arXiv preprints from January 1, 2026 through September 11, 2026 — 14:37:06 EST
We construct a smooth projective variety in positive characteristic whose $\mathbb{Q}_{\ell}$-coefficient etale cohomology ring is not the scalar extension of any graded $\mathbb{Q}$-algebra, providing an example of a new type of obstruction to characteristic zero liftability.
Let $G$ be a finite group, let $V$ be a finite-dimensional $G$-module over a field $k$, and let $U$ be a $G$-submodule of $V$. Wehlau conjectured that the corresponding Noether numbers satisfy $β\bigl(k[U]^G\bigr)\leq β\bigl(k[V]^G\bigr)$. We disprove this conjecture in characteristic $2$. For the dihedral group $D_8$, we construct an...
We study the inference-time behavior of deep linear encoder-only transformers through the lens of interacting particle systems. In this perspective, tokens are modeled as particles that interact dynamically through successive linear self-attention layers. We show that in embedding dimension two, for any key, query, and value matrices,...
This paper investigates the geometry of foliations on smooth algebraic varieties over an algebraically closed field of arbitrary characteristic $p \ge 0$. We address several specific features of foliations in positive characteristic, aiming to highlight both similarities and differences with the characteristic zero case. First, we...
Building on our previous general computational solution to Bellman's Lost-in-a-Forest Problem, we present a new approach and analytical formulas for the previously well-known escape path for the infinite unit-strip forest and unit broadworm by Zalgaller. Earlier studies addressed these problems exclusively through geometric methods....
In this paper, we study and characterise the natural embedding of the Ree-Tits octagons. Keywords: Ree-Tits Octagon, Metasymplectic space, generalised octagon, generalised polygon
Gaussian graphical model selection is usually studied under independent sampling, but in many applications the data arise as a single trajectory of a dependent stochastic process. We study exact recovery of the graph from one trajectory of random-scan Gaussian Glauber dynamics. Existing techniques for this problem either inherit the...
The compressible fluid-solid interaction (FSI) with a thermomechanical phase transition is formulated at large strains within the Eulerian frame. For the deviatoric part, the Jeffreys (also called anti-Zener) rheology with an additional viscosity is adopted. The core philosophy governing the mechanical solid-liquid transition is that...
Researchers often select top-performing options or winners, based on a data-driven criterion, such as treatments, models, or model features and then report effect estimates for the selected winners. Naive post-selection estimates, however, are known to suffer from the winner's curse, producing systematically overoptimistic results. We...
We study doubly reflected backward stochastic differential equations with jumps and two completely separated right-continuous with left limits barriers in a filtration generated by an inhomogeneous Levy process. We establish existence and uniqueness results under a stochastic Lipschitz condition on the driver by means of a...
We study polynomial holomorphic $1$-forms in $\mathbb{C}^2$ that are homologically trivial along the fibers of meromorphic pencils of the form $ φ= \frac{f^p}{g^q}, $ where $f,g$ are holomorphic functions (possibly polynomials) in general position and $(p,q)=1$. We first establish a homological characterization of relative exactness:...
The theorem of Mendel and Naor (2013) associates to every compact metric probability space a large ultrametric subset carrying a probability measure controlled from above on balls by the original measure. Building on Bartal's Ramsey decompositions (2021) and the author's previous proofs of the ultrametric skeleton theorem for doubling...
We construct a vector space whose defining characteristics are rooted in univariate regular variation of random variables. Specifically, the base vector space $\mathbb{V}_b$ consists of random variables whose limiting tail probabilities, when scaled by regularly varying functions of the form $b(s)=s^αL(s)$, are finite. Defining a...
Tarski's geometry of solids reconstructs point-like objects from concentric families of spherical regions rather than taking points as primitive entities. We formalize this reconstruction in Coq within a nominal mereological framework inspired by Lesniewski. The main question is how a regional, point-free geometry can support a...
While the cosmological implications of the Swampland Conjectures are usually discussed in the context of inflationary model building, they also have implications for the violent, non-adiabatic dynamics that can follow inflation or any displacement of string moduli. We study this question through the lens of self-resonant preheating,...
Cosmic strings are not yet confirmed, topological defects formed in the early Universe. They can bend light or gravitational waves, which causes an effect similar to the gravitational lensing. Our goal is to check whether cosmic string could be detected as a lenses of gravitational waves by the Einstein Telescope (ET). To do that the...
The CO luminosity-to-H$_2$ mass conversion factor ($α_{CO}$) remains a debated uncertainty in determining molecular gas masses of high-redshift dusty star-forming galaxies (DSFGs). Dynamical mass constraints have often favored $α_{CO}=0.8$~$M_{\odot}~{(K~km~{s}^{-1}~{pc}^{2})}^{-1}$, whereas dust- and radiative-transfer-based methods...
GRB 230812B is a bright long-duration GRB with a luminous, long-lived afterglow and an AstroSat/CZTI polarization measurement during the prompt phase, enabling a joint study of its prompt spectral evolution, polarization, and broadband afterglow. Time-resolved spectroscopy of the prompt emission shows that during the rising phase, the...
Silicon is an attractive host for scalable quantum photonics, but the absence of bright telecom-band emitters with optically addressable spin states has limited its use for spin-photon interfaces. Here we demonstrate the Al1-center, an aluminum--carbon defect in silicon, as a bright waveguide-integrated single-photon emitter with a...
Intelligence appears under different names in different fields: as data compression in statistics and machine learning, as universal computation in dynamical systems, and as adaptive behavior in agents. Each field carries its own objective, and the two most influential drives often fail in mirror image: novelty search, which seeks...
The Astro2020 Decadal recommended the development of a suite of next generation astronomical observatories spanning the X-ray to near-IR spectrum. These programs require fast, extremely low noise detectors to fulfill their science goals. To address this technology gap, Stanford X-ray Astronomy and Observational Cosmology (XOC) group,...
Single polycyclic aromatic hydrocarbon molecules embedded in organic matrices have proven to be an excellent family of narrow-linewidth quantum emitters. Extending this host-guest setting to van der Waals materials offers the opportunity to combine the preeminent properties of molecular emitters with the access to the versatility of...
We investigate the recombination dynamics of localized defect emission in monolayer WSe$_2$ using time-resolved photoluminescence over the temperature range from 4 to 120 K. The defect emission comprises a dominant sub-nanosecond exponential component and two weak, long-lived power-law channels extending from a few nanoseconds to...
Manganese telluride ($\text{MnTe}$) has recently emerged as a prototypical $g$-wave altermagnet, providing an ideal platform to investigate the non-equilibrium excitations of altermagnetic order. Here, we report simultaneous spatial mapping of the local equilibrium orientation of the Néel vector, $\varphi_L(\mathbf{r})$, alongside the...
The characterization of electron transfer through the emitting surface is of crucial importance for optimizing existing and developing new photocathodes. Here we propose and develop a method for the direct determination of the electron escape probability in high-efficiency semiconductor photocathodes. The proposed method is based on...