arXiv preprints from January 1, 2026 through September 19, 2026 — 07:20:49 EST
Let $X$ be a normal variety, and let $π\colon\tilde X\to X$ be the successive blowup along subvarieties $Z_1,\dotsc,Z_n\subseteq X$ of codimension at least two that have simple normal crossings and satisfy $Z_h\not\supseteq Z_i$ whenever $h<I$. We prove that the relative cone of curves $\overline{\operatorname{NE}}(\tilde X/X)$ is...
We prove the André--Oort conjecture for hypersurfaces $V \subset Y(1)^n \cong \mathbb{A}^n_\mathbb{C}$ defined by an equation $a_1 x_1^m + \ldots + a_n x_n^m = b$, where $a_1, \ldots, a_n, b \in \overline{\mathbb{Q}}$ and $m \in \mathbb{Z}_{>0}$. Unlike previous proofs, our result is both effective and uniform in the height of the...
In 1854 Riemann presented his Habilitationsvortrag {\it Über die Hypothesen welche der Geometrie zu Grunde liegen} to the Faculty of Philosophy of the University of Göttingen. The lecture does not contain analytical developments and Riemann never explained the reason for this choice. According to Dedekind this choice was done in order...
Let $k=\overline{\mathbb{F}_2}$. We construct a nine-dimensional $F$-rational affine variety $X$ admitting a locally closed embedding $X\hookrightarrow \mathbb{P}_k^{19}$ together with a dense open set $U\subseteq (\mathbb{P}^{19})^\vee$ such that $X\cap H$ is not $F$-rational (or even $F$-injective) for all $H\in U$. We also...
This paper solves the Wehrl-type entropy problem for arbitrary compact connected semisimple Lie groups. Let $G$ be a compact connected semisimple Lie group, and let $π:G\to U(V_λ)$ be a finite-dimensional irreducible unitary representation associated with the highest weight $λ$. We prove that coherent projectors are the unique...
Taming the exponential increase of the Hilbert space dimension with system size in the simulation of gapped quantum lattice models is of the highest relevance for understanding and designing exotic quantum materials, where nonlocal interactions are of particular interest. High-order linked-cluster expansions provide access the...
Human videos contain rich causal evidence for robot manipulation: they reveal how hand motion induces object motion and produces task-relevant changes in object state. In this work, we study articulated objects such as doors, drawers, cabinets, laptops, ovens, and hinged containers that are ubiquitous in daily life and present unique...
The strong matroid secretary conjecture asserts that every matroid admits a $1/e$-competitive secretary algorithm, matching the classical single-choice guarantee. We formulate a finite linear program whose value is the optimal ordinal competitive ratio of any fixed matroid; for all matroids of positive rank on seven elements and...
We evaluate six frontier language models on the two-agent $\log(N)$-Questions game. A questioner sees $N$ Wikipedia lead paragraphs and must identify a secretly chosen target using exactly $\log_2 N$ yes/no questions. An answerer sees only the target and the question, and replies with one word. Both roles run on the same provider, so...
Mixed-signal SoCs rely on nominally input-only analog pins to acquire off-chip signals, but the directionality of these interfaces is generally treated as a functional property rather than explicitly verified as a security property. This work identifies and experimentally demonstrates a directionality-based class of analog and...
Scaling laws predict how loss decreases with increases in computation. We show, contrary to conventional wisdom, that architectural interventions can modify scaling exponents in pre-training, leading to exponential improvements in performance with increases in computation. As an anchoring point, we consider the architectural...
Factory work is a promising early scenario for embodied AI: assigning repetitive manual jobs to robots has clear economic payoff, and a structured station keeps the jobs tractable for current policies. Vision-Language-Action (VLA) models now dominate as the policy paradigm for these robots. The inference latency of VLA models directly...
As models scale, reward hacking becomes more frequent, more sophisticated, and more consequential. Does it leave a telltale signature in model representations? This work analyzes how reward hacking is represented internally in frontier open source LLMs, and how those representations can be used to understand and discover the range of...
The Model Context Protocol (MCP) has emerged as the dominant interface for connecting autonomous agents to external data sources and execution environments. The ecosystem's transition from local process execution to remote Streamable HTTP deployments introduces unmeasured architectural and security constraints at scale. This paper...
Self-emulsifying drug delivery systems (SEDDS) can improve the oral bioavailability of poorly soluble drugs, but identifying high-performing formulations remains experimentally intensive. We present Andromeda 2, an agentic system that reasons over structured in-house experimental evidence and invokes computational and experimental...
This paper addresses leader-follower formation control using only relative bearing and velocity measurements. Bearing-based leader-follower control strategies commonly use fixed control gains, for which the guaranteed convergence rates explicitly depend on the persistence of excitation (PE) properties of the desired formations. We...
Can an attacker turn influence over an artificial intelligence (AI) adviser into a harmful quantum error-correction update? We identify an ambiguity in passive syndrome records that obstructs recovery selection, then show how additional calibration measurements support certified recovery updates under uncertainty and drift. In an...
This note establishes a geometric foundation for trajectory-manifold representations of deterministic nonlinear systems in a behavioral setting motivated by data-enabled predictive control. For a discrete-time system $x_{k+1}=f(x_k,u_k)$ with measured state and a $C^r$ transition map, $r\geq 1$, we consider the...
This paper establishes the necessary and sufficient conditions for asymptotic stability of the time-varying Kalman filter applied to a linear time invariant system with semidefinite initial state covariance and positive definite process and measurement noise. Rather than analyze the discrete Riccati equation as in the classic...
As data center (DC) loads increasingly penetrate the power grid, there is an urgent need for grid operators to provide clear dynamic specifications to DC owners to ensure safe grid operation. To this end, we study two salient behaviors of large language model (LLM) training loads: abrupt ramps at job initiation and termination, which...
Large Language Models (LLMs) are now routinely trained using synthetic data, since high-quality human data has been exhausted by the ever increasing needs of larger and larger models. However, recursive training on synthetic data frequently induces model collapse, a degenerative feedback loop where models progressively forget the true...
This paper addresses the problem of designing time-optimal control profiles for point-to-point control of a gantry crane moving in a two dimensional plane. It is assumed that the hoisting motor completes the hoisting maneuver at a constant rate and completes its transition in the same time that it takes for the cart to reach its...
Region-of-attraction (ROA) certificates for polynomial systems become expensive as state dimension and degree grow: direct sum-of-squares (SOS) formulations require combinatorially growing monomial bases. Quadratization represents a polynomial vector field exactly on an invariant manifold of a quadratic system, allowing a quadratic...
Two-stage stochastic Mixed-Integer Linear Programs are a canonical modeling tool to optimize power system operations under uncertainty, yet their extensive-form counterparts scale linearly with the number of scenarios and quickly become computationally prohibitive under day-ahead time constraints. We propose an Input Convex Neural...
The O-RAN control plane is becoming agentic: autonomous AI agents, deployed as rApps by different vendors, independently close control loops over shared radio resources. We demonstrate on a live O-RAN system that this independence is unsafe. Two agents with individually correct objectives, one protecting a latency SLA and one...