arXiv subjects

Zhixin Hu

Publications and source records attributed to Zhixin Hu.

5 recordsLinked to original sources

arXiv2026

VGPT-RSI for RH-Adjacent Formal Progress: Boundary Certificates, Verified Finite Lagarias Inequalities, and Explicit Failure Localization

The Riemann Hypothesis remains one of the central unsolved problems in mathematics. Rather than claiming proof, we investigate whether a verifiable AI-assisted reasoning system can produce reliable, formally checked partial progress while explicitly identifying the remaining mathematical obstructions. We apply the Verifiable Growing Physical Transformer with Recursive Self-Improvement (VGPT-RSI) to two RH-adjacent certification tasks. First, we construct and verify a finite RH-boundary certificate for inequality on a parameterized safe lower curve over a region. The numerical boundary curve is converted into a certificate-backed lower curve, audited using outward-rounded interval arithmetic and Arb/FLINT ball arithmetic, and then checked in Rocq/CoqInterval for the parameterized theorem. Second, we initiate a formal Lagarias-route certificate. Lagarias criterion states that RH is equivalent to the global inequality. We formalize the finite quantity and produce a Coq-checked finite certificate. The final system identifies the exact unresolved mathematical bottlenecks: formalizing the Lagarias equivalence, proving the global tail theorem beyond any finite cutoff, and potentially reducing counterexamples to colossally abundant or related extremal integers. These results demonstrate that VGPT-RSI can produce certified RH-adjacent formal progress, organize proof dependencies, and avoid overclaiming when the remaining obstruction is genuinely mathematical.

cs.AI↗

arXiv2026

Physical Transformer

Digital AI systems spanning large language models, vision models, and generative architectures that operate primarily in symbolic, linguistic, or pixel domains. They have achieved striking progress, but almost all of this progress lives in virtual spaces. These systems transform embeddings and tokens, yet do not themselves touch the world and rarely admit a physical interpretation. In this work we propose a physical transformer that couples modern transformer style computation with geometric representation and physical dynamics. At the micro level, attention heads, and feed-forward blocks are modeled as interacting spins governed by effective Hamiltonians plus non-Hamiltonian bath terms. At the meso level, their aggregated state evolves on a learned Neural Differential Manifold (NDM) under Hamiltonian flows and Hamilton, Jacobi, Bellman (HJB) optimal control, discretized by symplectic layers that approximately preserve geometric and energetic invariants. At the macro level, the model maintains a generative semantic workspace and a two-dimensional information-phase portrait that tracks uncertainty and information gain over a reasoning trajectory. Within this hierarchy, reasoning tasks are formulated as controlled information flows on the manifold, with solutions corresponding to low cost trajectories that satisfy geometric, energetic, and workspace-consistency constraints. On simple toy problems involving numerical integration and dynamical systems, the physical transformer outperforms naive baselines in stability and long-horizon accuracy, highlighting the benefits of respecting underlying geometric and Hamiltonian structure. More broadly, the framework suggests a path toward physical AI that unify digital reasoning with physically grounded manifolds, opening a route to more interpretable and potentially unified models of reasoning, control, and interaction with the real world.

cs.LG↗

arXiv2024

Interlayer coupling rotatable magnetic easy-axis in MnSe2 mono- and bi-layers

Interlayer coupling plays a critical role in tuning the electronic structures and magnetic ground states of two-dimensional materials, influenced by the number of layers, interlayer distances, and stacking order. However, its effect on the orientation of the magnetic easy axis remains underexplored. In this study, we demonstrate that interlayer coupling can significantly alter the magnetic easy-axis orientation, as shown by the magnetic easy-axis of monolayer 1T-MnSe2 tilting 67° from the z-axis, while aligning with the z-axis in the bilayer. This change results from variations in orbital occupations near the Fermi level, particularly involving nonmetallic Se atoms. Contrary to the traditional focus on magnetic metal atoms, our findings reveal that Se orbitals play a key role in influencing the easy-axis orientation and topological Chern numbers. Furthermore, we validated our conclusions by changing stacking orders, introducing charge doping, applying in-plane biaxial strains, and substituting non-metallic atoms. Our results highlight the pivotal role of interlayer coupling in tuning the magnetic properties of layered materials, with important implications for spintronic applications.

cond-mat.mtrl-sci↗

arXiv2023

Discovery and construction of surface kagome electronic states induced by p-d electronic hybridization

Kagome-lattice materials possess attractive properties for quantum computing applications, but their synthesis remains challenging. Herein, we show surface kagome electronic states (SKESs) on a Sn-terminated triangular Co3Sn2S2 surface, which are imprinted by vertical p-d electronic hybridization between the surface Sn (subsurface S) atoms and the buried Co kagome lattice network in the Co3Sn layer under the surface. Owing to the subsequent lateral hybridization of the Sn and S atoms in a corner-sharing manner, the kagome symmetry and topological electronic properties of the Co3Sn layer is proximate to the Sn surface. The SKESs and both hybridizations were verified via qPlus non-contact atomic force microscopy (nc-AFM) and density functional theory calculations. The construction of SKESs with tunable properties can be achieved by the atomic substitution of surface Sn (subsurface S) with other group III-V elements (Se or Te), which was demonstrated theoretically. This work exhibits the powerful capacity of nc-AFM in characterizing localized topological states and reveals the strategy for synthesis of large-area transition-metal-based kagome lattice materials using conventional surface deposition techniques.

cond-mat.mtrl-sci↗

arXiv2018

Wafer-scale fabrication of 2D van der Waals heterojunctions for efficient and broadband photodetection

A variety of fabrication methods for van der Waals heterostructures have been demonstrated; however, their wafer-scale deposition remains a challenge. Here we report few-layer van der Waals PtS2/PtSe2 heterojunction photodiodes fabricated on a 2" SiO2/Si substrate that is only limited by the size of work chamber of the growth equipment, offering throughputs necessary for practical applications. Theoretical simulation results show that the bandgap of PtS2 is shrunk to half of its original size in the PtS2/PtSe2 heterostructures, while PtSe2 exhibits a limited response to the coupling. Both PtSe2 and PtS2 layers in the coupled system are still semiconductors. Dynamic photovoltaic switching in the heterojunctions is observed at zero-volt state under laser illuminations of 532 to 2200 nm wavelengths. The PtS2/PtSe2 photodiodes show excellent characteristics in terms of a high photoresponsivity of 361 mAW-1, an external quantum efficiency (EQE) of 84%, and a fast response speed (66 ms). The wafer-scale production of 2D photodiodes in this work accelerates the possibility of 2D materials for practical applications in the next-generation energy-efficient electronics.

cond-mat.mes-hall↗