arXiv subjects

Yuhu Wang

Publications and source records attributed to Yuhu Wang.

3 recordsLinked to original sources

arXiv2026

Prime multipliers of order ten: norm spectra, local charts, and selective lifting

Write P(N) for the assertion that every principal minor of the Fourier matrix of order N is nonzero. The square-free principal-minor conjecture was previously known for a few uniform small-multiplier families, including several families with two prime factors; broader higher-factor results were non-uniform, apart from isolated exact verifications. We prove a near-complete prime-multiplier theorem for the composite base 10: P(10p) holds for every prime p \notin {2,5,11}. The proof begins with the complete cyclotomic norm spectrum of the principal minors of the order-ten Fourier matrix. Its rational-prime support is {2,3,5,11,31}. Ordinary finite-characteristic lifting settles the norm-safe multipliers. A known small-multiplier theorem handles one norm-exceptional case; another is settled by retaining the prime-ideal chart in which each carrier degenerates. This yields a flag-selective lifting lemma and an active-rank norm budget. The chart analysis also isolates the limitation at the remaining square-free exception: active carriers can cover every local chart, so the first-order argument stops. We discuss this obstruction, the non-uniformity of fixed-base lifting, and the difficulties in passing to general square-free orders. All finite calculations are exact and have been independently confirmed.

math.NT↗

arXiv2026

Principal nonsingularity of the Fourier matrices of orders \(70\) and \(143\)

We give computer-assisted proofs that every principal minor of each of the \(70\times70\) and \(143\times143\) Fourier matrices is nonzero. A lifting theorem of Caragea, Lee, Malikiosis, and Pfander reduces the two assertions to the nonvanishing of all principal minors of the Fourier matrix of order \(10\) in characteristic \(7\), and of order \(11\) in characteristic \(13\), respectively. We realize primitive roots in \(\mathbb F_{7^4}\) and \(\mathbb F_{13^{10}}\) and evaluate all \(2^{10}\) and \(2^{11}\) principal determinants by exact, division-free arithmetic. None vanishes. The lifting theorem in fact yields the stronger conclusions that every \(10\)-principal minor of the order-\(70\) matrix and every \(11\)-principal minor of the order-\(143\) matrix is nonzero. Self-contained standard-library verifiers for the finite-field calculations accompany the paper.

math.NT↗

arXiv2025

RoadSceneBench: A Lightweight Benchmark for Mid-Level Road Scene Understanding

Understanding mid-level road semantics, which capture the structural and contextual cues that link low-level perception to high-level planning, is essential for reliable autonomous driving and digital map construction. However, existing benchmarks primarily target perception tasks such as detection or segmentation, overlooking the reasoning capabilities required to infer road topology and dynamic scene structure. To address this gap, we present RoadSceneBench, a lightweight yet information-rich benchmark designed to evaluate and advance visual reasoning in complex road environments. Unlike large-scale perception datasets, RoadSceneBench emphasizes relational understanding and structural consistency, encouraging models to capture the underlying logic of real-world road scenes. Furthermore, to enhance reasoning reliability, we propose Hierarchical Relational Reward Propagation with Temporal Consistency (HRRP-T), a training framework for Vision-Language Models (VLMs) in which reward signals adaptively promote spatial coherence and semantic alignment throughout the reasoning process. This paradigm enables models to move beyond static recognition toward geometry-aware and temporally consistent reasoning. Extensive experiments demonstrate that our method achieves state-of-the-art performance across diverse road configurations. RoadSceneBench thus provides a compact yet powerful foundation for studying mid-level road semantics and fostering structure-aware autonomous perception. Our dataset is available at https://github.com/XiyanLiu/RoadSceneBench.

cs.CV↗