Tootfinder

Some results on spectra and certain norms
Danielle Witt
https://arxiv.org/abs/2510.04199 https://arxiv.org/pdf/2510.04199

Some results on spectra and certain norms
Given the norms of powers $(\lVert x^n\rVert)_{n\geq 0}$ of a Banach algebra element $x$, the largest possible value of the minimum modulus on the spectrum of $x$ is determined. It is also shown that, given a Banach algebra element $x$ and a compact set $K\subset\mathbb{C}$ with maximum modulus no more than the spectral radius of $x$, there exists a Banach algebra element $y$ with $\lVert y^n\rVert=\lVert x^n\rVert$ for all $n\geq 0$ and spectrum equal to the union of the spectrum of $x$ and $K…

Backward stochastic differential equations with nonlinear Young drivers II
Jian Song, Huilin Zhang, Kuan Zhang
https://arxiv.org/abs/2509.05183 https://arx…

Backward stochastic differential equations with nonlinear Young drivers II
This paper continues our previous work (Part I, arXiv:2504.18632v3) on the well-posedness of backward stochastic differential equations (BSDEs) involving a nonlinear Young integral of the form $\int_{t}^{T}g(Y_{r})η(dr,X_{r})$, with particular focus on the case where the driver $η(t,x)$ is unbounded. To address this setting, we develop a new localization method that extends solvability from BSDEs with bounded drivers to those with unbounded ones. As a direct application, we derive a nonlinear…

Spectropolarimetry of synchrotron radiation from relativistic electrons with anisotropic pitch-angle and various energy distributions
Paul C. W. Lai, Kaye J. Li, Y. X. Jane Yap, Kinwah Wu, Albert K. H. Kong
https://arxiv.org/abs/2509.04572

Spectropolarimetry of synchrotron radiation from relativistic electrons with anisotropic pitch-angle and various energy distributions
For synchrotron radiation from relativistic electrons having a power-law energy distribution with a power-law index $p$ in an optically thin medium with a locally uniform magnetic field, it is generally adopted that the spectral index $α= (p-1)/2$ and the degree of linear polarisation $Π_{\rm L,pl} = (p +1)/(p+7/3)$, and hence that $Π_{\rm L,pl} = (α+1)/(α+5/3)$. These ($α$, $Π_{\rm L,pl}$; $p$) relations are derived assuming that the electrons have an isotropic momentum distribution and…

Tracking Electron, Proton, and Solvent Motion in Proton-Coupled Electron Transfer with Ultrafast X-rays
Abdullah Kahraman, Michael Sachs, Soumen Ghosh, Benjamin I. Poulter, Estefan\'ia Sucre-Rosales, Elizabeth S. Ryland, Douglas Garratt, Sumana L. Raj, Natalia Powers-Riggs, Subhradip Kundu, Christina Y. Hampton, David J. Hoffman, Giacomo Coslovich, Georgi L. Dakovski, Patrick L. Kramer, Matthieu Chollet, Roberto A. Mori, Tim B. van Driel, Sang-Jun Lee, Kristjan Kunnus, Amy A. Cordo…

Tracking Electron, Proton, and Solvent Motion in Proton-Coupled Electron Transfer with Ultrafast X-rays
Proton-coupled electron transfer (PCET) is foundational to catalysis, bioenergetics, and energy conversion, yet capturing and disentangling the coupled motions of electrons, protons, and solvent has remained a major experimental challenge. We combine femtosecond optical spectroscopy, site-specific ultrafast soft X-ray absorption spectroscopy, and time-resolved X-ray scattering with advanced calculations to disentangle the elementary steps of PCET in solution. Using a ruthenium polypyridyl model…

Feebly Interacting Particles: FIPs at LHCb
J. Alimena, J. Boyd, G. Cacciapaglia, A. Casais Vidal, X. Cid Vidal, S. Collaviti, A. De Oyanguren Campos, G. Dalla Valle Garcia, G. Elor, G. Ferretti, D. Gorbunov, E. Goudzovski, J. Hajer, J. Jerhot, B. Kishor Jashal, V. Kholoimov, J. Klaric, F. Kling, E. Kriukova, Y. Kyselov, G. Lanfranchi, C. Langenbruch, A. Merli, M. Ovchinnykov, J. Pfaller, G. Perez, P. Reimitz, I. Sanderswood, L. Shchutska, E. Torro Pastor, Y. Tsai, A. Usachov, L. Vale S…

Feebly Interacting Particles: FIPs at LHCb
With the establishment and maturation of the experimental programs searching for new physics with sizeable couplings at the LHC, there is an increasing interest in the broader particle and astrophysics community for exploring the physics of light and feebly-interacting particles as a paradigm complementary to a New Physics sector at the TeV scale and beyond. FIPs@LHCb continues the successful series of the FIPs workshops, FIPs 2020 and FIPs 2022. The main focus of the workshop was to explore th…

Subgroup perfect codes of $S_n$ in Cayley sum graphs
Ankan Shaw, Biswajit Mondal, Satya Bagchi
https://arxiv.org/abs/2509.05069 https://arxiv.org/pdf/2509.…

Subgroup perfect codes of $S_n$ in Cayley sum graphs
A perfect code in a graph $Γ= (V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent, and every vertex in $V \setminus C$ is adjacent to exactly one vertex in $C$. Let $ G $ be a finite group, and let $ S $ be a square-free normal subset of $ G $. The Cayley sum graph of $ G $ with respect to $ S $ is a simple graph with vertex set $ G $ and two vertices $ x $ and $ y $ are adjacent if $ xy\in S .$ A subset $ C $ of $ G $ is called perfect code of $ G $ if there exists a …

Beyond Linear Diffusions: Improved Representations for Rare Conditional Generative Modeling
Kulunu Dharmakeerthi, Yousef El-Laham, Henry H. Wong, Vamsi K. Potluru, Changhong He, Taosong He
https://arxiv.org/abs/2510.02499

Beyond Linear Diffusions: Improved Representations for Rare Conditional Generative Modeling
Diffusion models have emerged as powerful generative frameworks with widespread applications across machine learning and artificial intelligence systems. While current research has predominantly focused on linear diffusions, these approaches can face significant challenges when modeling a conditional distribution, $P(Y|X=x)$, when $P(X=x)$ is small. In these regions, few samples, if any, are available for training, thus modeling the corresponding conditional density may be difficult. Recog…

A high-lying isomer in ^{92}Zr with lifetime modulated by the atomic charge states: a proposed approach for a nuclear gamma-ray laser
C. X. Jia, S. Guo, B. Ding, X. H. Zhou, C. X. Yuan, W. Hua J. G. Wang, S. W. Xu, C. M. Petrache, E. A. Lawrie, Y. B. Wu, Y. D. Fang, Y. H. Qiang, Y. Y. Yang, J. B. Ma, J. L. Chen, H. X. Chen, F. Fang, Y. H. Yu, B. F. Lv, F. F. Zeng, Q. B. Zeng, H. Huang, Z. H. Jia, W. Liang, W. Q. Zhang, J. H. Li, J. H. Xu, M. Y. Liu, Y. Zheng, Z. Bai, S. L. Jin, K. Wang…

A high-lying isomer in ^{92}Zr with lifetime modulated by the atomic charge states: a proposed approach for a nuclear gamma-ray laser
The nuclides ^{92}Zr are produced and transported by using a radioactive beam line to a lowbackground detection station. After a flight time of about 1.14 μs, the ions are implanted into a carbon foil, and four γ rays deexciting the 8+ state in ^{92}Zr are observed in coincidence with the implantation signals within a few nanoseconds. We conjecture that there exists an isomer located slightly above the 8^{+} state in ^{92}Zr. The isomeric lifetime in highly charged states is extended signific…

On entry-exit formulas for degenerate turning point problems in planar slow-fast systems
Renato Huzak, Kristian Uldall Kristiansen
https://arxiv.org/abs/2510.02770 https://

On entry-exit formulas for degenerate turning point problems in planar slow-fast systems
In this paper, we study degenerate entry-exit problems associated with planar slow-fast systems having an invariant line $\{(x,y)\,:\,y=0\}$ with a turning point at $x=0$. The degeneracy stems from the fact that the slow flow has a saddle-node of even order $2n$, $n\in \mathbb N$, at the turning point, i.e. $x' = -x^{2n}(1+o(1))$ for $ε=0$. We are motivated by the appearance of such turning point problems (for $n=1$) in the graphics $(I_2^1)$ and $(I_4^1)$, through a nilpotent saddle-node sing…

The inter-universal Teichm\"uller theory and new Diophantine results over rational numbers. II
Zhong-Peng Zhou
https://arxiv.org/abs/2510.05448 https://

The inter-universal Teichmüller theory and new Diophantine results over rational numbers. II
[This is an older version of the paper, which will be updated soon.] In the present paper, we continue our research on the generalized Fermat equation $x^r + y^s = z^t$ with signature $(r, s, t)$, where $r, s, t \ge 2$ are positive integers such that $\frac{1}{r} + \frac{1}{s} + \frac{1}{t} < 1$. All known positive primitive solutions for the generalized Fermat equation when $\frac{1}{r} + \frac{1}{s} + \frac{1}{t} < 1$ are related to the Catalan solutions $1^n + 2^3 = 3^2$ and nine non-Catal…

Bromine-methanol etching of semiconductor crystals $Cd_{1-x}Zn_{x}Te_{1-y}Se_{y}$ with different selenium concentrations
S. V. Naydenov, G. M. Babenko, O. K. Kapustnyk, I. M. Pritula
https://arxiv.org/abs/2509.24532

Bromine-methanol etching of semiconductor crystals $Cd_{1-x}Zn_{x}Te_{1-y}Se_{y}$ with different selenium concentrations
The effect of the selenium concentration in the composition of the $Cd_{1-x}Zn_{x}Te_{1-y}Se_{y}$ semiconductor crystals on their etching with a bromine-methanol solution was studied. A thermodynamic model is proposed to describe the degree of etching of $Cd_{1-x}Zn_{x}Te$ and $Cd_{1-x}Zn_{x}Te_{1-y}Se_{y}$ crystals. A thermodynamic law is obtained for the first time to describe the change in the etching rate of $Cd_{1-x}Zn_{x}Te_{1-y}Se_{y}$ crystals with different selenium concentrations. Exp…

Human brain high-resolution diffusion MRI with optimized slice-by-slice B0 field shimming in head-only high-performance gradient MRI systems
Patricia Lan, Sherry S. Huang, Chitresh Bhushan, Xinzeng Wang, Seung-Kyun Lee, Raymond Y. Huang, Jerome J. Maller, Jennifer A. McNab, Ante Zhu
https://arxiv.org/abs/2510.03586

Human brain high-resolution diffusion MRI with optimized slice-by-slice B0 field shimming in head-only high-performance gradient MRI systems
The purpose of this study is to propose a brain tissue-selective, optimized slice-by-slice B0 field shimming for high-resolution brain diffusion MRI. We incorporated actual gradient fields of X, Y, and Z gradient coils in the calculation of the shimming coefficients in dynamic slice-by-slice B0 field shimming to minimize B0 field inhomogeneity (i.e., Delta B0) in deep-learning segmented brain tissues. Diffusion MRI with oscillating gradient spin echo (OGSE) at 55 Hz and pulsed gradient spin ech…

Bimagnon dispersion of La2CuO4 probed by resonant inelastic X-ray scattering
A. Singh, H. Y. Huang, K. Tsutsui, T. Tohyama, S. Komiya, J. Okamoto, C. T. Chen, A. Fujimori, D. J. Huang
https://arxiv.org/abs/2510.02772

Bimagnon dispersion of La2CuO4 probed by resonant inelastic X-ray scattering
We report on the study of the magnetic excitations of Mott insulator La2CuO4 by using resonant inelastic x-ray scattering (RIXS) and cluster calculations within the framework of exact diagonalization. Our results demonstrate experimentally that the bimagnon excitation in Cu L-edge RIXS is enhanced if the incident x-ray energy is slightly above the absorption edge. Through incident-energy-dependent momentum-resolved RIXS, we investigated the excitation of the bimagnon with predominantly A1 symme…

Development of Deep Neural Network First-Level Hardware Track Trigger for the Belle II Experiment
Y. -X. Liu, T. Koga, H. Bae, Y. Yang, C. Kiesling, F. Meggendorfer, K. Unger, S. Hiesl, T. Forsthofer, A. Ishikawa, Y. Ahn, T. Ferber, I. Haide, G. Heine, C. -L. Hsu, A. Little, H. Nakazawa, M. Neu, L. Reuter, V. Savinov, Y. Unno, J. Yuan, Z. Xu
https://

Development of Deep Neural Network First-Level Hardware Track Trigger for the Belle II Experiment
The Belle II experiment at the SuperKEKB accelerator is designed to explore physics beyond the Standard Model with unprecedented luminosity. As the beam intensity increased, the experiment faced significant challenges due to higher beam-induced background, leading to a high trigger rate and placing limitations on further luminosity increases. To address this problem, we developed trigger logic for tracking using deep neural network (DNN) technology on an FPGA for the Belle II hardware trigger s…

Evolutionary Map of the Universe: Detection of the Wolf-Rayet Star WR40
A. C. Bradley, Z. J. Smeaton, M. D. Filipovic, N. F. H. Tothill, R. Z. E. Alsaberi, J. D. Collier, Y. A. Gordon, A. M. Hopkins, H. Zakir
https://arxiv.org/abs/2510.02615

Evolutionary Map of the Universe: Detection of the Wolf-Rayet Star WR40
We present a radio-continuum detection of the well-known Wolf-Rayet star WR40 at 943.5 MHz using observations from the EMU survey. We find that the shell surrounding WR40, known as RCW 58, has a flux density of 158.9+/-15.8 mJy and the star itself is 0.41+/-0.04 mJy. The shell size is found to be 9' x 6', which matches well with the shell in Halpha and is similarly matched to the shell at 22 um in infrared. Using Gaia data, we derive a linear size of 7.32(+/-0.34) x 4.89(+/-0.23) pc at a distan…

A Generalized $\chi_n$-Function
Cheng Lyu, Mu Yuan, Dabin Zheng, Siwei Sun, Shun Li
https://arxiv.org/abs/2509.20880 https://arxiv.org/pdf/2509.20880

A Generalized $χ_n$-Function
The mapping $χ_n$ from $\F_{2}^{n}$ to itself defined by $y=χ_n(x)$ with $y_i=x_i+x_{i+2}(1+x_{i+1})$, where the indices are computed modulo $n$, has been widely studied for its applications in lightweight cryptography. However, $χ_n $ is bijective on $\F_2^n$ only when $n$ is odd, restricting its use to odd-dimensional vector spaces over $\F_2$. To address this limitation, we introduce and analyze the generalized mapping $χ_{n, m}$ defined by $y=χ_{n,m}(x)$ with $y_i=x_i+x_{i+m} (x_{i+m-1…

Automorphism Groups of the $PSL_2(q)$ Commuting Involution Graphs
James Bryden, Peter Rowley
https://arxiv.org/abs/2509.25901 https://arxiv.org/pdf/2509.25…

Automorphism Groups of the $PSL_2(q)$ Commuting Involution Graphs
Given a finite group $G$ and a conjugacy class of involutions $X$ of $G$, we define the commuting involution graph $\mathcal{C}(G,X)$ to be the graph with vertex set $X$ and $x,y \in X$ adjacent if and only if $x \neq y$ and $xy =yx$. In this paper the automorphism group of the graph $\mathcal{C}(G,X)$ is determined when $G = PSL_2(q)$.

Decoherence mitigation for geometric quantum computation
X. Y. Sun, P. Z. Zhao
https://arxiv.org/abs/2509.03856 https://arxiv.org/pdf/2509.03856

Decoherence mitigation for geometric quantum computation
Geometric phases depend only on the evolution path determined by the closed circuit in the projective Hilbert space but not on evolution details of the quantum system, leading to geometric quantum computation possessing some intrinsic robustness against control errors. Coordinated with dynamical decoupling, geometric quantum computation admits additional resilience to the environment-induced decoherence. However, the previous schemes of geometric quantum computation protected by dynamical decou…

Correlation-driven 3d Heavy Fermion behavior in LiV2O4
Min-Yi-Nan Lei, Z. H. Chen, H. T. Wang, Y. Fan, N. Guo, T. X. Jiang, Yanwei Cao, T. Zhang, Rui Peng, Haichao Xu
https://arxiv.org/abs/2509.05237

Correlation-driven 3d Heavy Fermion behavior in LiV2O4
LiV2O4 is a spinel-structured compound that stands out as the first known 3d-electron system exhibiting typical heavy fermion behavior. A central question is how such strong mass renormalization emerges in the absence of f-electrons. In this work, we investigate the three-dimensional electronic structure of LiV2O4 thin films using angle-resolved photoemission spectroscopy (ARPES). We identify that an electron-like flat band is derived from a1g orbitals, along with a highly dispersive e'g band s…

Rapid onset of a Comptonisation zone in the repeating tidal disruption event XMMSL2 J140446.9-251135
R. D. Saxton, T. Wevers, S. van Velzen, K. Alexander, Z. Liu, A. Mummery, M. Giustini, G. Miniutti, F. Fuerst, J. J. E. Kajava, A. M. Read, P. G. Jonker, A. Rau, D. -Y. Li
https://arxiv.org/abs/2510.02905

Rapid onset of a Comptonisation zone in the repeating tidal disruption event XMMSL2 J140446.9-251135
We report here on observations of a tidal disruption event, XMMSL2 J1404-2511, discovered in an XMM-Newton slew, in a quiescent galaxy at z=0.043. X-ray monitoring covered the epoch when the accretion disc transitioned from a thermal state, with kT~80 eV, to a harder state dominated by a warm, optically-thick corona. The bulk of the coronal formation took place within 7 days and was coincident with a temporary drop in the emitted radiation by a factor 4. After a plateau phase of ~100 days, the …

Level sets of the Takagi function
Lai Jiang, Ting-Ting Ying, Yi-Yang Zhang
https://arxiv.org/abs/2508.21683 https://arxiv.org/pdf/2508.21683

Level sets of the Takagi function
In this paper, we investigate the Takagi function, $$ T_r(x) = \sum_{n=0}^{\infty} \frac{ϕ(r^n x)}{r^n} ,\quad x\in [0,1], \quad r \in \mathbb{Z}^+, $$ where $ϕ(x)={\rm dist}(x,\mathbb{Z})$ represents the distance from $x$ to the nearest integer. We generalize the concept of local level sets and find that the expected number of local level sets contained in a level set $L_r(y)$, with $y$ chosen at random, is $1 + 1/r$ for every even integer $r \geq 2$.

The failure of the Ehlers--Kundt conjecture in the impulsive case
Moriz L. Frauenberger, James D. E. Grant, Roland Steinbauer
https://arxiv.org/abs/2509.24989 https://

The failure of the Ehlers--Kundt conjecture in the impulsive case
In 1962, Ehlers and Kundt conjectured that plane waves are the only class of complete Ricci-flat~\emph{pp}-waves, i.e.\ metrics on ${\mathbb R}^4$ of the form \[ ds^2=2du\,dv+dx^2+dy^2+H(x,y,u)du^2\,. \] Recently, Flores and Sánchez gave a proof of the conjecture in the fundamental case of spatially polynomially bounded profile functions $H$. However, impulsive pp-waves, i.e., waves with concentrated profile functions of the form $H(x,y,u)=f(x,y)\,δ(u)$ ($δ$, the Dirac measure) have been fou…

I never knew Nintendo's X and Y buttons were named after vector components.
https://bsky.app/profile/did:plc:lxj6fo7atoir35pvn3idij42/post/3lzr3ij3rvk2w via Time Extension.

Finding the diameter of a tree with distance queries
D\'aniel Gerbner, Andr\'as Imolay, Kartal Nagy, Bal\'azs Patk\'os, Krist\'of Z\'olomy
https://arxiv.org/abs/2509.23326

Finding the diameter of a tree with distance queries
We study the number of distance queries needed to identify certain properties of a hidden tree $T$ on $n$ vertices. A distance query consists of two vertices $x,y$, and the answer is the distance of $x$ and $y$ in $T$. We determine the number of queries an optimal adaptive algorithm needs to find two vertices of maximal distance up to an additive constant, and the number of queries needed to identify the hidden tree asymptotically. We also study the non-adaptive versions of these problems, dete…

Closed-form $\ell_r$ norm scaling with data for overparameterized linear regression and diagonal linear networks under $\ell_p$ bias
Shuofeng Zhang, Ard Louis
https://arxiv.org/abs/2509.21181

Closed-form $\ell_r$ norm scaling with data for overparameterized linear regression and diagonal linear networks under $\ell_p$ bias
For overparameterized linear regression with isotropic Gaussian design and minimum-$\ell_p$ interpolator $p\in(1,2]$, we give a unified, high-probability characterization for the scaling of the family of parameter norms $ \\{ \lVert \widehat{w_p} \rVert_r \\}_{r \in [1,p]} $ with sample size. We solve this basic, but unresolved question through a simple dual-ray analysis, which reveals a competition between a signal *spike* and a *bulk* of null coordinates in $X^\top Y$, yielding closed-form …

Diameter Bounds for Friends-and-Strangers Graphs
Amogh Akella, Rupert Li
https://arxiv.org/abs/2509.23511 https://arxiv.org/pdf/2509.23511

Diameter Bounds for Friends-and-Strangers Graphs
Consider two $n$-vertex graphs $X$ and $Y$, where we interpret $X$ as a social network with edges representing friendships and $Y$ as a movement graph with edges representing adjacent positions. The friends-and-strangers graph $\mathsf{FS}(X,Y)$ is a graph on the $n!$ permutations $V(X)\to V(Y)$, where two configurations are adjacent if and only if one can be obtained from the other by swapping two friends located on adjacent positions. Friends-and-strangers graphs were first introduced by De…

Vestigial $d$-wave charge-$4e$ Superconductivity from Bidirectional Pair Density Waves
Ethan Huecker, Yuxuan Wang
https://arxiv.org/abs/2510.05209 https://…

Vestigial $d$-wave charge-$4e$ Superconductivity from Bidirectional Pair Density Waves
We analyze the leading vestigial instability due to the melting of a bidirectional pair-density-wave state in two dimensions. In a previous work by one of the authors, it was found that the interplay between pair-density-wave fluctuations with ordering momenta along the $x$ and $y$ directions can provide a strong attractive interaction for charge-$4e$ superconductivity in the $d$-wave channel. In this work, we go beyond the artificial large-$M$ mean-field theory previously adopted and compute t…

Primes of the form $ax by$ in certain intervals with small solutions
Yuchen Ding, Takao Komatsu, Honghu Liu
https://arxiv.org/abs/2510.01781 https://arxiv.…

Primes of the form $ax+by$ in certain intervals with small solutions
Let $1

The \'etale fundamental group and $F$-divided sheaves in characteristic $p>0$
Xiaotao Sun, Lei Zhang
https://arxiv.org/abs/2509.24360 https://arxiv.…

The étale fundamental group and $F$-divided sheaves in characteristic $p>0$
We investigate how the étale fundamental group controls local systems in characteristic $p$, namely $F$-divided sheaves. In analogy with Grothendieck-Malcev's results for discrete groups, we show that if a morphism $f \colon Y \to X$ of smooth projective varieties over $k=\bar{k}$ induces a surjection on the étale fundamental groups, then the pullback functor ${\rm Fdiv}(X)\to {\rm Fdiv}(Y)$ is fully faithful. If $f$ is surjective and the induced map is an isomorphism, then the functor is an …

On the Performance of Amplitude-Based Models for Low-Rank Matrix Recovery
Huanmin Ge, Zhiqiang Xu
https://arxiv.org/abs/2509.24699 https://arxiv.org/pdf/25…

On the Performance of Amplitude-Based Models for Low-Rank Matrix Recovery
In this paper, we focus on low-rank phase retrieval, which aims to reconstruct a matrix $\mathbf{X}_0\in \mathbb{R}^{n\times m}$ with ${\mathrm{ rank}}(\mathbf{X}_0)\le r$ from noise-corrupted amplitude measurements $\mathbf{y}=|\mathcal{A}(\mathbf{X}_0)|+\boldsymbolη$, where $\mathcal{A}:\mathbb{R}^{n\times m}\rightarrow \mathbb{R}^{p}$ is a linear map and $\boldsymbolη\in \mathbb{R}^p$ is the noise vector. We first examine the rank-constrained nonlinear least-squares model $\hat{\…

Very cool population genomic look into local adaptation against gene flow at a relatively small spatial scale, urban/rural gradients across metro Toronto in this month's @…
Signatures of selective sweeps in urban and rural white clover populations

Properties of Selector Proofs
Elijah Gadsby
https://arxiv.org/abs/2509.19373 https://arxiv.org/pdf/2509.19373

Properties of Selector Proofs
A serial property is a suitably enumerated sequence $\{F_n\}$ of formulas and is called selector provable in PA if there is a PA-recursive function $s(x)$ such that PA $\vdash \forall x (s(x){:}_{\text{PA}} \ulcorner F_x\urcorner)$ where $x{:}_{\text{PA}} y$ is a suitable proof predicate. These notions were introduced by Artemov in his analysis of consistency and the formalisation of metamathematics. These matters aside, the notion is intimately connected with that of relative consistency. Th…

Negative Lyapunov exponent of circle maps forced by expanding circle endomorphisms
Kirthana Rajasekar
https://arxiv.org/abs/2508.21645 https://arxiv.org/pd…

Negative Lyapunov exponent of circle maps forced by expanding circle endomorphisms
We study maps on the torus $\mathbb{T}^2$ that are of the form $F(x,y) = (bx, f_x(y))$, where $b\geq 2$ is an integer. We establish an open class of $C^1$-maps, with $f_x(y)$ that are typically non-monotonic in $x$, for which the Lyapunov exponents on the fibre are negative almost everywhere. For each fixed $f_x(y)$ and a base map $bx$ that is sufficiently expanding, we establish a uniform upper bound for the Lyapunov exponents; moreover, the uniform bound depends on selective characteristics o…

Speculative politics
As an anarchist (okay, maybe not in practice), I'm tired of hearing why we have to suffer X and Y indignity to "preserve the rule of law" or "maintain Democratic norms." So here's an example of what representative democracy (a form of government that I believe is inherently flawed) could look like if its proponents had even an ounce of imagination, and/or weren't actively trying to rig it to favor a rich donor class:
1. Unicameral legislature, where representatives pass laws directly. Each state elects 3 statewide representatives: the three most-popular candidates in a statewide race where each person votes for one candidate (ranked preference voting would be even better but might not be necessary, and is not a solution by itself). Instead of each representative getting one vote in the chamber, they get N votes, where N is the number of people who voted for them. This means that in a close race, instead of the winner getting all the power, the power is split. Having 3 representatives trades off between leisure size and ensuring that two parties can't dominate together.
2. Any individual citizen can contact their local election office to switch or withdraw their vote at any time (maybe with a 3-day delay or something). Voting power of representatives can thus shift even without an election. They are limited to choosing one of the three elected representatives, or "none of the above." If the "none of the above" fraction exceeds 20% of eligible voters, a new election is triggered for that state. If turnout is less than 80%, a second election happens immediately, with results being final even at lower turnout until 6 months later (some better mechanism for turnout management might be needed).
3. All elections allow mail-in ballots, and in-person voting happens Sunday-Tuesday with the Monday being a mandatory holiday. (Yes, election integrity is not better in this system and that's a big weakness.)
4. Separate nationwide elections elect three positions for head-of-state: one with diplomatic/administrative powers, another with military powers, and a third with veto power. For each position, the top three candidates serve together, with only the first-place winner having actual power until vote switches or withdrawals change who that is. Once one of these heads loses their first-place status, they cannot get it again until another election, even if voters switch preferences back (to avoid dithering). An election for one of these positions is triggered when 20% have withdrawn their votes, or if all three people initially elected have been disqualified by losing their lead in the vote count.
5. Laws that involve spending money are packaged with specific taxes to pay for them, and may only be paid for by those specific revenues. Each tax may be opted into or out of by each taxpayer; where possible opting out of the tax also opts you out of the service. (I'm well aware of a lot of the drawbacks of this, but also feel like they'd not necessarily be worse than the drawbacks of our current system.) A small mandatory tax would cover election expenses.
6. I'm running out of attention, but similar multi-winner elections could elect panels of judges from which a subset is chosen randomly to preside in each case.
Now I'll point out once again that this system, in not directly confronting capitalism, racism, patriarchy, etc., is probably doomed to the same failures as our current system. But if you profess to want a "representative democracy" as opposed to something more libratory, I hope you'll at least advocate for something like this that actually includes meaningful representation as opposed to the current US system that's engineered to quash it.
Key questions: "Why should we have winner-take-all elections when winners-take-proportionately-to-votes is right there?" and "Why should elected officials get to ignore their constituents' approval except during elections, when vote-withdrawal or -switching is possible?"
2/2
#Democracy

On Optimal Markovian Couplings of Levy Processes
Wei Yang Kang, Tau Shean Lim
https://arxiv.org/abs/2509.23086 https://arxiv.org/pdf/2509.23086

On Optimal Markovian Couplings of Levy Processes
We study the optimal Markovian coupling problem for two Pi-valued Feller processes {X_t} and {Y_t}, which seeks a coupling process {(X_t, Y_t)} that minimizes the right derivative at t = 0 of the expected cost E^{(x,y)}[c(X_t, Y_t)], for all initial states (x,y) in Pi^2 and a given cost function c on Pi. This problem was first formulated and solved by Chen (1994) for drift-diffusion processes and later extended by Zhang (2000) to Markov processes with bounded jumps. In this work, we resolve the…

Architecture of planetary systems with and without outer giant planets I. Inner planet detections around HD 23079, HD 196067, and HD 86226
J. -B. Delisle, J. P. Faria, D. S\'egransan, E. Fontanet, W. Ceva, D. Barbato, S. G. Sousa, N. Unger, A. Leleu, F. Bouchy, M. Cretignier, R. F. D\'iaz, X. Dumusque, Y. G. C. Frensch, N. C. Hara, G. Laughlin, G. Lo Curto, C. Lovis, M. Marmier, M. Mayor, L. Mignon, C. Mordasini, F. Pepe, N. C. Santos, S. Udry

Architecture of planetary systems with and without outer giant planets I. Inner planet detections around HD 23079, HD 196067, and HD 86226
Understanding the link between outer giant planets (OGPs) and inner light planets (ILPs) is key to understanding planetary system formation and architecture. The correlation between these two populations of planets is debated both theoretically -- different formation models predict either a correlation or an anticorrelation -- and observationally. Several recent attempts to constrain this correlation have yielded contradictory results, due to small-number statistics and heterogeneous samples. W…

Necessary and Sufficient Conditions for the Maz'ya-Shaposhnikova Formula in (Fractional) Sobolev Spaces
Elisa Davoli, Giovanni Di Fratta, Rossella Giorgio, Andrea Pinamonti
https://arxiv.org/abs/2509.23226

Necessary and Sufficient Conditions for the Maz'ya-Shaposhnikova Formula in (Fractional) Sobolev Spaces
We investigate the asymptotic behavior, as $\varepsilon \to 0$, of nonlocal functionals $$ \mathcal{F}_{\varepsilon}(u) = \iint_{\mathbb{R}^N\times\mathbb{R}^N} ρ_{\varepsilon}(y-x)\,|u(x)-u(y)|^p\,dx\,dy,\qquad u\in L^p(\mathbb{R}^N),\quad 1\leqslant p<\infty, $$ associated with a general family of nonnegative measurable kernels $\{ρ_{\varepsilon}\}_{\varepsilon>0}$. Our primary aim is to single out the weakest moment-type assumptions on the family $\{ρ_{\varepsilon}\}_{\varepsi…

A characterization of a class of border continuous triangular conorms
Zhi-qiang Lai, Xue-ping Wang
https://arxiv.org/abs/2509.24190 https://arxiv.org/pdf/2…

A characterization of a class of border continuous triangular conorms
Let $T^*:[0,1]^2\rightarrow[0,1]$ be a continuous, non-decreasing and associative function with neutral element, $f: [0,1]\rightarrow [0,1]$ be a strictly monotone function and $f^{(-1)}:[0,1]\rightarrow[0,1]$ be the pseudo-inverse of $f$. This article characterizes the function $T: [0,1]^2 \rightarrow [0,1]$ defined by $T(x,y)=f^{(-1)}(T^*(f(x),f(y)))$ when it is a border continuous triangular conorm.

Generalized ODE reduction algorithm with bounded degree transformation
Shaoxuan Huang
https://arxiv.org/abs/2508.09754 https://arxiv.org/pdf/2508.09754

Generalized ODE reduction algorithm with bounded degree transformation
As a generalization of our previous result\cite{huang2025algorithm}, this paper aims to answer the following question: Given a 2-dimensional polynomial vector field $y^{\prime}=\frac{M(x,y)}{N(x,y)}$, how to find a rational transformation $y \to \frac{A(x,y)}{B(x,y)}$ with bounded degree numerator, the inverse of which transforms this vector field into a simpler form $y^{\prime}=\sum_{i=0}^nf_i(x)y^i$. Such a structure, often known as the generalized Abel equation and has been studied in variou…

JWST Observations of Starbursts: PAHs Closely Trace the Cool Phase of M82's Galactic Wind
Sebastian Lopez, Colton Ring, Adam K. Leroy, Serena A. Cronin, Alberto D. Bolatto, Laura A. Lopez, Vicente Villanueva, Deanne B. Fisher, Todd A. Thompson, Lee Armus, Torsten Boeker, Leindert A. Boogaard, Martha L. Boyer, Ryan Chown, Daniel A. Dale, Keaton Donaghue, Kimberly Emig, Simon C. O. Glover, Rodrigo Herrera-Camus, Ralf S. Klessen, Thomas S. -Y. Lai, Laura Lenkic, Rebecca C. Levy, David…

JWST Observations of Starbursts: PAHs Closely Trace the Cool Phase of M82's Galactic Wind
Stellar feedback drives multiphase gas outflows from starburst galaxies, but the interpretation of dust emission in these winds remains uncertain. To investigate this, we analyze new JWST mid-infrared images tracing polycyclic aromatic hydrocarbon (PAH) emission at 7.7 and 11.3~$μ$m from the outflow of the prototypical starburst M82 out to $3.2$ kpc. We find that PAH emission shows significant correlations with CO, H$α$, and X-ray emission within the outflow, though the strengths and behavior…

Fast, low noise CCD systems for future strategic x-ray missions
Haley R. Stueber, Abigail Y. Pan, Tanmoy Chattopadhyay, Steven W. Allen, Marshall W. Bautz, Kevan Donlon, Catherine E. Grant, Sven Herrmann, Beverly J. LaMarr, Andrew Malonis, Eric D. Miller, R. Glenn Morris, Peter Orel, Artem Poliszczuk, Gregory Y. Prigozhin, Daniel R. Wilkins
https://

Fast, low noise CCD systems for future strategic x-ray missions
Future strategic X-ray missions, such as the Advanced X-ray Imaging Satellite (AXIS) and those targeted by the Great Observatories Maturation Program (GOMaP), require fast, low-noise X-ray imaging spectrometers. To achieve the speed and noise capabilities required by such programs, the X-ray Astronomy and Observational Cosmology (XOC) Group at Stanford, in collaboration with the MIT Kavli Institute (MKI) and MIT Lincoln Laboratory (MIT-LL), is developing readout systems that leverage the high s…

Interaction-limited conductivity of twisted bilayer graphene revealed by giant terahertz photoresistance
A. L. Shilov, M. Kravtsov, J. Covey, M. A. Kashchenko, O. Popova, X. Zhou, I. Yahniuk, T. Taniguchi, K. Watanabe, A. I. Berdyugin, Y. Wang, S. D. Ganichev, V. Perebeinos, D. A. Svintsov, A. Principi, K. S. Novoselov, D. L. Maslov, D. A. Bandurin
https://

Interaction-limited conductivity of twisted bilayer graphene revealed by giant terahertz photoresistance
Identifying the microscopic processes that limit conductivity is essential for understanding correlated and quantum-critical states in quantum materials. In twisted bilayer graphene (TBG) and other twist-controlled materials, the temperature dependence of metallic resistivity follows power-law scaling, with the exponent spanning a broad range, rendering standard transport measurements insufficient to unambiguously identify the dominant scattering processes and giving rise to competing interpret…

Critical dynamics and superconducting state preparation in the quenched Kitaev chain with pairing imbalance
Y. B. Shi, Y. X. Zhang, S. W. Liu, Z. Song
https://arxiv.org/abs/2509.21540

Critical dynamics and superconducting state preparation in the quenched Kitaev chain with pairing imbalance
The dynamical balance of the pairing term plays a crucial role in the emergence of topological superconductivity in the p-wave spinless Kitaev chain, particularly in the non-Hermitian regime. In this work, we systematically investigate the effects of non-Hermitian pairing terms on both equilibrium and nonequilibrium phenomena in the Kitaev chain. Our analysis focuses on two representative forms of pairing imbalance: uniform and staggered. We demonstrate that a uniform imbalance induces only min…

Explicit Constructions of Maximal 3-Zero-Sum-Free Subsets in $(\mathbb{Z}/4\mathbb{Z})^n$
Alfonso Davila Vera
https://arxiv.org/abs/2509.01735 https://arxi…

Explicit Constructions of Maximal 3-Zero-Sum-Free Subsets in $(\mathbb{Z}/4\mathbb{Z})^n$
We address Nathan Kaplan's 2014 CANT problem: the largest $H \subseteq (\mathbb{Z}/4\mathbb{Z})^n$ with no distinct $x, y, z \in H$ such that $x + y + z \equiv 0 \pmod{4}$. A universal optimal construction, $H = \{ v \mid v_1 \equiv 1 \text{ or } 3 \pmod{4} \}$, achieves size $4^n/2$ and density 0.5 for all $n$, proven maximal via $|H|^2 \leq (4^n - |H|) \cdot |H|$. Verified computationally to $n=10$; code at https://github.com/DynMEP/ZeroSumFreeSets-Z4/releases/ta…

Can the AI bubble please burst next week at the latest?
I'm already done with faculty talk praising AI this and AI that and forcing teaching to fully go tech-bro-style. Next term starts September 15, I just don’t want to set up “AI-safe exams” and having students use AI for everything at the same time
Oh, and don’t be so negative, we’re all using X and Y and the newest Z, it’s awesome! It just hallucinate or lies a bit, but so friendly, the nice bot, don’t you see? Magic!

Convex Order and Arbitrage
Erica Zhang
https://arxiv.org/abs/2510.01599 https://arxiv.org/pdf/2510.01599

Convex Order and Arbitrage
Wiesel and Zhang [2023] established that two probability measures $μ,ν$ on $\mathbb{R}^d$ with finite second moments are in convex order (i.e. $μ\preceq_c ν$) if and only if $W_2(ν,ρ)^2-W_2(μ,ρ)^2 \leq \int |y|^2ν(dy) - \int |x|^2μ(dx).$ Let us call a measure $ρ$ maximizing $W_2(ν,ρ)^2-W_2(μ,ρ)^2$ the optimal $ρ$. This paper summarizes key findings by Wiesel and Zhang, develops new algorithms enhancing the search of optimal $ρ$, and builds on the paper throu…

Heat kernel asymptotics and analytic torsion on non-degenerate CR manifolds
Chin-Yu Hsiao, Rung-Tzung Huang, Guokuan Shao
https://arxiv.org/abs/2509.19167 https://

Finally a useful magic quadrant
Thanks to @… for the discovery.
#cybersecurity #vulnerability

Some results on the ideal-based cozero-divisor graph of a commutative ring
F. Farshadifar
https://arxiv.org/abs/2508.13222 https://arxiv.org/pdf/2508.13222…

Some results on the ideal-based cozero-divisor graph of a commutative ring
Let R be a commutative ring with identity and I be an ideal of R. The cozero-divisor graph with respect to I, denoted by $Γ''_I(R)$, is the graph of R with vertices {x \in R -I :xR +I \not=R} and two distinct vertices $x$ and $y$ are adjacent if and only if $x \not \in yR+I$ and $y \not \in xR+I$.In this paper, we obtained some results on $Γ''_I(R)$.

Constructing crowded Hausdorff $P$-spaces in set theory without the axiom of choice
Eleftherios Tachtsis, Eliza Wajch
https://arxiv.org/abs/2510.11935 https://

Constructing crowded Hausdorff $P$-spaces in set theory without the axiom of choice
For an infinite set $X$, a closed under finite unions family $\mathcal{Z}$ with $[X]^{<ω}\subseteq\mathcal{Z}\subseteq\mathcal{P}(X)$, and any $\mathcal{A}\subseteq\mathcal{P}(X)$, the topology $τ_{\mathcal{A}}[\mathcal{Z}]=\{V\in\mathcal{A}: (\forall x\in V)(\exists z\in \mathcal{Z})(x\cap z=\emptyset \wedge \{y\in\mathcal{A}: x\subseteq y\subseteq X\setminus z\}\subseteq V)\}$ on $\mathcal{A}$ is investigated to give answers to the following open problem in various models of $\mathbf{ZF}$ o…

High-quality Tungsten-doped Vanadium Dioxide Thin Films Fabricated in an Extremely Low-oxygen Furnace Environment
Vishwa Krishna Rajan, Ken Araki, Robert Y. Wang, Liping Wang
https://arxiv.org/abs/2509.01956

High-quality Tungsten-doped Vanadium Dioxide Thin Films Fabricated in an Extremely Low-oxygen Furnace Environment
This work reports the fabrication and characterization of high-quality tungsten-doped vanadium dioxide (WxV1-xO2, x = 0~3 at. %) by thermal oxidation of sputtered tungsten-vanadium alloyed thin films with different atomic percentages and high-temperature annealing in an extremely low oxygen atmosphere (5 to 20 ppm) along with reduction of surface over-oxides in high vacuum (1 mPa). Oxidation parameters such as temperature, time and nitrogen purging rate are first optimized for obtaining high qu…

Tree covers of size $2$ for the Euclidean plane
Artur Bikeev, Andrey Kupavskii, Maxim Turevskii
https://arxiv.org/abs/2508.16875 https://arxiv.org/pdf/2508…

Tree covers of size $2$ for the Euclidean plane
For a given metric space $(P,ϕ)$, a tree cover of stretch $t$ is a collection of trees on $P$ such that edges $(x,y)$ of trees receive length $ϕ(x,y)$, and such that for any pair of points $u,v\in P$ there is a tree $T$ in the collection such that the induced graph distance in $T$ between $u$ and $v$ is at most $tϕ(u,v).$ In this paper, we show that, for any set of points $P$ on the Euclidean plane, there is a tree cover consisting of two trees and with stretch $O(1).$ Although the problem i…

Tonight comet #Lemmon was picked up by several wide-angle webcams in Europe: https://x.com/JAtanackov/status/1977456751831093352 at the Raxalpe in Austria (left) and https://bsky.app/profile/huubeggen.bsky.social/post/3m2zhian3722b in Abisko, Sweden, together with aurora. Its brightness - https://cobs.si/obs_list?id=2606 - is around 5.2 mag. now and the degree of condensation 5 to 7, so for these cameras the comets looks like a slightly fuzzy green five-mag. star.

The Path-product in Morse Homology with differential graded coefficients
Robin Riegel (IRMA)
https://arxiv.org/abs/2508.09583 https://arxiv.org/pdf/2508.09…

The Path-product in Morse Homology with differential graded coefficients
We will use the tools developed in [Rie24] to give a Morse-theoretic description of a string topology product on the homology of the space of paths in a manifold Y with endpoints in a submanifold X and a module structure on this homology over the Chas-Sullivan ring of Y . These operations have been defined and studied by Stegemeyer in [Ste25] in singular homology.

Search for a new scalar resonance decaying to a Higgs boson and another new scalar particle in the final state with two bottom quarks and two photons in proton-proton collisions at $\sqrt{s}$ = 13 TeV
CMS Collaboration
https://arxiv.org/abs/2508.11494

Search for a new scalar resonance decaying to a Higgs boson and another new scalar particle in the final state with two bottom quarks and two photons in proton-proton collisions at $\sqrt{s}$ = 13 TeV
A search is presented for a new scalar resonance, X, decaying to a standard model Higgs boson and another new scalar particle, Y, in the final state where the Higgs boson decays to a $\mathrm{b\bar{b}}$ pair, while the Y particle decays to a pair of photons. The search is performed in the mass range 240$-$100 \GeV for the resonance X, and in the mass range 70$-$800 GeV for the particle Y, using proton-proton collision data collected by the CMS experiment at $\sqrt{s}$ = 13 TeV, corresponding to…

Purely exponential Diophantine equations with four terms of consecutive bases: contribution to Skolem's conjecture
Maohua Le, Takafumi Miyazaki
https://arxiv.org/abs/2508.17601

Purely exponential Diophantine equations with four terms of consecutive bases: contribution to Skolem's conjecture
We study purely exponential Diophantine equations with four terms of consecutive bases. Notably, we prove that all solutions to the equation \[ n^x=(n+1)^y+(n+2)^z+(n+3)^w \] in positive integers $n,x,y,z$ and $w$ are given by $(n,x,y,z,w)=(2,5,1,1,2)$, $(3,3,2,1,1)$. Our proof of this result for each $n \ge 4$ provides an explicit modulus $M$ such that the corresponding equation has no solution already modulo $M$. This contributes to a classical problem posed by T. Skolem in 1930's on a local-…

Translates in Step-Two SI/Z Nilpotent Groups
Vignon Oussa
https://arxiv.org/abs/2508.18529 https://arxiv.org/pdf/2508.18529

Translates in Step-Two SI/Z Nilpotent Groups
We prove a linear--independence principle for finite families of translates in irreducible, square--integrable modulo the center (SI/Z) representations of step--two nilpotent Lie groups with one--dimensional center. Fix a one--parameter subgroup $\exp(\mathbb R X)$ and a noncentral element $Y$ (not assumed to commute with $X$). For every nonzero smooth vector $f$, any finite collection $\{π(\exp(x_k X))f\}_{k=1}^m$ of translates along $\exp(\mathbb R X)$, together with the single translate $π…

A Note on the formulation of the Neumann boundary condition for a nonlocal problem
Antonio Luiz Pereira
https://arxiv.org/abs/2509.16041 https://arxiv.org/…

A Note on the formulation of the Neumann boundary condition for a nonlocal problem
The nonlocal diffusion equation with continuous kernel $K(x,y$, with $ \int_{R} K(y,x) \, d \, y = 1$ has been proposed as a model for some evolution process with diffusion, including population models. However, in general, we don't have $ \int_Ω K(y,x) \, d \, y = 1$, as expected from its interpretation as a probability density. In this note, we propose a modification of the kernel, based on the idea of `reflection' at the boundary, familiar in one dimensional problems. We show that a sim…

A non-sequential arithmetical theory with pairing
Juvenal Murwanashyaka
https://arxiv.org/abs/2509.15191 https://arxiv.org/pdf/2509.15191

A non-sequential arithmetical theory with pairing
Albert Visser has shown that Robinson's $ \mathsf{Q} $ and Gregorczyk's $ \mathsf{TC} $ are not sequential by showing that these theories are not even poly-pair theories, which, in a strong sense, means these theories lack pairing. In this paper, we use Ehrenfeucht-Fraïssé games to show that the theory $ \mathsf{Q} + Θ$ we obtain by extending Robinson's $ \mathsf{Q} $ with an axiom $ Θ$ which says that the map $ π(x, y ) = (x+y)^2 + x $ is a pairing function is not sequential; in fact, we …

New Algorithmic Directions in Optimal Transport and Applications for Product Spaces
Salman Beigi, Omid Etesami, Mohammad Mahmoody, Amir Najafi
https://arxiv.org/abs/2509.21502 h…

New Algorithmic Directions in Optimal Transport and Applications for Product Spaces
We study optimal transport between two high-dimensional distributions $μ,ν$ in $R^n$ from an algorithmic perspective: given $x \sim μ$, find a close $y \sim ν$ in $poly(n)$ time, where $n$ is the dimension of $x,y$. Thus, running time depends on the dimension rather than the full representation size of $μ,ν$. Our main result is a general algorithm for transporting any product distribution $μ$ to any $ν$ with cost $Δ+ δ$ under $\ell_p^p$, where $Δ$ is the Knothe-Rosenblatt transport c…

Hodge Conjecture via Singular Varieties
Ananyo Dan, Inder Kaur
https://arxiv.org/abs/2509.25273 https://arxiv.org/pdf/2509.25273

Hodge Conjecture via Singular Varieties
In this article we study the cohomological and homological (due to Jannsen) Hodge conjecture for singular varieties. The motivation for studying singular varieties comes from the fact that any smooth projective variety X is birational to a (possibly singular) hypersurface Y in a projective space. We prove that odd dimensional hypersurfaces with $A_n$ singularities satisfy both versions of the conjecture and moreover their (smooth) resolutions satisfy the classical Hodge conjecture, thus produci…

Tur\'an densities of stars in uniformly dense hypergraphs
Hao Lin, Wenling Zhou
https://arxiv.org/abs/2510.12576 https://arxiv.org/pdf/2510.12576

Turán densities of stars in uniformly dense hypergraphs
A $3$-uniform hypergraph (or $3$-graph) $H=(V,E)$ is $(d,μ, \text{dot})$-dense if for any subsets $X, Y, Z\subseteq V$, the number of triples $(x,y,z)\in X\times Y\times Y$ with $\{x,y,z\}$ being an edge of $H$ is at least $d|X||Y||Z|-μ|V|^3$. Similarly, we say that $H$ is $(d,μ, \text{dot-edge})$-dense if for any subset $X\subseteq V$ and every pair set $P\subseteq V\times V$, the number of pairs $(x,(y,z))\in X\times P$ with $\{x,y,z\}$ being an edge…

Berry Trashcan With Short Range Attraction:Exact $p_x i p_y$ Superconductivity in Rhombohedral Graphene
Ming-Rui Li, Yves H. Kwan, Hong Yao, B. Andrei Bernevig
https://arxiv.org/abs/2509.16312

Berry Trashcan With Short Range Attraction:Exact $p_x+i p_y$ Superconductivity in Rhombohedral Graphene
We show the presence of analytic $p_x + i p_y$ superconducting ground states in the Berry Trashcan -- a minimal model of rhombohedral graphene valid for $n \ge 4$ layers -- under short-range attractive interactions. We demonstrate that the model, whose dispersion consists of a flat bottom surrounded by steep walls of prohibitive kinetic energy, serves as a building block to understand superconductivity in the moiré-free limit. We find that the ground-state chirality has a ``ferromagnetic'' cou…

Wide Separation Planets In Time (WISPIT): Discovery of a Gap H$\alpha$ Protoplanet WISPIT 2b with MagAO-X
Laird M. Close, Richelle F. van Capelleveen, Gabriel Weible, Kevin Wagner, Sebastiaan Y. Haffert, Jared R. Males, Ilya Ilyin, Matthew A. Kenworthy, Jialin Li, Joseph D. Long, Steve Ertel, Christian Ginski, Alycia J. Weinberger, Kate Follette, Joshua Liberman, Katie Twitchell, Parker Johnson, Jay Kueny, Daniel Apai, Rene Doyon, Warren Foster, Victor Gasho, Kyle Van Gorkom, Olivier G…

Wide Separation Planets In Time (WISPIT): Discovery of a Gap H$α$ Protoplanet WISPIT 2b with MagAO-X
Excellent (<25 mas) H$_α$ images of the star TYC 5709-354-1 led to the discovery of a rare H$_α$ protoplanet. This star was discovered by the WISPIT survey to have a large multi-ring transitional disk, and is hereafter WISPIT 2. Our H$_α$ images of 2025, April 13 and April 16 discovered an accreting (H$_α$ in emission) protoplanet: WISPIT 2b (r=309.43$\pm$1.56 mas; (~54 au deprojected), PA=242.21$\pm$0.41 degrees) likely clearing a dust-free gap between the two brightest dust rings in the t…

Breaking the curse of dimensionality for linear rules: optimal predictors over the ellipsoid
Alexis Ayme, Bruno Loureiro
https://arxiv.org/abs/2509.21174 https://

Breaking the curse of dimensionality for linear rules: optimal predictors over the ellipsoid
In this work, we address the following question: What minimal structural assumptions are needed to prevent the degradation of statistical learning bounds with increasing dimensionality? We investigate this question in the classical statistical setting of signal estimation from $n$ independent linear observations $Y_i = X_i^{\top}θ+ ε_i$. Our focus is on the generalization properties of a broad family of predictors that can be expressed as linear combinations of the training labels, $f(X) = \s…

On the analytic rank of the twin prime elliptic curve $y^2=x(x-2)(x-p)$
Kirti Joshi
https://arxiv.org/abs/2508.12340 https://arxiv.org/pdf/2508.12340

On the analytic rank of the twin prime elliptic curve $y^2=x(x-2)(x-p)$
Let $p\geq 7$ and suppose $(p,p-2)$ are twin prime numbers, in [Hatley, 2009], the elliptic curve $E_p:y^2=x(x-2)(x-p)$ was considered in the context of a conjecture by Jason Beers about the Mordell-Weil ranks of $E_p/\mathbb{Q}$. I show that for $p\equiv 3,5\bmod 8$, the analytic rank of $E_p$ is at least one (Theorem 1.1.2) in line with Beers' predictions. This is done by finding a formula (Theorem 4.1.1) for the global root number of $E_p$ for all twin prime pairs. I also show that Beers' co…

Information-Theoretic Fairness with A Bounded Statistical Parity Constraint
Amirreza Zamani, Abolfazl Changizi, Ragnar Thobaben, Mikael Skoglund
https://arxiv.org/abs/2508.12847

Information-Theoretic Fairness with A Bounded Statistical Parity Constraint
In this paper, we study an information-theoretic problem of designing a fair representation that attains bounded statistical (demographic) parity. More specifically, an agent uses some useful data $X$ to solve a task $T$. Since both $X$ and $T$ are correlated with some sensitive attribute or secret $S$, the agent designs a representation $Y$ that satisfies a bounded statistical parity and/or privacy leakage constraint, that is, such that $I(Y;S) \leq ε$. Here, we relax the perfect demographic …

Cluster Expansion and Decay of Correlations for Multidimensional Long-Range Ising Models
Lucas Affonso, Rodrigo Bissacot, Jo\~ao Maia, Jo\~ao F. Rodrigues, Kelvyn Welsch
https://arxiv.org/abs/2508.15666

Cluster Expansion and Decay of Correlations for Multidimensional Long-Range Ising Models
We develop the cluster expansion for the multidimensional multiscaled contours defined by three of us. These contours are suitable for long-range Ising models with interaction $J_{xy}=J(|x-y|)= J/|x-y|^α$, $J>0$, and $α>d$. As an application of the convergence of the cluster expansion at low temperatures, we study the decay of the truncated two-point correlation functions, showing that the decay is algebraic with coefficient $α$.

Search for Active and Inactive Ion Insertion Sites in Organic Crystalline Materials
Harshan Reddy Gopidi, Alae Eddine Lakraychi, Abhishek A. Panchal, Yiming Chen, V. S. Chaitanya Kolluru, Jiaqi Wang, Ying Chen, Liu Jue, Kamila Wiaderek, Maria K. Y. Chan, Yan Yao, Pieremanuele Canepa
https://arxiv.org/abs/2510.00278

Search for Active and Inactive Ion Insertion Sites in Organic Crystalline Materials
The position of mobile active and inactive ions, specifically ion insertion sites, within organic crystals, significantly affects the properties of organic materials used for energy storage and ionic transport. Identifying the positions of these atom (and ion) sites in an organic crystal is difficult, especially when the element has a low X-ray scattering power, such as lithium (Li) and hydrogen, which are difficult to detect with powder X-ray diffraction (XRD) methods. First-principles calcula…

Positive Solutions to the Lane-Emden Type Equation on the Upper Half Space Under Nonlinear Boundary Condition
Azam Nouri
https://arxiv.org/abs/2508.12218 https://

Positive Solutions to the Lane-Emden Type Equation on the Upper Half Space Under Nonlinear Boundary Condition
We prove that all positive solutions of $-Δu = u^{\frac{2n}{n-2}}$ on the upper half space $\mathbb{R}^n_{+}$ (for $n \geq 3$) satisfying the boundary condition $D_{x_n}u = -u^{\frac{n}{n-2}}$ are of the form $u(x) = a \left( \fracλ{λ^2 + |x-y|^2} \right)^{\frac{n-2}{2}}$, where $a = a(n)$, $λ> 0$, and $y = (y_1, \ldots, y_n)$ is a point in the lower half-space with $y_n < 0$.

Intricacies of Frustrated Magnetism in the Kondo Metal YbAgGe
D. G. Mazzone, C. B. Larsen, B. Ueland, X. Boraley, D. M. Pajerowski, Y. Skourski, J. Taylor, B. Fak, S. L. Bud'ko, R. McQueeney, P. C. Canfield, O. Zaharko
https://arxiv.org/abs/2509.02252

Intricacies of Frustrated Magnetism in the Kondo Metal YbAgGe
The combination of localized magnetic moments, their frustration and interaction with itinerant electrons is a key challenge of condensed matter physics. Frustrated magnetic interactions promote degenerate ground states with enhanced fluctuations, a topic that is predominantly studied in magnetic insulators. The coupling between itinerant and localized electrons in metals add complexity to the problem, and presently formulated only for extreme cases in which the itinerant electrons mediate exch…

Critical long-range percolation II: Low effective dimension
Tom Hutchcroft
https://arxiv.org/abs/2508.18808 https://arxiv.org/pdf/2508.18808

Critical long-range percolation II: Low effective dimension
In long-range percolation on $\mathbb{Z}^d$, points $x$ and $y$ are connected by an edge with probability $1-\exp(-β\|x-y\|^{-d-α})$, where $α>0$ is fixed and $β\geq 0$ is a parameter. As $d$ and $α$ vary, the model is conjectured to exhibit eight qualitatively different second-order critical behaviours, with a transition between mean-field and low-dimensional regimes when $d=\min\{6,3α\}$, a transition between long- and short-range regimes at a crossover value $α_c(d)$, and wi…

Lattice Models for Double Whittaker Polynomials and Motivic Chern Classes
Ben Brubaker, Daniel Bump, Andrew Hardt, Hunter Spink
https://arxiv.org/abs/2509.17312 https://

Lattice Models for Double Whittaker Polynomials and Motivic Chern Classes
We will describe solvable lattice models whose partition functions depend on two sets of variables, $x_1,\cdots,x_n$ and $y_1, y_2, \cdots $ that have different connections with the representation theory of $\text{GL}(n,F)$ where $F$ is a nonarchimedean local field. If the boundary conditions are chosen in one way, they are essentially the Motivic Chern classes that were used very effectively by Aluffi, Mihalcea, Schürmann and Su (AMSS) to study such problems. In particular, using this special…

Effective Generalized Fermat equation of signature $(2p, 2q, r)$ with odd narrow class number
Satyabrat Sahoo
https://arxiv.org/abs/2509.21083 https://arxi…

Effective Generalized Fermat equation of signature $(2p, 2q, r)$ with odd narrow class number
Fix a rational prime $r \geq 5$. In this article, we study the integer solutions of the generalized Fermat equation of signature $(2p,2q,r)$, namely $x^{2p}+y^{2q}=z^r$, where the primes $p,q \geq 5$ are varying. For each rational prime $r \geq 5$, we first establish a condition on the solutions of the $S$-unit equation over $\mathbb{Q}(ζ_r+ ζ_r^{-1})$ such that there exists a constant $V_{r}>0$ (depending on $r$) for which the equation $x^{2p}+y^{2q}=z^r$ with $p,q \geq V_r$ has no non-trivi…

Discovery of H$\alpha$ Emission from a Protoplanet Candidate Around the Young Star 2MASS J16120668-3010270 with MagAO-X
Jialin Li, Laird M. Close, Feng Long, Jared R. Males, Sebastiaan Y. Haffert, Alycia Weinberger, Katherine Follette, Sean Andrews, John Carpenter, Warren B. Foster, Kyle Van Gorkom, Alexander D. Hedglen, Gregory J. Herczeg, Parker T. Johnson, Maggie Y. Kautz, Jay K. Kueny, Rixin Li, Joshua Liberman, Joseph D. Long, Jennifer Lumbres, Sebastian Marino, Luca Matr`a, Eden …

Discovery of H$α$ Emission from a Protoplanet Candidate Around the Young Star 2MASS J16120668-3010270 with MagAO-X
2MASS J16120668-3010270 (hereafter 2MJ1612) is a young M0 star that hosts a protoplanetary disk in the Upper Scorpious star-forming region. Recent ALMA observations of 2MJ1612 show a mildly inclined disk ($i$=37$^\circ$) with a large dust-depleted gap (R$_\text{cav}\approx$0.4" or 53 au). We present high-contrast H$α$ observations from MagAO-X on the 6.5m Magellan Telescope and new high resolution sub-mm dust continuum observations with ALMA of 2MJ1612. On both 2025 April 13 and 16, we recover…

Information-Computation Tradeoffs for Noiseless Linear Regression with Oblivious Contamination
Ilias Diakonikolas, Chao Gao, Daniel M. Kane, John Lafferty, Ankit Pensia
https://arxiv.org/abs/2510.10665

Information-Computation Tradeoffs for Noiseless Linear Regression with Oblivious Contamination
We study the task of noiseless linear regression under Gaussian covariates in the presence of additive oblivious contamination. Specifically, we are given i.i.d.\ samples from a distribution $(x, y)$ on $\mathbb{R}^d \times \mathbb{R}$ with $x \sim \mathcal{N}(0,\mathbf{I}_d)$ and $y = x^\top β+ z$, where $z$ is drawn independently of $x$ from an unknown distribution $E$. Moreover, $z$ satisfies $\mathbb{P}_E[z = 0] = α>0$. The goal is to accurately recover the regressor $β$ to small $\ell_2…

Critical long-range percolation I: High effective dimension
Tom Hutchcroft
https://arxiv.org/abs/2508.18807 https://arxiv.org/pdf/2508.18807

Critical long-range percolation I: High effective dimension
In long-range percolation on $\mathbb{Z}^d$, points $x$ and $y$ are connected by an edge with probability $1-\exp(-β\|x-y\|^{-d-α})$, where $α>0$ is fixed and $β\geq 0$ is a parameter. As $d$ and $α$ vary, the model is conjectured to exhibit eight qualitatively different second-order critical behaviours, with a transition between mean-field and low-dimensional regimes when $d=\min\{6,3α\}$, a transition between long- and short-range regimes at a crossover value $α_c(d)$, and wi…

Almost sure global weak solutions and optimal decay for the incompressible generalized Navier-Stokes equations
Y. -X. Lin, Y. -G. Wang
https://arxiv.org/abs/2509.17171 https://

Almost sure global weak solutions and optimal decay for the incompressible generalized Navier-Stokes equations
In this paper, we consider the initial value problem of the incompressible generalized Navier-Stokes equations with initial data being in negative order Sobolev spaces, in the whole space $\mathbb{R}^d$ with $d \geq 2$. The generalized Navier-Stokes equations studied here is obtained by replacing the standard Laplacian in the classical Navier-Stokes equations by the fractional order Laplacian $-(-Δ)^\al$ with $\al \in \left( \frac{1}{2},\frac{d+2}{4} \right]$. After an appropriate randomizatio…

The X-ray Source Population of the Metal-Rich Globular Cluster NGC 6528
Bernard Leal, Kwangmin Oh, Jay Strader, Steve E. Zepf, Kristen Dage, S. Kim, C. Y. Hui
https://arxiv.org/abs/2508.10105

The X-ray Source Population of the Metal-Rich Globular Cluster NGC 6528
We present the first study of the X-ray sources in one of the most metal-rich globular clusters in the Galaxy, NGC 6528. Using relatively deep (66 ksec) archival imaging from the Chandra X-ray Observatory, we identify 18 sources within the half-light radius of the cluster, all in the range $L_X \sim 10^{31}$-$10^{32}$erg s$^{-1}$ (0.5-7 keV). By combining these data with photometry from the Hubble Space Telescope and other sources, we classify the X-ray sources as a likely mix of cataclysmic va…

Doping a spin-one Mott insulator: possible application to bilayer nickelate
Hanbit Oh, Hui Yang, Ya-Hui Zhang
https://arxiv.org/abs/2509.02673 https://arxi…

Doping a spin-one Mott insulator: possible application to bilayer nickelate
In this article, we review some recent theoretical developments on potential high-temperature superconductors and unconventional metallic states that can arise from doping a spin-one Mott insulator in the $d^{8}$ valence. These studies are particularly relevant-though not limited-to the recently discovered bilayer nickelate superconductor La$_3$Ni$_2$O$_7$. We focus on a ferromagnetic (FM) Kondo lattice model with mobile electrons in the $d_{x^2-y^2}$ orbital coupled to the localized spin momen…

Concentration and non-concentration of eigenfunctions of second-order elliptic operators with a divergence form in layered media
Matania Ben-Artzi (HUJ), Yves Dermenjian (I2M)
https://arxiv.org/abs/2509.06352

Concentration and non-concentration of eigenfunctions of second-order elliptic operators with a divergence form in layered media
Let $Ω$ ' $\subset$ R^d , d = 1, 2, . . . be an open bounded smooth domain, and $Ω= Ω'\times (0,H)\subset \mathbb{R}^d \times \mathbb\_+.$ The coordinates in $Ω$ are designated as x = (x ' , y) $\in$ $Ω$ ' x (0, H). The paper deals with the concentration (and non-concentration) properties (in sectors of $Ω$) of the eigenfunctions of the self-adjoint second-order elliptic operator $A = -\nabla\cdot\tilde{c}\nabla$ in $L^2(Ω,dx)$ with domain $D(A) = \{v\in H\_0^1(Ω); \tilde{c}\nabla v…

Boundedness of solutions of the first-order linear multidimensional difference equations
Andrii Chaikovskyi, Oleksandr Liubimov
https://arxiv.org/abs/2509.14842 https://

Boundedness of solutions of the first-order linear multidimensional difference equations
We investigate the boundedness of solutions of the first order linear difference equation of the form $x_{n+1} = Ax_{n} + y_{n}, \; n \geq 1$ where $A$ is a square matrix with complex entries, sequence $\{y_{n}\}_{n\geq 1}$ and initial value $x_1$ are supposed to be known. Firstly, we discuss the one-dimensional case of this equation $x_{n+1} = ax_{n} + y_{n}, \; n \geq 1$ where $a$ is a complex number. In particular, we obtain the sufficient conditions for boundedness or unboundedness of the s…

Evolution of spin excitations in superconducting La$_{2-x}$Ca$_{x}$CuO$_{4-\delta}$ from the underdoped to the heavily overdoped regime
S. Hameed, Y. Liu, M. Knauft, K. S. Rabinovich, G. Kim, G. Christiani, G. Logvenov, F. Yakhou-Harris, A. V. Boris, B. Keimer, M. Minola
https://arxiv.org/abs/2509.06680

Evolution of spin excitations in superconducting La$_{2-x}$Ca$_{x}$CuO$_{4-δ}$ from the underdoped to the heavily overdoped regime
We investigate high-energy spin excitations in hole-doped La$_{2-x}$Ca$_{x}$CuO$_{4-δ}$ films across a broad Ca doping range $x = 0.05-0.50$ using resonant inelastic x-ray scattering (RIXS). Polarization analysis and incident-photon energy detuning measurements confirm the persistence of collective paramagnon excitations up to $x = 0.50$. Consistent with previous studies on other cuprate families, we observe a pronounced crossover near $x = 0.15$, where paramagnon spectral weight is transferre…

Balancing Extensions in Posets of Large Width
Max Aires, Jeff Kahn
https://arxiv.org/abs/2509.11549 https://arxiv.org/pdf/2509.11549

Balancing Extensions in Posets of Large Width
We revisit classic balancing problems for linear extensions of a partially ordered set $P$, proving results that go far beyond many of the best earlier results on this topic. For example, with $p(x\prec y)$ the probability that $x$ precedes $y$ in a uniform linear extension, $δ_{xy} = \min\{p(x \prec y), p(y \prec x)\}$, and $δ(P)=\max δ_{xy}$, we show that $δ(P)$ tends to $1/2$ as $n := |P| \to\infty$ if $P$ has width $Ω(n)$ or $ω(\log(n))$ minimal elements, and is at least $1/…

Critical long-range percolation III: The upper critical dimension
Tom Hutchcroft
https://arxiv.org/abs/2508.18809 https://arxiv.org/pdf/2508.18809

Critical long-range percolation III: The upper critical dimension
In long-range percolation on $\mathbb{Z}^d$, points $x$ and $y$ are connected by an edge with probability $1-\exp(-β\|x-y\|^{-d-α})$, where $α>0$ is fixed and $β\geq 0$ is a parameter. As $d$ and $α$ vary, the model is conjectured to exhibit eight qualitatively different second-order critical behaviours, with a transition between mean-field and low-dimensional regimes when $d=\min\{6,3α\}$, a transition between long- and short-range regimes at a crossover value $α_c(d)$, and wi…

Sum of short exponential sums with prime numbers
Firuz Rakhmonov
https://arxiv.org/abs/2510.09102 https://arxiv.org/pdf/2510.09102

Sum of short exponential sums with prime numbers
For sufficiently large integers $K$, $x$, $y$, and $q$ satisfying $K \le y < x$, where $f(u) = αu^n + α_{n-1}u^{n-1} + \ldots + α_1 u$ is a polynomial of degree $n$ with real coefficients, $n$ is a fixed positive integer, $α$ is a real number such that $\left|α- \frac{a}{q}\right| \le \frac{1}{q^2}$, $(a, q) = 1$, $q \ge 1$ and $\mathscr{L} = \ln x$, an estimate of the form $$ \sum_{k=1}^K \left| \sum_{x - y < p \le x} e(kf(p)) \right| \ll K y \left( \frac{1}{q} + \frac…

2-Distance Coloring of Planar Graphs with Maximum Degree at Least 6
Sara Al Hajjar
https://arxiv.org/abs/2509.10861 https://arxiv.org/pdf/2509.10861…

2-Distance Coloring of Planar Graphs with Maximum Degree at Least 6
A k-distance r-coloring of a graph is a coloring of the vertices of the graph such that if the distance between 2 vertices x and y is less or equal to k, then x and y must have distinct colors. A planar graph is a graph that can be drawn with no edge crossing. We will study the 2-distance coloring of planar graphs with maximum degree at least 6.

Incommensurate magnetic order drives singular angular magnetoresistance in a Weyl semimetal
X. Yao, P. Chen, R. Verma, X. Zhao, H. -Y. Yang, L. DeBeer-Schmitt, A. A. Aczel, C. -M. Wu, D. Alba Venero, T. Ohhara, K. Munakata, M. Takahashi, Y. Noda, A. Bansil, B. Singh, P. Nikoli\'c, F. Tafti, J. Gaudet
https://arxiv.org/abs/2509.18398

Torsor Neron models of hyperkahler manifolds
Ljudmila Kamenova, Misha Verbitsky
https://arxiv.org/abs/2509.12369 https://arxiv.org/pdf/2509.12369

Torsor Neron models of hyperkahler manifolds
Let $M$ be a compact hyperkahler manifold equipped with a Lagrangian fibration $π:\; M \to X$, and $M'$ the smooth locus of $π$. We prove that over a complement to a codimension $\geq 2$ subset in $X$, the projection $π:\; M' \to X$ has a natural structure of a torsor over an abelian group bundle, which can be understood as a complex analytic variant of the Néron model construction. This gives an independent proof of a result by Y.-J. Kim.

Quasilinear problems with critical Sobolev exponent for the Grushin p-Laplace operator
Somnath Gandal, Annunziata Loiudice, Jagmohan Tyagi
https://arxiv.org/abs/2509.06138 https…

Quasilinear problems with critical Sobolev exponent for the Grushin p-Laplace operator
We study the following class of quasilinear degenerate elliptic equations with critical nonlinearity \begin{align*} \begin{cases}-Δ_{γ,p} u= λ|u|^{q-2}u+|u|^{p_γ^{*}-2}u & \text{ in } Ω\subset \mathbb{R}^N, \\ u=0 & \text{ on } \partial Ω, \end{cases} \end{align*} where $Δ_{γ, p}v:=\sum_{i=1}^N X_i(|\nabla_γu|^{p-2}X_i u)$ is the Grushin $p$-Laplace operator, $z:=(x, y) \in \mathbb{R}^N$, $N=m+n,$ $m,n \geq 1,$, where $\nabla_γ=(X_1, \ldots, X_N)$ is th…

Dichotomy in Low- and High-energy Band Renormalizations in Trilayer Nickelate $La_{4}Ni_{3}O_{10}$: a Comparison with Cuprates
X. Du, Y. L. Wang, Y. D. Li, Y. T. Cao, M. X. Zhang, C. Y. Pei, J. M. Yang, W. X. Zhao, K. Y. Zhai, Z. K. Liu, Z. W. Li, J. K. Zhao, Z. T. Liu, D. W. Shen, Z. Li, Y. He, Y. L. Chen, Y. P. Qi, H. J. Guo, L. X. Yang
https://

Dichotomy in Low- and High-energy Band Renormalizations in Trilayer Nickelate $La_{4}Ni_{3}O_{10}$: a Comparison with Cuprates
Band renormalizations comprise crucial insights for understanding the intricate roles of electron-boson coupling and electron correlation in emergent phenomena such as superconductivity. In this study, by combining high-resolution angle-resolved photoemission spectroscopy and theoretical calculations, we systematically investigate the electronic structure of the trilayer nickelate superconductor $La_{4}Ni_{3}O_{10}$ at ambient pressure. We reveal a dichotomy in the electronic band renormalizati…

Large deviation rates for supercritical multitype branching processes with immigration
Liuyan Li, Junping Li
https://arxiv.org/abs/2508.15428 https://arxiv…

Large deviation rates for supercritical multitype branching processes with immigration
Let $\{X_n\}_{n\geq0}$ be a $p$-type ($p\geq2$) supercritical branching process with immigration and mean matrix $M$. Suppose that $M$ is positively regular and $ρ$ is the maximal eigenvalue of $M$ with the corresponding left and right eigenvectors $\boldsymbol{v}$ and $\boldsymbol{u}$. Let $ρ>1$ and $Y_n=ρ^{-n}\Big[\boldsymbol{u}\cdot X_n -\frac{ρ^{n+1}-1}{ρ-1}( \boldsymbol{u}\cdot \boldsymbolλ)\Big]$, where the vector $\boldsymbolλ$ denotes the mean immigration rate. In this paper, we …

Separable integer partition classes with restrictions on consecutive parts
Y. Q. Chen, Thomas Y. He, X. M. Huang, T. T. Zou
https://arxiv.org/abs/2508.11766 https://

Separable integer partition classes with restrictions on consecutive parts
Recently, Andrews introduced separable integer partition classes and studied some well-known theorems. In this article, we will consider the types of partitions with restrictions on consecutive parts. We will show that such partitions are separable integer partition classes and then give the generating functions for such partitions.

Distribution of integer points on determinant surfaces and a $\text{mod-}p$ analogue
Satadal Ganguly, Rachita Guria
https://arxiv.org/abs/2508.14793 https://

Distribution of integer points on determinant surfaces and a $\text{mod-}p$ analogue
We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form $xy-zw=r$, where $r$ is a non-zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables $x, y, z, w$ as well as of $r$. We also establish an asymptotic formula for counting integer solutions with smooth weights to the congruence $xy-zw \equiv 1 (\text{mod }p)$, where $p$ is a large prime, with a strong bound on the error term.

Polynomial actions of rings of integers of global fields and quasirandomness of Paley-type graphs
Ethan Ackelsberg, Vitaly Bergelson
https://arxiv.org/abs/2509.17868 https://

Polynomial actions of rings of integers of global fields and quasirandomness of Paley-type graphs
The goal of this paper is to undertake an in-depth study of the phenomenon behind the Furstenberg--Sárközy theorem, which, in its modern form due to Kamae and Mendès-France, states that if $E$ is a set of integers with positive density and $P$ is an intersective polynomial, then there are distinct elements $x, y \in E$ such that $x - y = P(n)$ for some some $n$. In this paper, we identify an algebraic framework (rings of integers of global fields) for Furstenberg--Sárközy-type theorems. …

Geometry of critical discrete structures: percolation on the hierarchical lattice
Sanchayan Sen
https://arxiv.org/abs/2509.09589 https://arxiv.org/pdf/2509…

Geometry of critical discrete structures: percolation on the hierarchical lattice
Consider balls $Λ_n$ of growing volumes in the $d$-dimensional hierarchical lattice, and place edges independently between each pair of vertices $x\neq y\inΛ_n$ with probability $1-\exp(-βJ(x, y) )$ where $J(x, y) \asymp \| x-y \|^{-α}$ for some $0<α<5d/6$. We identify the critical window for this model and establish the metric scaling limit within the critical window. More precisely, we show that the metric scaling limit of the maximal components is Brownian, and that this model…

Incidence of lines, points, and planes in $PG(3,q)$ with respect to the twisted cubic
Krishna Kaipa, Puspendu Pradhan
https://arxiv.org/abs/2509.15332 https://

Incidence of lines, points, and planes in $PG(3,q)$ with respect to the twisted cubic
We consider the orbits of the group $G=PGL_2(q)$ on the points, lines and planes of the projective space $PG(3,q)$ over a finite field $\mathbb F_q$ of characteristic different from $2$ and $3$. The points of $PG(3,q)$ can be identified with projective space of binary cubic forms, and the set $\mathcal L$ of lines of $PG(3,q)$ can be thought of as pencils of cubic forms. The action of $G$ on $PG(1,q)$ naturally induces an action of $G$ on binary cubic forms $f(X,Y)$. The points of $PG(3, q)$ de…

Integer solutions of Pell equation in bounded regions
Kun Yi Ong, Eddie Shahril Bin Ismail
https://arxiv.org/abs/2509.17882 https://arxiv.org/pdf/2509.1788…

Integer solutions of Pell equation in bounded regions
The Pell equation $x^2 - Dy^2 = 1$ with non-square $D > 1$ has infinitely many integer solutions, yet most research has centered on the asymptotic behavior of fundamental units as $D$ varies. By contrast, the exact distribution of solutions for a fixed $D$ within bounded regions has received little attention. In this paper, we contribute to this direction by giving an explicit enumeration of all solutions to the Pell equation inside the square $|x| + |y| \leq λ$ for any $λ…

There is no prime functional digraph: Seifert's proof revisited
Adrien Richard
https://arxiv.org/abs/2509.19940 https://arxiv.org/pdf/2509.19940…

There is no prime functional digraph: Seifert's proof revisited
A functional digraph is a finite digraph in which each vertex has a unique out-neighbor. Considered up to isomorphism and endowed with the directed sum and product, functional digraphs form a semigroup that has recently attracted significant attention, particularly regarding its multiplicative structure. In this context, a functional digraph $X$ divides a functional digraph $A$ if there exists a functional digraph $Y$ such that $XY$ is isomorphic to $A$. The digraph $X$ is said to be prime if i…