arXiv preprints from January 1, 2026 through September 22, 2026 — 18:26:17 EST
We prove that deciding whether an ideal in a polynomial ring contains a trinomial is impossible on a Turing machine. More precisely, from an integer polynomial $P$ we compute generators of an ideal $I_P$ in a polynomial ring over $\mathbb{Q}$ such that $I_P$ contains a trinomial if and only if $P$ has an integral zero. By the MRDP...
The use of agentic large language models obviates human interpretation of scientific results, and will lead to substantial distrust in the literature.
Astrophysical observations of our universe have been key to our understanding of how the universe works. Shortly after the turn of the millennium, the National Research Council delivered \textit{Connecting Quarks with the Cosmos: Eleven Science Questions for the New Century}. In the subsequent quarter-century, we have made substantial...
The bidirectional reflectance factor (BRF) characterizes the directional radiative properties of terrestrial surfaces. However, existing three-dimensional (3D) radiative transfer models require complex scene construction and computationally intensive radiative transfer solvers, limiting efficient generation of multi-angle...
We prove interior Hölder regularity for solutions of the stationary kinetic Fokker-Planck equation in non-divergence form in space dimension one. The estimate is independent of any small-oscillation condition on the diffusion coefficient.
Many parameter-efficient methods generate the parameters of a large neural network from a low-dimensional latent representation. Given an architecture $Φ$ with $P_Φ$ parameter slots, we write $\boldsymbolθ_f=\mathcal{G}(\boldsymbolξ_f)$, where $\mathcal{G}\colon\mathbb{R}^M\to\mathbb{R}^{P_Φ}$ is a parameter generator and...
We present the algebraic structure of bosonic quantum error-correcting codes on genus-two Riemann surfaces. We explicitly construct the code words as automorphic forms and analytically generate the full tower of code spaces at all weights. We prove a fundamental no-go theorem: for any genus greater than one, the stabilizer group is...
Let $R$ be a ring that is essentially of finite type over a field and $I\subseteq R$ be an ideal. In this article it is shown that the minimal number of generators of the symbolic powers $I^{(n)}$ is bounded above by a polynomial in $n$. Furthermore, if $R$ is assumed to be a domain and $\mathcal I=\{I_n\}_{n\ge 0}$ is an...
Multi-photon dissipation -- a key resource for bosonic qubits -- is usually realized by parametrically pumping a Josephson coupler at the cost of spurious nonlinear terms. Here we instead engineer it using a dc-voltage-biased SQUID, such that these parasitic terms average out. We activate the conversion of one, two, or four photons of...
Searches for Dysonian waste heat have operated almost exclusively in the mid-infrared and are therefore sensitive primarily to technology radiating at 100-600K. We argue that mature, computation-dominated civilisations may instead dissipate much of their energy at far lower temperatures. The Landauer cost of irreversible computation...
We introduce a family of effective theories and use them to define a specific type of coarse-grained models for canonical loop quantum gravity. Each effective theory is characterized by two parameters and it consists mainly of a Hilbert space of coarse states and an effective Hamiltonian operator. The construction of the coarse...
We study the free energy of the critical $O(N)$ vector model at large $N$ on $S^{1}\times S^{2}$ with an angular velocity $\hatμ$ without the singlet constraint. The leading high-temperature behaviour is determined analytically both as an expansion about $\hatμr=0$ and $\hatμ^{2}r^{2}=1$ where $r$ is the radius of the sphere. We...
We rethink the definition of privacy in multi-server, graph-replicated private information retrieval (PIR) systems, by introducing a novel setting where the user's privacy is governed by the servers' storage structure. In classical graph-replicated PIR, the user retrieves a single message stored at the servers, while hiding the...
Analytical signal-processing blocks are interpretable and reliable, but their optimality depends on assumptions that practical hardware and channels violate. Learned replacements can adapt, but often discard the structure that makes the original solution understandable. Here we introduce deformable matched filtering, a platform in...
We complete the classification of non-Kähler steady pluriclosed soliton on compact complex surfaces, as initiated by Streets. The underlying complex structure must be a Hopf surface, with any finite primary cover being of class 1. Moreover, the soliton metric is unique up to biholomorphism.
For an integer $t\geq-1$, let $θ_t$ be the largest real root of $g_t(X)=X^3-tX^2-(t+3)X-1$, and let $R_t=\mathbb{Z}[θ_t]\subseteq\mathcal{O}_t=\mathcal{O}_{\mathbb{Q}(θ_t)}$. We prove that if the additive order index $q=[\mathcal{O}_t:R_t]$ is prime, then $[\mathcal{O}_t^\times:R_t^\times]=q$ exactly for $(t,q)=(3,3)$ and $(5,7)$, and...
Hyperanalytic functions, in the sense established by the mathematician Avron Douglis, are Douglis algebra-valued functions defined via a hypercomplex structure rather than the standard Cauchy-Riemann equations characteristic of traditional complex analysis. The classes of polyhyperanalytic and meta-hyperanalytic functions represent...
In a remarkable work published in Analysis and PDE 8 (2015) 1541-1563, M. Fazly, J. Wei, and X. Xu establish the following pointwise estimate \[-Δu \geq \frac 2{n-4} \frac{|\nabla u|^2}u + \sqrt{\frac 2{p+1- \frac 8{n(n-4)}}} |x|^{\frac σ2} u^\frac{p+1}2 \quad \text{in } \mathbf R^n\] for any bounded, positive, $C^4$-solution $u$ to...
We solve the Nielsen realisation problem for high-dimensional aspherical manifolds in a new class of special cases. Mainly, we focus on actions of cyclic groups of prime order. A novelty is that it gives topological solutions to the problem with certain high-dimensional fixed point sets, whereas previous solutions of this type were...
The problem of global minimization of nonconvex quadratic functions subject to box constraints is studied. Applying Gershgorin theorem we reduce the main matrix A to its diagonal form which is used to obtain difference of convex representation of the quadratic function. Then ε-subdifferentials of DC components are studied and used to...
For every $1\le d<n$, we prove joint equidistribution, as the height tends to infinity, of $d$-dimensional $K$-subspaces in a rigid adelic space over a number field $K$, together with their archimedean Grassmannian images and the $K$-linear isometry classes of the normalized subspace and quotient. We identify the leading constant,...
Let $ζ(G)$ denote the minimum number of parts in a partition of $V(G)$ in which every part induces either a clique or an independent set. Erdős and Gimbel asked whether, for $G_n\sim G(n,1/2)$, the difference $χ(G_n)-ζ(G_n)$ tends to infinity with high probability. We resolve this problem along the full sequence $n\to\infty$ and prove...
We establish sharp endpoint mapping properties for the wave operators $W_\pm(H,-Δ)$ of two-dimensional Schrödinger operators $H=-Δ+V$ with real-valued decaying potentials $V$. Together with the known non-endpoint $L^p$ theory, our results give a complete classification of the $L^p$ mapping properties of the two-dimensional wave...
The independence complex and the perfect matching complex of a graph are simplicial complexes encoding, respectively, its independent sets and perfect matchings. Determining the homotopy types and other topological properties of these complexes is, in general, a difficult problem, and explicit descriptions are known only for...
Let $\mathcal{A}$ be the normalized class of analytic functions $f$ in the unit disc $\mathbb{D} := \{z \in \mathbb{C} : \vert{}z\vert{} < 1\}$. For $β> 1$, let $\mathcal{N}(β)$ denote the subclass of $\mathcal{A}$ satisfying $\text{Re}\{1 + z f''(z)/f'(z)\} < β$ for $z \in \mathbb{D}$. The main purpose of this paper is to establish...