arXiv preprints from January 1, 2026 through September 21, 2026 — 18:30:28 EST
We construct counterexamples to Rockafellar's sum conjecture in which two maximally monotone operators satisfy the interior-domain condition but their sum is not maximally monotone. We give one counterexample on $c_0$ and another on $\ell^1$ with its usual norm. We establish a general construction theorem that computes the entire...
We study lower and upper box dimension prints for bounded subsets of \(\mathbb R^n\), defined by weighted covering numbers for independently oriented rectangular boxes with prescribed ordered side-length bounds. The limits range over all eccentricities, including unbounded aspect ratios. For every non-empty bounded set, we identify...
We characterize the standard modules of $\GL_{2m}(\C)$ that are distinguished by $\GL_m(\HH)$. Let $δ_1,\dots, δ_{2m}$ be characters of $\mathbb{C}^\times$. Assume that $S = δ_1 \times \cdots \times δ_{2m}$ is a standard module of $\GL_{2m}(\mathbb{C})$. For each $i$, define ${δ_i^*} (z) = δ_i(\overline{z})^{-1}$ for $ z \in...
We resolve two problems left open by Johnson and Kollár in their paper Arcology: Question 21 and the openness issue arising in Example 14.
We study an inextensible open filament with free ends in a planar Stokes fluid. The system reduces to a third-order nonlocal curvature equation coupled to an elliptic equation for the tension. We prove local well-posedness for nearly critical initial data in supported Sobolev spaces $\widetilde H^s$, $-1/2<s\le0$, satisfying the...
We prove that the best constant in the one-dimensional Lieb-Thirring inequality with exponent one is $4/(3\sqrt{3}π)$, confirming the Lieb-Thirring conjecture in this case.
This paper presents a unified invariant-domain-preserving (IDP) framework for hybrid discretizations of hyperbolic conservation laws, including active flux and PAMPA methods, in which cell averages are updated conservatively while cell-boundary point values evolve under a possibly non-conservative operator. The main challenge is to...
Let $X=(X_1,\dots,X_n)\in\{0,1\}^n$ have a multivariate totally positive ($\mathrm{MTP}_2$) law. We prove that $$ \sum_{i<j}\mathbb{E}\left[\left|\mathrm{Cov}(X_i,X_j \mid X_{[n]\setminus\{i,j\}})\right|\right] \le n/2, $$ and more generally a weighted MaxCut inequality for the fully conditioned covariances. As an application, we...
We prove that the intrinsic jump set of every locally integrable function on an equiregular Carnot-Carathéodory space is intrinsically countably rectifiable. A key new ingredient is a local scalar Whitney extension theorem for intrinsic $C^1$ functions.
Motivated by Wasserstein measures of dependence, we study the largest possible 2-Wasserstein distance between a joint distribution and the product of its prescribed marginals. For two uniform marginals, Catalano and Lavenant conjectured that the monotone and antimonotone couplings maximize the distance from the independent coupling....
We analyze a stochastic Newton optimization scheme for locating the unique global minimizer of a general nonconvex objective function. The method couples a Newton algorithm to additive Gaussian noise with state-dependent variance. In the bounded domain setting, we prove global almost sure convergence. The proof is based on two...
A costly inherited trait can spread when its descendants create a favorable local environment. We ask which finite contact structures sustain such a collective competitor and what their advantage costs. Individuals play a donation game, conferring benefit $b$ at cost $c$. Reciprocal weighted contacts determine averaged payoffs and...
We construct a $3$-generator $9$-relator group with unsolvable word problem. We use the group to construct two fixed-size Adian--Rabin families of group presentations, one with $4$ generators and $11$ relators, and another with $2$ generators and $10$ relators. As a consequence, $\#_7(S^2\times S^2)$ is topologically unrecognizable...
Recovering the linear relationships that govern a system from noisy measurements is a basic task across the physical and engineering sciences. Because every measured variable may carry an unknown amount of noise, classical regression must commit in advance to a set of structural assumptions: ordinary least squares requires a declared...
Most work on survival prediction focuses on estimating survival probabilities rather than predicting individual event times. Recent conformal methods have made it possible to construct prediction intervals for survival times with right-censored outcomes, but existing approaches are restricted to settings with covariates only measured...
We give the first deterministic polynomial time algorithm that approximates the permanent of arbitrary nonnegative rational matrices within a subexponential factor. For a matrix of order $n$, the approximation factor is \[ \exp\!\left(O\!\left(\frac{n(\log\log n)^2}{\log n}\right)\right)=\exp(o(n)). \] All previously known...
In modern AI Accelerators and GPGPUs, many concurrent cores repeatedly access the same shared data. This pattern occurs in attention, where different query tiles share the same K/V block, GEMM, where every tile in a row reads the same panel, and many other operators. We name this pattern parallel scan. Due to a significant amount of...
We determine the optimal sample complexity of low-rank quantum state tomography when each measurement may act jointly on at most $t$ samples. For sufficiently small $\varepsilon$, estimating an unknown state on $\mathbb{C}^d$ of rank at most $r$ to trace norm error $\varepsilon$ with constant success probability requires, and is...
Scientific workflow management (WMSs) systems automate execution, yet orchestrate using fixed, hand-tuned rules. LLM agents promise more autonomous orchestration, but it remains unclear where to introduce agentic reasoning, how to bound its risk, and when it actually helps. We present Avatar, an actor-based architecture comprising an...
Action-conditioned latent world models predict future visual representations, enabling zero-shot goal-conditioned robot planning and control. However, their predictions for fine-grained spatial and rotational actions are unreliable for full 7-DoF end-effector control. To address this gap, we introduce DUET-DINO, a simultaneous...
Credit default prediction is a tabular classification problem in which modest gains in F1 translate directly into reduced financial exposure. We ask whether Instantaneous Quantum Polynomial-time (IQP) circuits can produce features that improve a classifier over both its raw classical baseline and Kernel PCA - the strongest...
Geodesic polar coordinates (GPCs) provide an intrinsic parameterization over curved surfaces, but their accurate estimation remains challenging, particularly in the presence of anisotropic metrics, high curvature and complex topology. We introduce iLogMap, a method for computing GPCs in curved domains that recasts the angular...
Electric vehicle charging infrastructure presents a suite of novel cyber-physical threats. Among this infrastructure, charging stations are the most vulnerable elements. The software in the charging station supply equipment is particularly vulnerable. Currently, the software is an attack surface that is largely unprotected and poorly...
Recovering 3D human pose from monocular sports broadcasts remains challenging when players must be localized in a shared metric world coordinate system rather than only reconstructed relative to their own body. We introduce Field Converter, a geometry-initialized temporal residual framework for world-grounded 3D player pose estimation...
We provide an adaptive two-sided error testing algorithm for the binary rank of a $0,1$ matrix $M$ with query complexity $O(d^3\log(d+1)/ε^2)$, where $d$ is the tested binary rank bound and $ε$ is the distance parameter. This answers an open question posed by Parnas, Ron and Shraibman~\cite{parnas2021property}, who asked whether the...