Papers

We report the detection of a $\sim${{19}} GeV gamma-ray spectral excess (peak energy in observer frame) at $\sim$5.7$\sigma$ significance (3 degrees of freedom, without correction for trials and the look-elsewhere effect) in the Fermi-LAT data of the blazar 4FGL J0136.5$+$3906, based on $\sim${17} years of observations. The excess manifests as a distinct bump-like feature in the 100 MeV$-$1 TeV spectrum, with a flux of $\sim$3.6$\rm \times10^{-10}~ph~cm^{-2}~s^{-1}$. No similar feature is detected in nearby sources or background regions. The origin of this signal cannot be explained by standard blazar emission models and remains unknown. This Letter presents the observational finding without providing a definitive physical interpretation.

The TLA+ (temporal logic of actions) formal specification toolkit has seen widespread adoption in modeling modern distributed software systems including databases, storage systems, ledgers and coordination protocols. This popularity is despite its two significant limitations for software verification: Firstly, TLA+ offers no way to detect drift between software implementation and mathematical specification; secondly, TLC and TLAPS cannot provide satisfactory proofs of arbitrary temporal logic properties. We address the second limitation and take a first step towards the first by translating TLA+ specifications into Verus, an auto-active verifier built for Rust, via both a deterministic transpiler and an agentic translator. We demonstrate that our LLM-based pipeline is able to generate proof obligations from TLA+ specifications at scale, and to produce fully machine checkable proofs of both safety and liveness properties. Since temporal logic reasoning in Verus is a largely new task for LLMs, our work yields a valuable evaluation dataset, which we use to map out current generation model capabilities in Verus theorem proving.

We develop a dynamical mean-field framework for the full finite-time and stationary asymptotic Lyapunov spectra of random recurrent neural networks. At finite observation time, an exact log-determinant representation of tangent-propagator singular values leads to a closed-contour matrix Dyson equation for the smoothed spectral tail. In the stationary setting, a cocycle representation yields an operator equation for the asymptotic cumulative spectrum. Both formulations retain complete local gain histories and the repeated action of quenched connectivity. Direct singular-value calculations and network QR spectra support the predictions in the regimes examined, with sampling uncertainty and numerical cutoffs assessed separately. The stationary equation also recovers the known maximal exponent, and controlled gain-history replay illustrates how temporal correlations redistribute instability. This work was carried out in collaboration with ChatGPT 5.6 Sol. Toward the end of preparation we became aware of David G. Clark's contemporaneous work, Lyapunov spectrum of random neural networks[arXiv:2610.12426], which reports overlapping mean-field results for the full Lyapunov spectrum using a cavity approach.

A language model that keeps learning online must not slowly erode its own base capabilities. We ask which part of a modern LLM should absorb continual updates, by measuring how each choice changes the model's internal representations. On a 48-layer mixture-of-experts model with a native pretrained N-gram memory, we train a seven-task chain under three update mechanisms with identical data and budgets: updating only the N-gram memory table, continually training one shared LoRA adapter, and training a fresh LoRA per task that is merged into the backbone. We capture fixed-context representations at every layer and task boundary. Updating only the N-gram memory changes the base model's representations of general math and code inputs by 26%/15% (relative RMS), against 64%/35% for merged and 97%/39% for shared LoRA. This drift does not grow with the number of tasks: it reaches 25% after the first task and stays there for all seven, while both LoRA variants keep accumulating. Its generic behaviour is essentially unchanged (no code problem lost, math NLL -0.01), and every change is confined to inspectable, reversible table rows. The cost appears elsewhere: N-gram memory acquires new tasks more weakly and its stored tasks interfere with one another, losing as much old-task NLL as shared LoRA. We show that this forgetting is governed by drift on the learned tasks' own inputs, measured from the checkpoint at which each was learned, not by generic drift (Spearman rho=0.85; rho=0.71 on Llama-3-8B), and we derive the exact relations behind it: with a frozen head, every pairwise logit margin changes by the projection of drift onto a head-difference direction. These results support a design principle for long-running online learning: write new knowledge only into the memory table and keep the backbone fixed; the remaining problem, interference between stored tasks, then lies inside the memory.

We present a unified treatment of the data-fitting problems with quadratic (Hilbertian) regularization that arise in approximation theory, machine learning, engineering, and statistics. The generic problem is an optimization in the continuum: given $M$ linear measurements of an unknown function, one minimizes a convex data-fidelity term that is penalized by $\|\mathrm{L} f\|^2_{L_2}$, where $\mathrm{L} $ is a differential-like (spline-admissible) operator. The natural domain of the minimization is the native space $\mathcal{H}_\mathrm{L}$ of $\mathrm{L} $ - the largest Hilbert space over which the regularizer remains meaningful - for which we provide a concise and directly usable characterization. Central to our formulation is a measurement-adapted (conditioned) basis that decouples the null-space and spline components of the solution. This basis serves in three places. First, it tightens the formulation of our representer theorem, which confines the unique solution to an $M$-dimensional space without any orthogonality constraint on the coefficients. Second, it streamlines the implementation, as the exact discretization of the problem becomes an unconstrained convex program with closed-form solutions in the least-squares case, which covers ridge regression, Tikhonov regularization, and smoothing splines. Third, it makes the bridge with the minimum-mean-square-error estimation of generalized Gaussian processes, which is the topic of a companion paper.

This paper reviews recent progress in high-resolution timing, rate capability, and aging performance of particle detectors in the context of developments over the past 25 years. It focuses on MCP, SiPM, LGAD, 3D silicon, and SiEM detectors and compares their performance with that of gaseous timing detectors. In addition, preliminary results from a simplified simulation program, Mini-TCAD, are presented, indicating that hexagonal 3D silicon cells may provide better drift-time uniformity and timing resolution than square cells.

Evaluating an agent's ability to strictly satisfy diverse and procedurally complex requirements is essential to determining its practical reliability. Conducting such an evaluation demands agentic tasks that reconcile broad domain coverage with deep procedural complexity. Existing paradigms face a fundamental trade-off: expert-curated benchmarks achieve procedural depth but suffer from domain diversity bottlenecks, whereas crowdsourced benchmarks span diverse scenarios but lack execution rigor. To resolve this tension, we present SkillForgeBench, which leverages agent skills as unifying execution blueprints across three co-designed stages: (1) Resource Preparation uses domain-balanced skills to guide artifact retrieval, establishing broad workflow coverage; (2) Skill-driven Task Synthesis employs skills as procedural anchors to partition artifact roles, synthesize naturalistic task instructions, and package sandboxed scenarios for deep procedural execution; and (3) Holistic Evaluation Design translates skill-embedded requirements into fine-grained completion and process rubrics to enable strict requirement-level scoring. Comprising 842 sandboxed tasks across five major professional domains, SkillForgeBench reveals a steep capability hierarchy among eight mainstream agents, led by Opus 4.8 ($40.9\%$ strict completion). Requiring all constrains satisfaction uncovers severe capability bottlenecks across all model tiers that remain masked under individual rubric pass rates ($70.0\%$ to $85.7\%$ vs. $12.6\%$ to $40.9\%$). Crucially, under the external guidance from skills, top-tier agents obtain larger gains than low-tier agents (i.e., $\Delta 19.2\%$ for Opus 4.8 vs. $\Delta 5.8\%$ for Haiku 4.5). Finally, agents satisfy process rubrics far less frequently than completion rubrics (under $3\%$ for Haiku 4.5), proving that completion-only checks overestimate real-world agent reliability.

Robust motion planning and control for manipulators is the problem of guaranteeing safe execution and collision-free motion under disturbances. The Kinodynamic Motion Planning via Funnel Control (KDF) is a recently proposed planner that comes with robustness guarantees and is particularly attractive for collision-free control as it guarantees closed-loop evolution inside a funnel, i.e., a collision-free region around a nominal trajectory. Despite its attractive theoretical properties, the current approach for computing funnels is computationally demanding, which limits its expressiveness and performance. We address its current limitations by proposing a novel funnel planning and control solution. Our key tool to enable this is a neural Signed Configuration Distance Function (nSCDF) which allows us to estimate collision-free balls and gradients in a computationally efficient way. We use the nSCDF in our planner to compute a nominal trajectory, where path length and clearance are balanced. To track the trajectory with collision-avoidance guarantees, we design a funnel controller that exploits the geometric information from the nSCDF. From numerical experiments, we observe that our planner produces nominal paths $2$ times faster, while at the same time obtaining $20 \%$ shorter path length and $5$ times the clearance. Finally, we also observe improved motion performance and robustness properties when using the nSCDF for funnel control.

Invasive alien species (IAS) generate substantial ecological and economic damages that often transcend political boundaries, creating strong incentives for coordinated management. We develop a two-region ecological-economic model of IAS control that integrates prevention and eradication measures with population dynamics characterized by logistic growth and an Allee effect. We derive analytical results on the interaction between ecological thresholds and strategic behaviour and compare outcomes under cooperation (central planner) and non-cooperation (open loop Nash equilibrium and Markovian Nash equilibrium). We show that, under realistic control costs, neither prevention nor eradication can eliminate invasive populations in finite time, and complete prevention of cross-border spread is generally not optimal. In the absence of an Allee effect, the zero-population equilibrium is unstable, implying long-run persistence of the invasive species. By contrast, the presence of an Allee effect fundamentally alters system dynamics by making extinction locally stable and creating a basin of attraction within which eradication becomes feasible. This finding highlights the economic significance of ecological thresholds and demonstrates how delays in management can shift populations beyond critical levels, after which eradication is unlikely regardless of subsequent control efforts. Numerical simulations further show that cooperative management expands the set of initial conditions leading to eradication and consistently reduces aggregate social costs relative to decentralized management. The results provide a formal rationale for rapid intervention, precautionary regulation, and stronger multilateral cooperation in IAS management, particularly in jurisdictions such as the European Union where listing and control actions may be delayed pending evidence of harm.

Developing terminal-based agents for long-horizon execution demands synthetic tasks that tightly couple complex instructions with authentic, interactive environments. However, current automated synthesis suffers from a fundamental asymmetry: instruction-oriented methods fabricate low-fidelity, synthetic environments, whereas resource-oriented methods treat real artifacts merely as static inputs, degrading task instructions into shallow, trivial operations. To address this limitation, we introduce WorkBorne, a synthesis framework that uses artifact transitions as the central primitive for modeling the full life-cycle of agentic tasks. In WorkBorne, each transition specifies who performs the task, which artifacts anchor the initial state and intended outcome, and the corresponding relationship between them. Specifically, WorkBorne first constructs coherent and diverse artifact corpora from iterative web retrieval, then discovers non-trivial transitions by identifying meaningful input-output artifact assemblies and the relations that connect them. Each discovered transition is finally instantiated into grounded agentic tasks. We construct 1,061 artifact corpora and 7,882 task environments, yielding 15,485 high-quality trajectories, with 53.6% exceeding 30 assistant turns. Experiments on Qwen3.5-27B and Qwen3.5-35B-A3B show that WorkBorne substantially improves over base models (i.e., improving Terminal-Bench 2.1 from 43.1% to 61.8% and ClawEval General score from 75.0 to 80.2) and achieves the strongest overall performance among other synthesis baselines (e.g., TMax (Ivison et al., 2026), RST (Li et al., 2026a), Terminal-Universe (Wu et al., 2026a)). Further analysis shows that transition is strongly associated with execution depth, while corpus breadth and transition depth provide complementary scaling gains.

We prove that the realization functors obtained by alternating forward and backward HRS tilts of any torsion pair over a finite-dimensional algebra are equivalences from some step onward. The number of steps is bounded by the lengths of the indecomposable projective modules. The even hearts define an increasing filtration of ideals contained in a square-zero ideal. For a torsion pair induced by a two-term silting complex, we identify the successive layers with Buan-Zhou kernel ideals and compute them by reduction modulo the successive ideals. We also describe the largest quotient over which the complex becomes tilting and determine the exact stabilization index from the two parity heights. We construct algebras for which the HRS height is arbitrarily large, and compute their ideal filtrations.

Reinforcement learning (RL) is essential for adaptive decision-making, e.g., robust Meta-RL and domain randomization (DR), and efficient post-training of large language models (LLMs), where tasks are commonly structured as Markov decision processes or prompts. A central bottleneck in all these settings is the cost of agent-environment interactions required for task selection and policy optimization. Model predictive task sampling (MPTS) has emerged as a promising approach to improve sample efficiency by querying informative tasks via a risk predictive model (RPM) trained on optimization history. However, existing RPMs suffer from two failure modes: (i) sparse optimization histories, which limit RPMs' generalization across the task space, and (ii) a one-step lag in risk approximation, which causes biased difficulty estimation as the policy evolves. This work formalizes these failure modes, derives lagged-risk decompositions that expose the resulting temporal bias, and recasts risk prediction as an in-context sequence modeling problem. The developed RPM integrates a one-step look-ahead mechanism with a temporal-weighted sliding window to mitigate data non-stationarity and scarcity, without requiring additional rollouts. Empirically, our approach yields more reliable difficulty estimates and consistent performance gains across robust Meta-RL, DR, and prompt curriculum RL post-training of LLMs.

Language models are increasingly used to create synthetic survey samples, also called silicon samples. Decision models are a new class of language models that return a probability for each point of a rating scale instead of text. We ask whether these models, or the newest generative LLMs, can stand in for human respondents on a psychometric survey. We test fourteen decision models from eleven providers and 47 generative LLMs on an open Lithuanian organisational-psychology survey (n=263, 68 items), with 100 real respondent profiles, the Psychometric Similarity Score (PSS) and statistical baselines. The best generative model, MiniMax M3, reaches PSS 0.813. This is level with a Gaussian copula fit only on other respondents (0.824) and below a copula fit in sample (0.927). A second sample of 100 real people scores below the best models, so at this size PSS cannot rank them against real respondents. In 5 of 10 product lines the newest generative release scores below an earlier release of the same line beyond resampling noise, and none gains beyond it. With the default rounded readout, 13 of 14 decision models score below the generative reference gpt-5.4-mini. Of the 47 generative models, 33 reproduce the pattern of item correlations better than any decision model. Averaged over respondents, the probability vectors are much closer to the human item marginals than rounded answers. They also rank respondents about as well as a profile regression fit on 163 real people. As forecasts of each person's own answers, however, every decision model is worse than the answer frequencies of other respondents, mainly because its average vector differs from them. The profile regression improves on these frequencies by only 1.0%, so the profile fields say little about how a person answers. Synthetic respondents built on such profiles should therefore aim at sample-level fidelity.

Multi-human cooperative object manipulation is a highly challenging topic in humanoid control. While existing methods can handle simple collaborative carrying tasks, they struggle with role-dependent, long-horizon, and sequential cooperative manipulation. To address this issue, we propose a hierarchical commander-executor framework that enables multiple agents to accomplish complex collaborative tasks in distinct ways. Specifically, a commander combines instructions and scene information for joint semantic and geometric planning. It then decomposes the task into role-specific subtasks and generates shared object-centric coordination plans, specifying execution timing, target positions, and manipulation actions for each agent. Conditioned on the commander's high-level strategy and each agent's local observations, the executor learns a low-level physics-based policy through a solo-to-cooperative curriculum to realize coordinated human-object interactions. The planned object trajectory provides a shared coordination target, while root positions and grasping instructions specify role-dependent execution cues. We evaluate our method on a variety of object manipulation tasks, demonstrating its ability to execute long-horizon tasks that combine different types of collaboration and to scale from two-agent to multi-agent cooperation. Extensive experiments further show that our approach achieves higher success rates compared to state-of-the-art methods. Code will be made publicly available at https://github.com/TJU-3DV/Co-Manipulation.

In this paper, new existence and multiplicity results for positive periodic solutions of singular second-order problems under sublinear and superlinear growth assumptions at infinity are established. Two aspects of our results should be highlighted in comparison with the existing literature. On the one hand, they allow for the consideration of systems exhibiting mixed behavior: sublinear in one component and superlinear in another. On the other hand, in the superlinear case, the existence of up to four positive solutions is established, whereas only two were obtained in previous works. Our approach is based on a recently established vectorial version of the Krasnoselskii-Guo fixed point theorem in product spaces.

Self-force effects are essential for accurately describing the motion of small bodies in curved spacetime. The effective-source approach privides a promising route to higher-order self-force calculations. In this paper, we construct analytic electromagnetic effective source for geodesic motion in Schwarzschild spacetime. An angular completion and a tetrad decomposition express the vector-harmonic puncture modes as finite sums of scalar modes. We derive the coupling coefficients for both parity sectors and obtain the effective sources from the Maxwell mode equations. The point-particle delta contribution cancels, and representative eccentric-orbit results show finite mode sources near the particle. These expressions provide the source terms for future $1+1$-dimensional residual-field calculations.

MAB phases are nanolaminated ternary borides in which strong in-plane M-B bonds and weaker interlayer interactions drive their distinctive stability and functionality. Hydrostatic pressure offers a direct route to tune the in-plane and interlayer interactions that govern the stability and functionality of layered Y2GaB and Y2InB borides. Here, first-principles calculations are used to compare their structural, elastic, thermophysical, electronic, bonding, optical, and vibrational responses from 0 to 20 GPa. Elastic criteria show that Y2GaB is stable at 0, 5, and 10 GPa, whereas Y2InB is stable only at ambient pressure. Within the stable Y2GaB range, compression increases the elastic moduli, acoustic velocities, Debye temperature, and lattice thermal conductivity while reducing the elastic anisotropy. Both compounds are multiband metals and spin-orbit coupling modifies local dispersions without opening a gap. Y2GaB retains nine Fermi-surface sheets from 0 to 10 GPa, whereas Y2InB has eight at ambient pressure, with no pressure-induced topological reconstruction. Charge-density and overlap analyses indicate mixed ionic-covalent Y-B bonding within a delocalized metallic background. Optical parameters are anisotropic. Unit-cell phonon spectra contain positive frequencies at 0 and 10 GPa, although expanded-supercell calculations reveal low-frequency sensitivity. These results establish mechanically viable pressure windows and clarify substitution-driven structure-property relationships for these borides.

Optimal transport (OT) enables multivariate conformal prediction (CP) to construct flexible prediction sets that reflect the underlying complex distributional geometry while retaining distribution-free coverage guarantees. Existing OT-based methods typically rely on a fixed Euclidean transport cost, which can be suboptimal in terms of the volume of prediction sets. We propose Minimum-Volume OTCP, a framework that learns a Mahalanobis ground cost to directly minimize prediction-region volume over a class of positive-definite metrics. Using a metric Brenier representation, we derive a volume-based objective that depends explicitly on the Mahalanobis cost matrix and optimize it jointly with the transport map. We establish finite-sample marginal coverage of the output prediction sets and optimality of volume metrics. We further develop an individualized extension that learns covariate-dependent transport metrics, adapting the shape and orientation of prediction sets to heterogeneous conditional distributions. For this extension, we also show the asymptotic conditional coverage of our method. Simulations and real-data experiments demonstrate substantial reductions in prediction-set volume.

The variational theory of splines requires a native space: a Hilbert space over which the regularization energy $\|\mathrm{L} f\|_{L_2}^2$ is well defined and the minimum-energy interpolation problem admits a spline solution. In this paper, we characterize the operators $\mathrm{L}$ that enable the construction of such spaces. Our framework is based on the completion of a space $\mathcal{S}$ of test functions in a controlled Gelfand-triple configuration $\mathcal{S}\subset\mathcal{H}\subset\mathcal{S}'$, which we call a Hilbert-Gelfand space. This departs from the classical reproducing-kernel techniques. Our construction is substantially more general, as it supports arbitrary linear operators and singular behaviors, and it recovers the reproducing-kernel setting as a particular case. It is also complete and canonical: the admissibility conditions on $\mathrm{L}$ are necessary and sufficient, and $\mathrm{L}$ determines its native space as the unique Hilbert-Gelfand space on which it extends to a bounded surjection onto $L_2$. We first show that Hilbert-Gelfand spaces are in one-to-one correspondence with compatible Riesz pairs $(\mathrm{A},\mathrm{A}^{-1})$ of positive-definite operators $\mathcal{S}\to\mathcal{S}'$. We then extend this correspondence to conditional Riesz pairs, where $\mathrm{A}$ is only conditionally positive-definite, which is the scenario that is relevant to splines. The theory identifies the attainable null space of the energy as the unique admissible conditioning, realizes the abstract completions as concrete spaces of distributions, and provides a verifiable admissibility condition in terms of a dual energy functional. The framework is illustrated with the fractional Laplacian, which covers polyharmonic and thin-plate splines, and with ordinary differential operators, which cover exponential splines.

This work explores the edge state conduction properties of twinned and spiraled, 2D Sb2Te3 topological insulator crystals. We show the structure supports spatially continuous edge states within two spiral and knotted edge conduction channels. The channels are connected through a topological defect. This geometry introduces boundary conditions into the 2D crystal that modifies the edge state dispersion. Using a combination of low loss Electron Energy Loss Spectroscopy, Magnetic Force Microscopy and traditional carrier transport measurements we identify a distinct excitation at 0.155 eV in the spiral that seems to be related to two isolated states within the gap. This state is localized to the crystal edges. The modification of edge state bands using manipulation of a systems quantum geometry may open new avenues for the use of 2D topological systems.

We study prediction with expert advice over $T$ rounds with $K$ experts under heavy-tailed losses whose $(1+\epsilon)$-moment is bounded by $\theta>0$ for some $\epsilon\in(0,1]$. In this setting, existing algorithms designed for the case $\epsilon=1$ can be suboptimal when $\epsilon<1$, suffering an additional polynomial dependence on $K$. We characterize the minimax pseudo-regret rate as $\Theta((\theta T)^{\frac{1}{1+\epsilon}}(\log K)^{\frac{\epsilon}{1+\epsilon}})$ and establish gap-dependent lower bounds in a self-bounded environment. To attain this minimax rate without prior knowledge of either $\epsilon$ or $\theta$, we propose Adaptive Heavy-Tailed FTRL, which uses robust data-dependent scale adaptation together with truncation. We further develop Adaptive Heavy-Tailed OMD, which likewise requires neither $\epsilon$ nor $\theta$ and achieves near-optimal regret guarantees in both adversarial and self-bounded environments. Finally, when $\epsilon$ and $\theta$ are known, an FTRL algorithm with Shannon-entropy regularization achieves optimal regret guarantees in both environments.

5G edge network slicing must reconcile two coupled requirements: understanding high-level operator intent and reallocating scarce computing and bandwidth resources under dynamic contention. Centralized optimization can face computational and responsiveness challenges under rapidly changing edge contention, and Multi-Agent System (MAS)-based auctions can support resource arbitration but still depend on operator-defined economic parameters and priorities. Embedding a Large Language Model (LLM) directly in a recurring control loop, by contrast, may introduce non-negligible inference latency and non-deterministic behavior. This paper proposes a two-timescale architecture that addresses this gap: an LLM-based Strategist translates natural-language network intents into economic policy parameters (budget, income, and bidding-aggressiveness) at the macro scale, while a deterministic, Vickrey-inspired second-price mechanism run by SPADE-based slice agents resolves recurring resource contention at the operational scale, with the resulting allocations enforced by patching Kubernetes CPU limits and Calico CNI bandwidth annotations directly on User Plane Function pods. We evaluate the architecture end-to-end on a real Kubernetes/Open5GS edge cluster across two complementary scenarios, each repeated 30 times: a Smart-City scenario, in which natural-language public-safety intents propagate into measurable changes in slice bids and bandwidth allocations within a few auction rounds, and a Hierarchical-slicing scenario, in which the mechanism provides priority-dependent resource and QoE differentiation, adapts to abrupt demand changes, and preserves configured minimum guarantees while maintaining near-complete allocation of the shared bandwidth pool.

To solve a family of large linear systems where the system matrix depends on the family parameter quadratically, we propose a new solution approach. Our method employs the derivatives of solutions with respect to the parameter. It turns out that the accumulated solution derivatives of increasing order, evaluated at a single specially chosen parameter value, provide successively better approximations to solution subspaces for the whole linear system family. We show that the derivatives can be computed by a recurrence, involving, at each step, solving a linear system with the same matrix. Constructing an orthonormal basis for the subspace spanned by the derivatives then leads to an efficient solver where just a single (sparse) LU factorization (or a single preconditioner setup in an iterative scheme) suffices to solve the whole linear system family. We call the new method ODB (orthonormal derivative basis method). As shown in numerical tests, compared to conventional solution methods, the ODB method allows to drastically reduce computational costs.

We study the Gibbs measure of $H(h) = \Re\sum_{p^{j} \leq X}U_{p}^{j}/(j p^{j(\sigma + i h)})$, a random field modeling large values of the log-modulus of the Riemann zeta function on and near the critical line, where the $U_{p}$ are independent and uniformly distributed on the complex unit circle. Writing $t = \log \log T$, the cutoff $X$ and real part $\sigma$ may vary with $T$ subject to $T^{1/t^{\Phi}} \leq X \leq T^{1/t^{\phi}}$ and $0 \leq \sigma - 1/2 \leq C_{\sigma}t^{\Phi}/\log T$, for fixed $\Phi \geq \phi > 1/2$ and $C_{\sigma} > 0$. On $I_{\theta} = [ - (\log T)^{\theta},(\log T)^{\theta}]$, define the Gibbs measure $G_{\beta,\sigma,T}^{\mathrm{H}}(\mathrm{d}h) := e^{\beta H(h)}\mathrm{d}h/\int_{I_{\theta}}e^{\beta H(h')}\mathrm{d}h'$. For every fixed $\theta > - 1$ and inverse temperature $\beta > 0$, the limiting joint distributions of correlations (overlaps) among points sampled from this measure are determined after averaging over the Haar phases. At and below $\beta_{c}(\theta) = 2\sqrt{1 + (\theta \vee 0)}$, the limiting two-overlap distribution is concentrated at $q_{0} = |\theta \wedge 0|$. Above this threshold, it assigns masses $\beta_{c}(\theta)/\beta$ and $1 - \beta_{c}(\theta)/\beta$ to $q_{0}$ and $1$, respectively, and the limiting joint overlap distribution is described by a Poisson-Dirichlet process of parameter $\beta_{c}(\theta)/\beta$. Approximate Ghirlanda-Guerra identities are shown to hold uniformly for bounded deterministic functions of the sampled positions. This paper is the first in a series devoted to extending these results to $\log|\zeta|$ near the critical line.

Multi-subject, multi-step scoring requires consistent partial credit across grading conventions. We introduce TeachGrade, a training-free framework using teacher-graded examples. The Task Adapt module builds two frozen memories: Skill captures contextual teacher preferences beyond the rubric; CaseBank supplies local evidence. PreJudge provides retrieval cues; FinalJudge regrades the answer without preliminary scores. On 3,829 SAS-Bench answers across 12 tasks, official macro collaborative consistency score (CCS) rises from Native's 67.99 to 81.32 (+13.33 points), and pooled step exact match from 54.85% to 62.71%. Macro quadratic weighted kappa (QWK) reaches 84.71, exceeding Native, OpenJudge, ProofGrader, and Trojsten by 9.52, 3.50, 11.37, and 17.43 points, respectively, and leading on 8 tasks. Local Qwen3.8-27B gains 8.83 CCS and 4.08 QWK points, improving CCS on all 12 tasks. QWK gains over Native span 6.38–14.65 points on Portuguese automatic essay scoring (AES) and 2.16–2.24 on ASAP-SAS across label views, with lower mean absolute error. These results support reuse across languages, response formats, and backbones without weight updates.

The sudden growth in AI data centers is raising numerous environmental concerns. Low-frequency noise pollution is a concern for local residents, that may not just be an annoyance but also carry significant health impacts. An FDTD model of sound propagation over the topography near an AI data center is presented. The topography plays a large role in the level of noise pollution, with areas of sudden elevation on either side of the river near the AI data center more susceptible to high noise levels, while areas further afield largely protected from noise pollution by the topography. Understanding the role that topography plays in noise pollution, and capturing the noise pollution in specific topographies, can help identify areas where noise mitigation strategies might be best employed.

Mechanisation of a mathematical definition (also referred to as formalisation) has many benefits. Here, we focus on mechanising denotational semantic definitions of programming languages by embedding them in the Agda language. The Agda type-checker detects and reports any issues with the wellformedness and type correctness of the embedded definitions. To minimise the effort required, and to facilitate correlation of the original definition with its Agda embedding, mechanisation should not involve significant reformulation or extension. Here, we show how to embed conventional Scott-Strachey denotational definitions in Agda with almost no changes to $\lambda$-notation or domain equations. Agda notation for definitions of types and functions corresponds closely to the conventional meta-notation of denotational semantics. We have developed a collection of Agda modules with postulated types for commonly used domain constructors and their associated operations. We illustrate our approach with mechanisations of three denotational definitions: a model of the untyped $\lambda$-calculus, Plotkin's denotational semantics of PCF, and a semantics of a sublanguage of Scheme. In previous work, similar mechanisations in Agda have revealed several unsuspected wellformedness issues in published denotational definitions. Some of the postulated properties of our definitions are inconsistent with a classical set-theoretic interpretation of Agda. We conjecture that they would be consistent with an interpretation of Agda in a higher-order intuititionistic logic, such as that used by Simpson in his work on synthetic domain theory. After recalling previous work on mechanising domain theory, we consider the possibility of mechanising synthetic domain theory in Agda.

Let $\Gamma \le \mathrm{SL}(d+1,\mathbb R)$ be a torsion-free hyperbolic group dividing a properly and strictly convex domain $\Omega \subset \mathbb R\mathrm P^d$, and let $\rho: \Gamma \to \mathrm{SL}(d+1,\mathbb R)$ be the inclusion. We study representations of $\Gamma$ into the coaffine group that are deformations of $\rho\oplus 1 \in \mathrm{Hom}(\Gamma, \mathrm{GL}(d+2,\mathbb R))$ and that lie on the boundary of the locus of projective Anosov representations. In this setting, we identify a canonical limit set $\Lambda$ for the action and study its fine geometric features which are, in a suitable sense, stable. We prove the existence of an ending lamination that encodes the failure of the Anosov condition and the non-existence of a Cannon–Thurston map. Under certain conditions, we compute the Hausdorff dimension and show that the corresponding measure is positive.

Humanoid Behavior Foundation Models (BFMs) can execute impressive motions, but downstream applications such as loco-manipulation demand high whole-body positional accuracy. Existing BFMs suffer from a systematic command-execution gap, where executed motions deviate from desired ones. We show that additional test-time compute can improve execution without retraining the BFM. First, we introduce Test-Time Command Optimization (TTCO), which adapts the input command to the specific BFM to produce an executed trajectory closer to the desired motion. TTCO finds such commands by sampling-based optimization through closed-loop simulations of the BFM and robot dynamics. Across three BFMs on the AMASS dataset, TTCO reduces mean global body-position error by 79-84% in simulation. Second, we analyze test-time compute scaling and derive an approximate compute-optimal strategy that can sustain performance gains as the compute budget increases. Third, TTCO can generate BFM-specific action labels from recorded robot trajectories without requiring the original teleoperation body-motion commands. Simulation and real-robot experiments show that these labels are effective for training high-level loco-manipulation policies. This method also supports reusing existing demonstrations across BFMs.

Disagreements between randomized trials that address the same causal question pose challenges for the interpretation and synthesis of evidence. We sketch a causal framework for comparing the results of randomized trials that explicitly accommodates the possibility of trial engagement effects. Using counterfactual outcomes defined under joint interventions on treatment assignment and trial-related actions, we compare trial-native treatment effects with the effects transported from one trial to the population of another in a common target population. We show that standard conditions for transporting treatment effects across trial populations are not sufficient to guarantee agreement between transported and trial-native effects. Agreement additionally requires conditions governing how trial-related actions affect outcome across studies - for example, absence of trial engagement effects, equivalence of such effects across trials, or lack of interaction between trial engagement and treatment assignment. Our framework clarifies potential sources of disagreement across trials and extends existing approaches to study comparison to settings in which trial engagement effects may be present.