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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://

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…

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

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.

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…

This https://arxiv.org/abs/2410.14205 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCR_…

Modelling 1/f Noise in TRNGs via Fractional Brownian Motion
Security of oscillatory true random number generators remains not fully understood due to insufficient understanding of complex $1/f^α$ phase noise. To bridge this gap, we introduce fractional Brownian motion as a comprehensive theoretical framework, capturing power-law spectral densities from white to flicker frequency noise. Our key contributions provide closed-form tractable solutions: (1) a quasi-renewal property showing conditional variance grows with power-law time dependence, enabling…

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…

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…

This https://arxiv.org/abs/2208.04506 has been replaced.
link: https://scholar.google.com/scholar?q=a

Second Order Ensemble Langevin Method for Sampling and Inverse Problems
We propose a sampling method based on an ensemble approximation of second order Langevin dynamics. The log target density is appended with a quadratic term in an auxiliary momentum variable and damped-driven Hamiltonian dynamics introduced; the resulting stochastic differential equation is invariant to the Gibbs measure, with marginal on the position coordinates given by the target. A preconditioner based on covariance under the law of the dynamics does not change this invariance property, and …

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 …