arXiv preprints from January 1, 2026 through September 22, 2026 — 01:56:14 EST
We investigate a minimal extension of the SM consisting of a $\mathbb{Z}_3$-stabilized complex scalar dark matter (CSDM) candidate, a down-type vector-like quark (VLQ), and a charged vector-like lepton (VLL). The additional vector-like fermions not only enable the CSDM to reproduce the observed relic abundance beyond the...
The effects of disorder on topological phases of matter are typically either preservation of topology or its destruction. For example, the quantum Hall effect's quantization and chiral edge mode remain robust until a strong-disorder percolation transition exits the topological phase. Disorder can also enlarge a preexisting topological...
Attractors are effective low-dimensional structures, defined in a chosen set of observables, that trajectories from different initial states approach; hydrodynamic attractors are those on which the late-time evolution is governed by hydrodynamic constitutive relations. Motivated by nuclear collisions and ultracold atomic gases, this...
Let u be a morphism of algebraic varieties. Given m integer or infinite, we prove that the set of points whose fiber has size m is a constructible set.
We show that the Tate module of the $\ell$-adic unramified cohomology $H^3_{\nr}(X, {\Q_\ell}/{\Z_\ell})$ of a smooth projective surface $X$ over a local or strictly local field $k$ of residue characteristic prime to $\ell$ vanishes under suitable conditions. We apply this to answer some questions concerning the left and ...
We give a self-contained exposition of metric differentiability for Lipschitz mappings from sets in Euclidean spaces into arbitrary metric spaces, together with the corresponding area and co-area formulas. The novelty is a new metric implicit function theorem for mappings into metric spaces, which is then used to give a direct and...
Classically, the places of $\mathbb{Q}$ are often regarded as a one-point compactification of $\mathrm{Spec}(\mathbb{Z})$, with the real place corresponding to a formal ``prime'' added at infinity. Re-examining this picture from a topos-theoretic perspective reveals a subtler geometry: while the non-Archimedean places are identified...
We define symplectic Dirac operators on homogeneous spaces and study their representation-theoretic role. For an invariant polarization, the symplectic Dirac operator decomposes into two symplectic Dolbeault operators. We compute their commutator as the natural symplectic analogue of the square of the classical Dirac operator. Our...
For $n\ge 3$ and $c\in(0,1)$, let $\mathcal{GT}(n,c)$ denote the class of geodesic metric trees of valence at most $n$ whose branch points are uniformly relatively separated with constant $c$. We prove that $\mathcal{GT}(n,c)$ has no bi-Lipschitz universal element. More precisely, we construct a family...
Let $M$ be a complete open $5$-manifold with nonnegative Ricci curvature. If its universal cover $\tilde M$ has Euclidean volume growth, then $π_1(M)$ is finitely generated and virtually $\mathbb Z^k$ for some $0\le k\le4$. This confirms a conjecture of Pan and Rong \cite{PR18} in dimension five; see also \cite{BNS25,BrNaSe25}. In...
We study one-dimensional spinless bosons with semirelativistic spinless-Salpeter dispersion and attractive pairwise contact interactions. Because the dispersion becomes linear at large momentum, the contact interaction is marginal by power counting and produces a logarithmic ultraviolet divergence. We construct the renormalized...
We study word maps with constants on quasisimple algebraic groups over a local field $L$. We prove that, for such a group $G=\mathbf{G}(L)$ and a word $w\in (G\ast\mathbf{F}_r)\setminus G$, either $w$ has a so-called Tomanov-small critical constant or the minimal dimension of the word image $w(G^r)\subseteq G$ of such a word is...
Modern science and engineering increasingly rely on time-varying data, yet the mathematical tools used to model temporal phenomena are often developed within separate disciplines, obscuring common principles and limiting the transfer of ideas across fields. This chapter presents the theory of narratives, an abstract framework for...
As an extension of the Point Estimate Method (PEM) to evaluate probabilistic moments of quantities of interest (QoI) in general $n$-dimensional spaces, the Quadratic Point Estimate Method (QPEM) has been recently developed. This new method is defined to fully represent up to fifth-order input moments in the Gaussian space, providing...
Execution feedback can guide coding agents toward correct repository repairs, but only when the tests capture the behavior requested by the issue. Agent-generated tests can encode incomplete or incorrect behavioral targets; when the same trajectory writes both the patch and the test, their errors can agree and create false confidence....
An input may activate few hidden units even when different inputs collectively use an entire network. We study the statistical complexity of this input-dependent sparsity in the one-hidden-layer ReLU model of Awasthi et al. (COLT 2024). For width $s$, at most $k$ active units per input, and effective weight and bias bounds $W,B$,...
Amari's contributions to information geometry and machine learning are well known. Here, we revisit Amari's work on Bayesian duality which has not received as much attention. We connect Amari's Bayesian duality to a convex duality of Bayes' rule. Using this connection, we present a generalization of Amari's Bayesian duality and...
Visual encoders construct a representation of the image input for Vision-Language models. How much conceptual, as opposed to immediately visible, information does this representation contain? We use canonical color as a controlled test case to ask whether vision encoders make canonical-color information linearly accessible, even when...
Autoregressive (AR) video diffusion models have shown great potential in real-time video generation. Recent methods distill pretrained bidirectional video diffusion models into causal AR students through Distribution Matching Distillation (DMD), but the generated videos often suffer from over-saturation and over-smoothing issues,...
Dexterous manipulation involves contact-rich and fine-grained interactions with the physical world, posing significant challenges for existing vision-language-action (VLA) models due to severe visual occlusions and complex contact dynamics. While recent works have incorporated tactile sensing into robotic manipulation, most approaches...
Normalization renders large parts of neural networks effectively scale invariant, inducing a hidden feedback loop in which learning-rate schedules and weight decay interact through the parameter norm to control the effective step taken by the optimizer. We show that this interaction is governed by an exact discrete-time law: a single...
Long horizon Large Language Model (LLM) agents rely on external memory systems to preserve user preferences and task knowledge across extended interactions. Conventional retrieval mechanisms optimize semantic compatibility rather than downstream utility, frequently introducing outdated, misleading, or conflicting evidence into the...
While research on recursive self-improvement (RSI) has predominantly automated model training pipelines, reliable autonomous development demands a missing pillar: post-hoc monitoring and auditing to understand what models learn and ensure safe alignment. Mechanistic interpretability tools are essential to bridge this gap, among which...
These days we are witnessing many mobile applications based on the recommended systems, which have become a great technology which is been used by the various mobile applications according to the situation. Recommendation provided by the mobile application is a key element for the person who is traveling to several places. For any...
We study the problem of navigating cluttered indoor environments with a humanoid robot. Unlike conventional methods that model navigation as a 2D path planning problem, humanoid traversal in cluttered environments requires continuous geometry-aware whole-body adaptation, including coordinated arm placement, torso adjustment, and gait...