arXiv subjects

Zeming Sun

Publications and source records attributed to Zeming Sun.

17 recordsLinked to original sources

arXiv2026

Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory

Recent LLM-based mathematical reasoning agents have begun to tackle research-level problems and, in several cases, have contributed to the resolution of open problems. However, scaling and orchestrating such agents effectively remains challenging, due to the difficulty of coordinating parallel proof search while keeping intermediate claims organized and reliable. In this paper, we propose Danus, an orchestration system for research-level mathematical reasoning centered on a shared fact graph as a global memory-management mechanism. Danus consists of a main agent that performs planning and coordination, multiple worker agents that carry out proof search in parallel, and a stateless verifier that checks proposed mathematical claims before they are admitted into the fact graph. Each verified fact is stored together with its proof and logical dependencies, allowing the system to build long arguments incrementally while keeping the shared proof state organized. The main agent periodically summarizes the evolving proof state, redirects workers across promising directions, and supports interaction with human mathematicians through progress reports. We evaluate Danus through six research-level case studies in algebraic geometry, singularity theory, and combinatorics, illustrating how the fact-graph memory mechanism enables Danus to construct long, detailed mathematical proofs. Our results suggest that fact-graph-based orchestration provides an effective route toward scaling mathematical reasoning agents for long-horizon research problems. Danus is open source at https://github.com/frenzymath/Danus.

cs.AI↗

arXiv2026

On some open problems in commutative algebra resolved by Rethlas

We report on a collection of open problems in commutative algebra and related areas that have been resolved (proved or disproved) using the Rethlas natural-language automated reasoning system. The problems are drawn from several published lists, including Open Problems in Commutative Ring Theory (Cahen-Fontana-Frisch-Glaz), Erman-Sam's survey of Boij-S\"oderberg theory. For each problem we record the precise statement and a self-contained proof produced (with no human intervention) by Rethlas and subsequently verified by human experts.

math.AC↗

arXiv2026

Optimal bend-and-break for foliations

We show that for every foliation $\mathcal{F}$ of rank $r$ on a normal projective variety, the optimal constant in the bend-and-break inequality for tangent rational curves is $r+1$. The proof combines the method of Bogomolov--McQuillan and the bend-and-shatter method developed by Jovinelly--Lehmann--Riedl. The proof of the main result of this paper substantially uses generative AI, particularly the Rethlas system.

math.AG↗

arXiv2026

LeanSearch v2: Global Premise Retrieval for Lean 4 Theorem Proving

Proving theorems in Lean 4 often requires identifying a scattered set of library lemmas whose joint use enables a concise proof -- a task we call global premise retrieval. Existing tools address adjacent problems: semantic search engines find individual declarations matching a query, while premise-selection systems predict useful lemmas one tactic step at a time. Neither recovers the full premise set an entire theorem requires. We present LeanSearch v2, a two-mode retrieval system for this task. Its standard mode applies a hierarchy-informalized Mathlib corpus with an embedding-reranker pipeline, achieving state-of-the-art single-query retrieval without domain-specific fine-tuning (nDCG@10 of 0.62 vs. 0.53 for the next-best system). Its reasoning mode builds on standard mode as its retrieval substrate, targeting global premise retrieval through iterative sketch-retrieve-reflect cycles. On a 69-query benchmark of research-level Mathlib theorems, reasoning mode recovers 46.1% of ground-truth premise groups within 10 retrieved candidates, outperforming strong reasoning retrieval systems (38.0%) and premise-selection baselines (9.3%) on the same benchmark. In a controlled downstream evaluation with a fixed prover loop, replacing alternative retrievers with LeanSearch v2 yields the highest proof success (20% vs. 16% for the next-best system and 4% without retrieval), confirming that retrieval quality propagates to proof generation. We have open-sourced all code, data, and benchmarks. Code and data: https://github.com/frenzymath/LeanSearch-v2 . The standard mode is publicly available with API access at https://leansearch.net/ .

cs.IR↗

arXiv2026

The Absolute Anabelian Geometry of Virtual Curves of Arbitrary Genus

The objective of this paper is to further study the anabelian object referred to as \emph{pointed virtual curves}. Building upon previous work that investigated these fundamental-group-theoretic pullbacks of Galois sections in the genus-zero situation, we extend the central anabelian results to curves of arbitrary genus. To facilitate this generalization, we introduce the group-theoretic notion of an inclusion of CAVC-type and the categorical-theoretic notion of a virtual decuspidaloid. Furthermore, we establish a criterion regarding the "geometricity" of certain virtual curves, providing group-theoretic conditions under which a section of an arithmetic fundamental group arises from a rational point.

math.NT↗

arXiv2026

Automated Conjecture Resolution with Formal Verification

Recent advances in large language models have significantly improved their ability to perform mathematical reasoning, extending from elementary problem solving to increasingly capable performance on research-level problems. However, reliably solving and verifying such problems remains challenging due to the inherent ambiguity of natural language reasoning. In this paper, we propose an automated framework that integrates natural language reasoning with formal verification to tackle research-level mathematical problems. Our framework consists of two components: an informal reasoning agent, Rethlas, and a formal verification agent, Archon. Rethlas combines reasoning primitives with our theorem search engine, Matlas, to explore solution strategies and construct candidate proofs. Archon, equipped with LeanSearch, translates informal arguments into formalized Lean 4 projects through task decomposition, iterative refinement, and automated proof synthesis, ensuring machine-checkable correctness. Using this framework, we resolve an open problem in commutative algebra and formally verify the resulting proof in Lean 4 with essentially no human involvement. Additional case studies illustrate the capabilities of Rethlas in informal mathematical reasoning and discovery, as well as the ability of Archon to formalize research-level proofs in Lean 4. Our experiments demonstrate that strong theorem retrieval tools enable the discovery and application of cross-domain mathematical techniques, while the formal agent can autonomously fill nontrivial gaps in informal arguments. More broadly, our work illustrates a promising paradigm for mathematical research in which informal and formal reasoning systems, equipped with theorem retrieval tools, operate in tandem to produce verifiable results, reduce human effort, and support human-AI collaborative mathematical research.

cs.LG↗

arXiv2025

Microscopic Investigation of rf Vortex Nucleation in Nb3Sn Films Using a Near-Field Magnetic Microwave Microscope

We use a near-field magnetic microwave microscope to investigate and compare rf vortex nucleation in two superconducting radio-frequency (SRF)-quality Nb3Sn films fabricated by different methods: a conventional vapor-diffused film and an electrochemically plated film followed by thermal annealing, both of which are deposited on Nb substrates. The microscope applies a localized rf magnetic field to the sample surface and measures the resulting third-harmonic response P3f, which is particularly sensitive to rf vortex nucleation triggered by surface defects. Both Nb3Sn films exhibit nontrivial P3f(T) structures below 7 K that display the key signatures associated with rf vortex nucleation at local defects. The electrochemical film additionally shows multiple P3f(T) structures between 14 K and 16 K that are absent in the vapor-diffused sample. Our results highlight the influence of fabrication method on rf vortex penetration properties and demonstrate the utility of third-harmonic response as a local diagnostic tool for surface defects in Nb3Sn films.

cond-mat.supr-con↗

arXiv2025

The Absolute Anabelian Geometry of Virtual Curves Arising from Sections of Arithmetic Fundamental Groups of Configuration Spaces

The objective of this paper is to study the anabelian object referred to as \emph{pointed virtual curves}. Namely, given a family of curves $Y \rightarrow X$ over a field $k$ under suitable conditions, we consider the fundamental-group-theoretic pullback of a Galois section $G_{k} \rightarrow \Pi_{X}$. We show that, in various aspects, such pullbacks exhibit anabelian properties analogous to those of the fundamental group of a curve over $k$.

math.NT↗

arXiv2023

Measurements of the amplitude-dependent microwave surface resistance of an Au/Nb bilayer

Surface properties are critical to the capabilities of superconducting microwave devices. The native oxide of niobium-based devices is thought to consist of a thin normal conducting layer. To improve understanding on the importance of this layer, an attempt was made to replace it with a more easily controlled gold film. A niobium sample host microwave cavity was used to measure the surface resistance in continuous wave operation at 4.0 GHz and 5.2 GHz. Sample conditions studied include temperatures ranging from 1.6 K to 4.2 K with RF magnetic fields on the sample surface ranging from 1 mT to the maximum field before the superconducting properties were lost (quench field). The nominal film thickness of the gold layer was increased from 0.1 nm to 2.0 nm in five steps to study the impact of the normal layer thickness on surface resistance on a single niobium substrate. The 0.1 nm film was found to reduce the surface resistance of the sample and to enhance the quench field. With the exception of the final step from a 1.5 nm gold film to 2.0 nm, the magnitude of the surface resistance increased substantially with gold film thickness. The nature of the surface resistance field-dependence appeared to be roughly independent from the gold layer thickness. This initial study provides new perspectives and suggests avenues for optimizing and designing surfaces for resonant cavities in particle accelerators and quantum information applications.

cond-mat.supr-con↗

arXiv2023

Thermodynamic route of Nb3Sn nucleation: Role of oxygen

Intermetallic Nb3Sn alloys have long been believed to form through Sn diffusion into Nb. However, our observations of significant oxygen content in Nb3Sn prompted an investigation of alternative formation mechanisms. Through experiments involving different oxide interfaces (clean HF-treated, native oxidized, and anodized), we demonstrate a thermodynamic route that fundamentally challenges the conventional Sn diffusion mechanism for Nb3Sn nucleation. Our results highlight the critical involvement of a SnOx intermediate phase. This new nucleation mechanism identifies the principles for growth optimization and new synthesis of high-quality Nb3Sn superconductors.

cond-mat.mtrl-sci↗

arXiv2023

Surface oxides, carbides, and impurities on RF superconducting Nb and Nb3Sn: A comprehensive analysis

Surface structures on radio-frequency (RF) superconductors are crucially important in determining their interaction with the RF field. Here we investigate the surface compositions, structural profiles, and valence distributions of oxides, carbides, and impurities on niobium (Nb) and niobium-tin (Nb3Sn) in situ under different processing conditions. We establish the underlying mechanisms of vacuum baking and nitrogen processing in Nb and demonstrate that carbide formation induced during high-temperature baking, regardless of gas environment, determines subsequent oxide formation upon air exposure or low-temperature baking, leading to modifications of the electron population profile. Our findings support the combined contribution of surface oxides and second-phase formation to the outcome of ultra-high vacuum baking (oxygen processing) and nitrogen processing. Also, we observe that vapor-diffused Nb3Sn contains thick metastable oxides, while electrochemically synthesized Nb3Sn only has a thin oxide layer. Our findings reveal fundamental mechanisms of baking and processing Nb and Nb3Sn surface structures for high-performance superconducting RF and quantum applications

cond-mat.mtrl-sci↗

arXiv2023

ZrNb(CO) RF superconducting thin film with high critical temperature in the theoretical limit

Superconducting radio-frequency (SRF) resonators are critical components for particle accelerator applications, such as free-electron lasers, and for emerging technologies in quantum computing. Developing advanced materials and their deposition processes to produce RF superconductors that yield nanoohms surface resistances is a key metric for the wider adoption of SRF technology. Here we report ZrNb(CO) RF superconducting films with high critical temperatures (Tc) achieved for the first time under ambient pressure. The attainment of a Tc near the theoretical limit for this material without applied pressure is promising for its use in practical applications. A range of Tc, likely arising from Zr doping variation, may allow a tunable superconducting coherence length that lowers the sensitivity to material defects when an ultra-low surface resistance is required. Our ZrNb(CO) films are synthesized using a low-temperature (100 - 200 C) electrochemical recipe combined with thermal annealing. The phase transformation as a function of annealing temperature and time is optimized by the evaporated Zr-Nb diffusion couples. Through phase control, we avoid hexagonal Zr phases that are equilibrium-stable but degrade Tc. X-ray and electron diffraction combined with photoelectron spectroscopy reveal a system containing cubic ZrNb mixed with rocksalt NbC and low-dielectric-loss ZrO2. We demonstrate proof-of-concept RF performance of ZrNb(CO) on an SRF sample test system. BCS resistance trends lower than reference Nb, while quench fields occur at approximately 35 mT. Our results demonstrate the potential of ZrNb(CO) thin films for particle accelerator and other SRF applications.

cond-mat.mtrl-sci↗

arXiv2023

Smooth, homogeneous, high-purity Nb3Sn superconducting RF resonant cavity by seed-free electrochemical synthesis

Workbench-size particle accelerators, enabled by Nb3Sn-based superconducting radio-frequency (SRF) cavities, hold the potential of driving scientific discovery by offering a widely accessible and affordable source of high-energy electrons and X-rays. Thin-film Nb3Sn RF superconductors with high quality factors, high operation temperatures, and high-field potentials are critical for these devices. However, surface roughness, non-stoichiometry, and impurities in Nb3Sn deposited by conventional Sn-vapor diffusion prevent them from reaching their theoretical capabilities. Here we demonstrate a seed-free electrochemical synthesis that pushes the limit of chemical and physical properties in Nb3Sn. Utilization of electrochemical Sn pre-deposits reduces the roughness of converted Nb3Sn by five times compared to typical vapor-diffused Nb3Sn. Quantitative mappings using chemical and atomic probes confirm improved stoichiometry and minimized impurity concentrations in electrochemically synthesized Nb3Sn. We have successfully applied this Nb3Sn to the large-scale 1.3 GHz SRF cavity and demonstrated ultra-low BCS surface resistances at multiple operation temperatures, notably lower than vapor-diffused cavities. Our smooth, homogeneous, high-purity Nb3Sn provides the route toward high efficiency and high fields for SRF applications under helium-free cryogenic operations.

cond-mat.mtrl-sci↗

arXiv2023

Kinetic Insights into Bridge Cleavage Pathways in Periodic Mesoporous Organosilicas

Bridging functionalities in periodic mesoporous organosilicas (PMOs) enable new functionalities for a wide range of applications. Bridge cleavage is frequently observed during anneals required to form porous structures, yet the mechanism of these bridge cleavages has not been completely resolved. Here, we reveal these chemical transformations and their kinetic pathways on sub-millisecond timescales induced by laser heating. By varying anneal times and temperatures, the transformation dynamics of bridge cleavage and structural transformations, and their activation energies, are determined. The structural relaxation time for individual reactions and their effective local heating time are determined and compared, and results directly demonstrate the manipulation of different molecules through kinetic control of the sequence of reactions. By isolating and understanding the earliest stage of structural transformations, this study identifies the kinetic principles for new synthesis and post-processing routes to control individual molecules and reactions in PMOs and other material systems with multi-functionalities.

cond-mat.mtrl-sci↗

arXiv2023

Thermal annealing of sputtered Nb3Sn and V3Si thin films for superconducting radio-frequency cavities

Nb3Sn and V3Si thin films are promising candidates as thin films for the next generation of superconducting radio-frequency (SRF) cavities. However, sputtered films often suffer from stoichiometry and strain issues during deposition and post annealing. In this study, we explore the structural and chemical effects of thermal annealing, both in-situ and post-sputtering, on DC-sputtered Nb3Sn and V3Si films of varying thickness on Nb or Cu substrates, extending from our initial studies [1]. Through annealing at 950 {\deg}C, we successfully enabled recrystallization of 100 nm thin Nb3Sn films on Nb substrate with stoichiometric and strain-free grains. For 2 um thick films, we observed the removal of strain and a slight increase in grain size with increasing temperature. Annealing enabled a phase transformation from unstable to stable structure on V3Si films, while we observed significant Sn loss in 2 um thick Nb3Sn films after high temperature anneals. We observed similar Sn and Si loss on films atop Cu substrates during annealing, likely due to Cu-Sn and Cu-Si phase generation and subsequent Sn and Si evaporation. These results encourage us to refine our process to obtain high-quality sputtered films for SRF use.

cond-mat.mtrl-sci↗

arXiv2023

Electrochemical Polishing of Chemical Vapor Deposited Niobium Thin Films

Combining chemical vapor deposition (CVD) with electrochemical polish (EP) operations is a promising route to producing performance-capable superconducting films for use in the fabrication of cost-effective components for superconducting radiofrequency (SRF) particle accelerators and superconducting quantum computers. The post-deposition EP process enables a critically necessary reduction in surface roughness of niobium thin films to promote optimal superconducting surface conditions. In this work, surface morphology, roughness, and crystal orientation of the CVD-grown and EP-polished niobium films were investigated. The grain growth and polishing mechanisms were analyzed. The CVD films were found to comprise steps, kinks, and pyramidal features, resulting in undesirable large peak-to-valley distances. The electrochemical polish was demonstrated to significantly diminish the height of pyramids and effectively minimize the overall surface roughness. In contrast to buffered chemical polishing (BCP), EP results showed a probable dependence on crystal orientation, suggesting this process was influenced by locally enhanced current density and thickness variations of oxide dielectrics. These understandings identify the EP principles tied to CVD-grown Nb films that allow further refinement of surface profiles for film-based SRF applications

cond-mat.mtrl-sci↗

arXiv2022

Theory of Nb-Zr Alloy Superconductivity and First Experimental Demonstration for Superconducting Radio-Frequency Cavity Applications

Niobium-zirconium (Nb-Zr) alloy is an old superconductor that is a promising new candidate for superconducting radio-frequency (SRF) cavity applications. Using density-functional and Eliashberg theories, we show that addition of Zr to a Nb surface in small concentrations increases the critical temperature $T_c$ and improves other superconducting properties. Furthermore, we calculate $T_c$ for Nb-Zr alloys across a broad range of Zr concentrations, showing good agreement with the literature for disordered alloys as well as the potential for significantly higher $T_c$ in ordered alloys near 75%Nb/25%Zr composition. We provide experimental verification on Nb-Zr alloy samples and SRF sample test cavities prepared with either physical vapor or our novel electrochemical deposition recipes. These samples have the highest measured $T_c$ of any Nb-Zr superconductor to date and indicate a reduction in BCS resistance compared to the conventional Nb reference sample; they represent the first steps along a new pathway to greatly enhanced SRF performance. Finally, we use Ginzburg-Landau theory to show that the addition of Zr to a Nb surface increases the superheating field $B_{sh}$, a key figure of merit for SRF which determines the maximum accelerating gradient at which cavities can operate.

cond-mat.supr-con↗