arXiv preprints from January 1, 2026 through September 7, 2026 — 07:35:40 EST
Recent video generators often omit audio or synthesize it in a separate stage, limiting reciprocal modeling of visual dynamics and acoustic events. We present DreamX-Creator 1.0, a compact native joint audio-video generation system centered on a 7B generator. Conditioned on a first frame and a text prompt, the generator jointly...
Users of a deployed language model routinely encounter behaviours that testing almost never surfaces, since deployment puts the model through orders of magnitude more interactions than any evaluation can simulate. Automated auditors make testing cheap to scale and flexible enough to cover almost any specified behaviour, yet their lack...
The chiral limit of the Bistritzer--MacDonald model for twisted bilayer graphene has exactly flat bands at magic angles. We show that exact flatness can persist beyond the chiral limit with nonchiral tunnelling potentials in the usual symmetry class. We construct a family of nonchiral tunnelling potentials for which the Hamiltonian...
We study statistical manifolds $(M,g,\nabla,\nabla^{*})$ endowed with a nonzero $(1,1)$-tensor field $Θ$ satisfying the gauge equation \[ \nabla_X(ΘY)=Θ(\nabla_X^{*}Y). \] We first characterize this condition in terms of the statistical difference tensor \[ K=\nabla-\nabla^{g}. \] When $Θ$ is parallel with respect to the Levi-Civita...
This article investigates the problem of assigning multiple identical interceptors over multiple identical aerial threats, where all interceptors are launched in a single salvo. For this problem, two strategies have been studied in the literature: (A) to spread all interceptors as evenly as possible over all threats, and (B) to...
Differential privacy provides a rigorous framework for protecting private information, typically achieved by adding random noise to query results. The generalized Gaussian family is a flexible class of additive noise distributions indexed by the shape parameter $p$ and includes the Laplace and Gaussian distributions as special cases...
In this paper, we obtain a full characterization of the finite positive Borel measures $μ$ on $\mathbb D$ for which the embedding $$ \operatorname{id}:\mathcal D_{p-1}^p\longrightarrow L^p(μ),\qquad p>2, $$ is bounded. More precisely, for any dyadic system $\mathcal D$ on $\mathbb T$, we prove that this embedding is bounded if and...
In this paper, we establish a new type of stability phenomenon for the topological entropy of Hamiltonian diffeomorphisms of closed surfaces. For a closed surface endowed with an area form $(Σ,ω)$ and a Hamiltonian diffeomorphism $φ$ of $(Σ,ω)$, we show that for every $\varepsilon>0$ there exists $A=A(φ,\varepsilon)>0$ such that \[...
In this work we are concerned with the controllability of time-varying lumped control systems governed by a semilinear differential equation. We consider the semilinear system as a perturbation of a linear system. Assuming the underlying linear system is controllable, and the nonlinear forcing function satisfies a boundedness...
In this paper, we initiate the study of colored exponential random graph models (ERGMs), a class of exponential-family models for networks with multiple types of edge relations. Using the framework of probability graphons, we first derive a variational representation for the limiting free energy, whose maximizers determine the...
We study the existence of gravitational radiation at infinity for pure-radiation Robinson-Trautman metrics with one spacelike Killing vector and a cosmological constant $Λ$ of arbitrary sign. These metrics describe "photon rockets" with point, string, and sheet sources moving through spacetime while emitting null radiation. For $Λ\neq...
Polymath8b proved that $H_1 = \liminf (p_{n+1}-p_n) \leq 246$. In this paper we show how the Bombieri-Vinogradov theorem can be combined with newer equidistribution estimates for smooth moduli to obtain the improved bound $H_1 \leq 240$.
We develop two methods for proving infinite girth from boundary dynamics. First, we use topologically free extreme boundary actions to give a boundary-dynamical proof of infinite girth for finitely generated acylindrically hyperbolic groups. The second combines Nakamura's criterion with, respectively, flag-space and Roller-boundary...
We prove that when the J-equation does not admit a smooth solution, there is always only a finite number of obstructing optimally destabilizing curves and divisors on compact Kähler manifolds of any dimension. For threefolds, this establishes the unconditional finiteness of all optimally destabilizing subvarieties. We moreover...
The motivation for this paper is the investigation of the trade-offs implicit in probabilistic models used in machine learning. Models are often used to make predictions in the form of conditional probabilities. However, a pair of conditional distributions p(x|y) and p(y|x) may not be compatible with any joint distribution p(x,y)....
The work introduces the novel Dunkl two-photon and Dunkl-Schrödinger algebras as reflection-extended counterparts of the standard six-dimensional two-photon and Schrödinger algebras. These extensions are realized through the presence of an involutive generator representing a reflection, and they reduce to the undeformed two-photon and...
We construct, for every even $n \ge 2$, a positive cone on $F_n \times \mathbb{Z}$ that is finitely generated as a semigroup, extending the previously known construction for $n = 2$. Malicet, Mann, Rivas and Triestino proved that $F_n \times \mathbb{Z}$ admits an isolated left-order if and only if $n$ is even. Since every finitely...
We determine the exact dimensional range in which a normalized longest signed sum, which we call a Bang vector, always satisfies the real polarization inequality: this prescription is universally valid if and only if \(n\leq 14\). For every \(n\geq 15\) we construct \(n\) unit vectors whose all-positive sum is, up to global sign, the...
We investigate the fake stationarity properties of solutions to forward Stochastic Volterra Integral Equations (SVIEs) with affine drift and long-memory (regular) kernels, both on finite horizons and in the long-run regime. By either deriving explicit closed-form specifications for the deterministic initial condition $φ$ and the...
Fushchych and Shtelen defined approximate symmetry by expanding the solution of a perturbed differential equation in the small parameter, replacing the original equation by a triangular system for the expansion coefficients. We extend this construction to arbitrary order. A coefficient-map formulation yields the order-$p$...
We present a quantum computing framework for simulating open-quantum-system approaches based on Markovian and non-Markovian dynamics, which is relevant to heavy-ion collisions. To simulate the non-Markovian evolution on quantum computers, we introduce an auxiliary two-level pseudomode that carries the memory forward and couples to...
We identify a memory effect produced by phonon scattering in a superfluid: a localized scattering event generates a far-field pressure pulse with vanishing time integral but a nonzero first temporal moment, corresponding to a permanent shift in a prepotential for the far-field velocity. The effect is controlled by the soft factor for...
We establish finite-energy Cauchy stability for vacuum and matter spacetimes with $T^2$ symmetry on $T^3$, under general constitutive equations satisfying hyperbolicity and mild asymptotic conditions at vacuum and large mass-energy density. First, using the area of the symmetry orbits as a time function, we introduce the JKL...
While WhisperX accelerates speech transcription via intra-audio batching, it isolates audio segments, losing the historical context needed for coherent punctuation and terminology transcription. Conversely, standard Whisper retains context sequentially but suffers from slow inference and hallucination loops. To achieve the best of...
Germanium is a leading platform for semiconductor spin qubits and spintronics. Yet its electron and hole spin dynamics remain understood primarily through phenomenological models. Here, we predict electronic transport and spin relaxation in bulk Ge entirely from first principles, combining hybrid-functional band structures with fully...