arXiv subjects

Hengyu Wang

Publications and source records attributed to Hengyu Wang.

6 recordsLinked to original sources

arXiv2026

Mockenhaupt's Three-Term Hardy-Littlewood Majorant Conjecture

For an integer $k \ge 0$, let $f_k(x) = 1 + e(x) + e((k+2)x)$ and $g_k(x) = 1 + e(x) - e((k+2)x)$ on $\mathbb{T} = \mathbb{R}/\mathbb{Z}$, where $e(x) = e^{2πi x}$. Mockenhaupt conjectured that $\|g_k\|_{L^p(\mathbb{T})} > \|f_k\|_{L^p(\mathbb{T})}$ whenever $2k < p < 2k+2$. The conjecture was previously known for $k \le 5$. We give a single analytic proof valid for every $k \ge 4$; in particular, this settles all previously open cases $k \ge 6$ and establishes the conjecture for every $k \ge 0$. The proof reduces the norm comparison to resonant Fourier coefficients on the two-torus and represents these coefficients, after analytic continuation, by triple-Bessel integrals. Neumann's product formula and the Weber-Schafheitlin formula yield a quantitative positive lower bound for the leading mode, while the remaining odd modes are controlled by a uniform tail estimate. The leading mode is then shown to dominate the tail for every $k \ge 4$. AI Usage. The mathematical argument of this paper was produced by the auto-research system Apex Math, an AI system built by Apex Intelligence. See Appendix A for the complete AI usage statement.

math.CA↗

arXiv2026

ASI-Bench: At the Dawn of Artificial Superintelligence

Artificial superintelligence (ASI) requires AI to move beyond mastering existing knowledge toward exploring the unknown, creating new knowledge, and turning new ideas into verifiable results. However, the capabilities of today's AI systems are still largely built on learning, compressing, and applying existing human knowledge. Accordingly, existing benchmarks primarily test whether AI can produce correct answers based on learned knowledge, or whether it can complete tasks under extensive human guidance. We therefore introduce ASI-Bench, the first benchmark to jointly evaluate AI systems' capabilities of innovative exploration and autonomous scientific execution across general research domains, and the first to progressively withdraw human methodological guidance within the same research project to test how far AI can proceed on its own. Built by over 40 experts with the cost of 31,000+ human hours, ASI-Bench contains 60 project-level research tasks across 11 scientific domains and progressively reduces methodological guidance to test whether AI can independently select methods, conduct research, and produce verifiable results. All tasks undergo expert review, AI-assisted auditing, sandbox execution, and scorer validation. Across 18 state-of-the-art agent--model configurations, the average score drops from 50.91 with full methodological guidance to 29.10 with only the method specified and 26.62 when agents must determine the method themselves. This sharp decline shows that current systems remain heavily dependent on human guidance and are still far from autonomously conducting end-to-end, project-level scientific research. ASI-Bench is open to the world. We invite researchers and builders everywhere to contribute new tasks, challenge the limits of today's AI, and help accelerate humanity's collective path toward artificial superintelligence at https://asibench.apexin.ai/submit.

cs.AI↗

arXiv2026

Halpern Iteration Achieves $\tilde{\mathcal{O}}(ε^{-1/p})$ $p$th-Order Oracle Complexity for Monotone Variational Inequalities

We study second- and higher-order methods for solving smooth monotone variational inequalities (MVI). Monteiro and Svaiter (SIAM J. Optim., 2012) showed that a second-order method, NPE, converges at the rate of $\mathcal{O}(T^{-1.5})$. For convex-concave minimax optimization, a subset of MVI problems, Chen, Liu, Luo, and Zhang (COLT 2025) recently improved the complexity to $\tilde{\mathcal{O}}( T^{-1.75})$ . However, it is open whether the conjectured complexity for MVI can be improved. In this paper, by using a large-step inexact Halpern iteration, we propose a novel Halpern-NPE method that achieves an even faster rate of $\tilde{\mathcal{O}}(T^{-2})$ for solving MVIs. We also provide the $p$th-order generalization of our method. We first introduce an Anchored Tensor Method (ATM) that achieves the rate of $\mathcal{O}(T^{-(p-1)})$, and then combine it with the Halpern iteration to achieve a faster convergence rate of $\tilde{\mathcal{O}}(T^{-p})$. This improves all prior results for $p \ge 2$ and matches the classical extragradient method for $p=1$.

math.OC↗

arXiv2026

Learning from all particles in high-energy collisions

Particle colliders stand as an irreplaceable pillar of inquiry for exploring the fundamental building blocks of matter and forces of the Universe, yet fully decoding complex collision event information remains a significant challenge. Recent advances in artificial intelligence (AI) have revolutionized complex data analysis across scientific disciplines, inspiring novel strategies to extract the rich information embedded in collider events. Here we introduce two complementary concepts -- the holistic approach and Advanced Color Singlet Identification -- to enhance signal-background separation, which is a critical prerequisite for precise physics measurements. By leveraging all reconstructed particles and inferring their parentage via deep learning, these methods improve the precision of key Higgs physics benchmark measurements by up to sixfold and enable realistic prospects for observing rare Higgs decays previously deemed inaccessible. Our results demonstrate how integrating particle-level information with modern AI technologies can substantially boost the discovery potential of high-energy colliders, paving a new path to unravel the fundamental physical laws underlying particle physics experiments.

hep-ex↗

arXiv2026

A Pathway to Sub-meV Detection of the Dark Universe: Robust Electron Avalanche in the PN junction at 10 mK

The search for light dark matter and cosmic primordial neutrinos necessitates detectors with sub-millielectronvolt (sub-meV) energy thresholds. While superconducting quantum sensors have approached this sensitivity, they often face significant challenges regarding readout complexity and scalability. To address these limitations, we propose a hybrid Superconductor-Insulator-P-N (S-I-P-N) detector architecture. This concept combines the high sensitivity of superconducting Cooper pair breaking with the massive intrinsic gain of semiconductor electron avalanches. A critical prerequisite for this scheme is operation at millikelvin (mK) temperatures, raising the critical fundamental question of whether silicon PN junctions can sustain avalanche multiplication in a regime where carrier freeze-out is severe. Here, we experimentally validate the critical semiconductor amplification stage of the proposed detector. We demonstrate that Silicon Photomultipliers (SiPMs) retain robust Geiger-mode avalanche capabilities at 10 mK. We report a single-photoelectron gain of order 10$^6$ and a dark count rate as low as 5~mHz/mm$^2$, 7 orders of magnitude lower than at room temperature. These results confirm the viability of high-gain semiconductor readout in the deep cryogenic regime, clearing the primary obstacle regarding the semiconductor component for the realization of scalable, sub-meV threshold S-I-P-N detectors.

physics.ins-det↗

arXiv2025

Prospect for measurement of CP-violating parameters of $B_s^0 \to ϕγ$ at the Tera Z factory

$b \to sγ$ transition is a critical flavor-changing neutral current (FCNC) process that could be used to probe CP violation (CPV) and new physics (NP). We quantify the anticipated precision for measuring $B_s^0 \to ϕγ$ at the CEPC Z pole operation, showing that the relative statistical uncertainty could be as low as 0.16\%, improved by approximately two orders of magnitude compared to existing measurements. Additionally, we perform a time-dependent analysis of the $B_s^0 \to ϕγ$ decay, accounting for $B_s^0/\bar{B}_s^0$ mixing extract the mixing-induced and CP-violating parameters $\boldsymbol{\mathcal{A}_{ϕγ}^Δ}$, $\boldsymbol{C_{ϕγ}}$ and $\boldsymbol{S_{ϕγ}}$. Using central value from LHCb measurement as input, we evaluate the anticipated accuracy of measurements of these parameters. The projected statistical uncertainties are $σ_{A_{ϕγ}^Δ{}^{\text{stat}}} = 0.021$, $σ_C^{\text{stat}} = 0.0092$ and $σ_S^{\text{stat}} = 0.0096$, and the systematic uncertainties are $σ_{A_{ϕγ}^Δ{}^{\text{syst}}} = 0.035$, $σ_C^{\text{syst}} = 0.0027$ and $σ_S^{\text{syst}} = 0.0064$. Furthermore, the 1$σ$ sensitivity boundaries for NP in this study are found to be $\mathcal{A}_{ϕγ}^Δ< -0.05$ or $\mathcal{A}_{ϕγ}^Δ> 0.15$, $\mathcal{C}_{ϕγ} < -0.02$ or $\mathcal{C}_{ϕγ} > 0.04$, and $\mathcal{S}_{ϕγ} < -0.04$ or $\mathcal{S}_{ϕγ} > 0.04$. We also conduct a relevant detector optimization study by establishing the correlation between the anticipated precision and the intrinsic resolution of the ECAL, as well as the performance of the PID system.

hep-ex↗