quantitative behavior of $\alpha$-Yang-Mills-Higgs fields on surfaces
Wanjun Ai, Jiayu Li, Miaomiao Zhu
https://arxiv.org/abs/2509.06380 https://arxiv.…

The quantitative behavior of $α$-Yang-Mills-Higgs fields on surfaces
We investigate the blow-up behavior of $α$-Yang--Mills--Higgs ($α$-YMH) fields over closed Riemannian surfaces with the target fiber $F = S^{K-1} \subset \mathbb{R}^K$ being the round sphere, focusing on the establishment of the $α$-energy identity and the no-neck property during the bubbling process. A central innovation is the identification of a hidden Jacobian structure through Hodge decomposition and a new conservation law. Furthermore, we derive a Pohozaev-type identity for $α$-YMH fi…

Anisotropic modifications to the transport phenomena and observables in a hot QCD medium at finite baryon asymmetry
Shubhalaxmi Rath
https://arxiv.org/abs/2508.04934 https://

Anisotropic modifications to the transport phenomena and observables in a hot QCD medium at finite baryon asymmetry
We have studied how the transport of charge and heat as well as associated observables become influenced by a weak-momentum anisotropy arising due to the asymptotic expansion of baryon asymmetric matter in the initial stages of heavy ion collisions. This study facilitates the understanding of the local equilibrium property of the medium through the Knudsen number, and explores the correlation between the heat flow and the charge flow through the Lorenz number in the Wiedemann-Franz law for an a…

Entanglement negativity in free fermions: twisted characteristic polynomial, universal bounds, and area laws
Ryota Matsuda, Zongping Gong
https://arxiv.org/abs/2507.20947 https:…

Entanglement negativity in free fermions: twisted characteristic polynomial, universal bounds, and area laws
We present a general and simple formula for computing the entanglement negativity in free fermions. Our formula allows for deriving several universal bounds on negativity and its rate of change in dynamics. The bound on negativity directly relates the clustering property of correlations in free-fermion states to the entanglement area law, and provides the optimal condition for the area law in mixed free fermion states with long-range correlations. In addition, we establish an area-law bound on …

Unconditional energy dissipation of Strang splitting for the matrix-valued Allen-Cahn equation
Chaoyu Quan, Tao Tang, Dong Wang
https://arxiv.org/abs/2508.03992 https://

Unconditional energy dissipation of Strang splitting for the matrix-valued Allen-Cahn equation
The energy dissipation property of the Strang splitting method was first demonstrated for the matrix-valued Allen-Cahn (MAC) equation under restrictive time-step constraints [J. Comput. Phys. 454, 110985, 2022]. In this work, we eliminate this limitation through a refined stability analysis framework, rigorously proving that the Strang splitting method preserves the energy dissipation law unconditionally for arbitrary time steps. The refined proof hinges on a precise estimation of the double-we…

On the surjectivity of the conditional expectation given a real random variable
Julien Guyon, Thibault Jeannin, Benjamin Jourdain
https://arxiv.org/abs/2508.02416 https://

On the surjectivity of the conditional expectation given a real random variable
In this paper, we investigate the distributions of random couples $(X,Y)$ with $X$ real-valued such that any non-negative integrable random variable $f(X)$ can be represented as a conditional expectation, $f(X)=\mathbb{E}[g(Y)|X]$, for some non-negative measurable function $g$. It turns out that this representation property is related to the smallness of the support of the conditional law of $X$ given $Y$, and in particular fails when this conditional law almost surely has a non-zero absol…

Additive properties and absorption laws for generalized inverses
Yukun Zhou, Jianlong Chen, Nestor Thome
https://arxiv.org/abs/2508.04363 https://arxiv.org…

Additive properties and absorption laws for generalized inverses
Let $a,~f$ be elements in a ring with pseudo core inverses $a^{\scriptsize\textcircled{\tiny D}}$, $f^{\scriptsize\textcircled{\tiny D}}$, and let $b=f-a$. We prove that the absorption law $a^{\scriptsize\textcircled{\tiny D}}(a+f)f^{\scriptsize\textcircled{\tiny D}}=a^{\scriptsize\textcircled{\tiny D}}+f^{\scriptsize\textcircled{\tiny D}}$ holds if and only if $1+a^{\scriptsize\textcircled{\tiny D}}b$ is invertible and the additive property $f^{\scriptsize\textcircled{\tiny D}}=(1+a^{\scriptsi…

Finland bans Russians, Belarusians from buying property over security concerns: https://benborges.xyz/2025/07/16/finland-bans-russians-belarusians-from.html

The Order of Physical Law
Ted Sichelman
https://arxiv.org/abs/2507.14145 https://arxiv.org/pdf/2507.14145

The Order of Physical Law
First-order legal relations specify the duties of legal actors. For instance, the duty not to trespass derives from a first-order law. Second-order legal relations generally concern the intentional, volitional acts of legal actors exercising legal powers to change first-order laws or legal relations. For example, a landowner may exercise a second-order power to change another legal actor's duty not to trespass into a legal permission to enter the landowner's property. This article adapts the no…

Eliciting reference measures of law-invariant functionals
Felix-Benedikt Liebrich, Ruodu Wang
https://arxiv.org/abs/2507.13763 https://arxiv.org/pdf/2507.1…

Eliciting reference measures of law-invariant functionals
Law-invariant functionals are central to risk management and assign identical values to random prospects sharing the same distribution under an atomless reference probability measure. This measure is typically assumed fixed. Here, we adopt the reverse perspective: given only observed functional values, we aim to either recover the reference measure or identify a candidate measure to test for law invariance when that property is not {\em a priori} satisfied. Our approach is based on a key observ…

#HotTake:
Liberalism is a syncretic religion where the highest deity is the State and all other deities are subject to it. Liberalism asserts this distinction by classifying political systems as deriving from "natural law" and religions as faith systems. Classical liberalism divided the world into "primitive" beliefs and "enlightened" beliefs. Atheistic anarchism aligns with this distinction by opposing the state and capitalism through logic, rather than asserting that the state and capitalism are themselves systems of faith. Atheistic anarchism further reinforces the narrative of the liberal state by aligning with the liberal understanding of religion as a "primitive" institution.
Graeber et al pointed out the connections between property rights as a form of fedishism (magic) and the evolution of currency, debt, taxes, and the state from temples.

Lorentz invariant materials and metamaterials
Jon Lasa-Alonso, Gabriel Molina-Terriza
https://arxiv.org/abs/2506.20784 https://arxiv.…

Lorentz invariant materials and metamaterials
We show that electromagnetic constitutive relations of materials, defined by a scalar permittivity, $\varepsilon$, and permeability, $μ$, are the same for all inertial observers provided that $\varepsilonμ= 1$ is satisfied. To highlight the practical power of our general result, we discuss schemes in which this property plays a significant role, such as Fresnel-Fizeau optical drag or modified Snell's law for moving dielectrics. We also proof that such a particular behavior can be extended to …

The Markov property for $\varphi^4_3$ on the cylinder
Nikolay Barashkov, Trishen S. Gunaratnam
https://arxiv.org/abs/2506.21466 https://

The Markov property for $φ^4_3$ on the cylinder
We prove that the $φ^4_3$ model satisfies a version of Segal's axioms in the special case of three-dimensional tori and cylinders. As a consequence, we give the first proof that this model satisfies a Markov property and we characterize its boundary law up to absolutely continuous perturbations. In addition, we use Segal's axioms to give an alternative construction of the $φ^4_3$ Hamiltonian on two-dimensional tori as compared with Glimm (Comm. Math. Phys., 1968). We exploit this probabilisti…

Electric field control of third-order nonlinear Hall effect
Jiaju Yang, Lujun Wei, Yanghui Li, Lina Chen, Wei Niu, Jiarui Chen, Jun Du, Yong Pu
https://arxiv.org/abs/2506.10657

Electric field control of third-order nonlinear Hall effect
The third-order nonlinear Hall effect (NLHE) serves as a sensitive probe of energy band geometric property, providing a new paradigm for revealing the Berry curvature distribution and topological response of quantum materials. In the Weyl semimetal TaIrTe4, we report for the first time that the sign of the third-order NLHE reverses with decreasing temperature. Through scaling law analysis, we think that the third-order NLHE at high (T > 23 K) and low (T < 23 K) temperatures is dominated by Berr…