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Yunfeng Shi

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cond-mat.mtrl-sci math.DS math-ph math.MP math.SP Artificial Intelligence Computation and Language

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preprint2026arXiv

OProver: A Unified Framework for Agentic Formal Theorem Proving

Recent progress in formal theorem proving has benefited from large-scale proof generation and verifier-aware training, but agentic proving is rarely integrated into prover training, appearing only at inference time. We present OProver, a unified framework for agentic formal theorem proving in Lean 4, in which failed proof attempts are iteratively revised using retrieved compiler verified proofs and Lean compiler feedback. OProver is trained through continued pretraining followed by iterative post-training: each iteration runs agentic proving, indexes newly verified proofs into OProofs and the retrieval memory, uses repair trajectories as SFT data, and uses unresolved hard cases for RL. OProofs is built from public Lean resources, large-scale proof synthesis, and agentic proving traces, containing 1.77M Lean statements, 6.86M compiler-verified proofs, and serialized trajectories with retrieved context, failed attempts, feedback, and repairs. Across five benchmarks, OProver-32B attains the best Pass@32 on MiniF2F (93.3%), ProverBench (58.2%), and PutnamBench (11.3%), and ranks second on MathOlympiad (22.8%) and ProofNet (33.2%) more top placements than any prior open-weight whole-proof prover.

preprint2021arXiv

A Multi-scale Analysis Proof of the Power-law Localization for Random Operators on ${\Z}^d$

In this paper we give a multi-scale analysis proof of \textit{power-law} localization for random operators on ${\Z}^d$ for \textit{arbitrary} $d\geq1$.

preprint2020arXiv

Long-time Anderson Localization for the Nonlinear Schrodinger Equation Revisited

In this paper, we confirm the conjecture of Wang and Zhang (J. Stat. Phys. 134 (5-6): 953--968, 2009) in a long time scale, i.e., the displacement of the wavefront for $1D$ nonlinear random Schroedinger equation is of logarithmic order in time $|t|$.

preprint2020arXiv

On linear stability of KAM tori via the Craig-Wayne-Bourgain method

In this paper, we prove the Melnikov's persistency theorem by combining the traditional Kolmogorov-Arnold-Moser (KAM) technique and the Craig-Wayne-Bourgain (CWB) method. The aim of this paper is twofold. One is to establish the linear stability of the perturbed invariant tori by using the CWB method without the second Melnikov condition. The other one is to illustrate the CWB method in detail and make the CWB method more accessible.

preprint2015arXiv

Two-Dimensional Van der Waals Epitaxy Kinetics in a Three-Dimensional Perovskite Halide

The exploration of emerging materials physics and prospective applications of two-dimensional materials greatly relies on the growth control of their thickness, phases, morphologies and film-substrate interactions. Though substantial progresses have been made for the development of two-dimensional films from conventional layered bulky materials, particular challenges remain on obtaining ultrathin, single crystalline, dislocation-free films from intrinsically non-Van der Waals-type three-dimensional materials. In this report, with the successful demonstration of single crystalline ultrathin large scale perovskite halide material, we reveal and identify the favorable role of weak Van der Waals film-substrate interaction on the nucleation and growth of the two-dimensional morphology out of non-layered materials compared to conventional epitaxy. We also show how the bonding nature of the three-dimensional material itself affects the kinetic energy landscape of ultrathin films growth. By studying the formation of fractal perovskites assisted with Monte Carlo simulations, we demonstrate that the competition between the Van der Waals diffusion and surface free energy of the perovskite leads to film thickening, suggesting extra strategies such as surface passivation may be needed for the growth of monolayer and a few layers films.

preprint2012arXiv

Dominant shear bands observed in amorphous ZrCuAl nanowires under simulated compression

We observed the formation of dominant shear bands in model ZrCuAl metallic glass (MG) nanowires (18-nm-long) in molecular dynamics simulations, which implies size-independent incipient plasticity in MG materials. The MG nanowires were prepared using the simulated casting technique to ensure proper relaxation of sample surfaces. Under uniaxial compression, shear bands initiate at the surfaces and lead to reduced icosahedral short-range order. The shear band formation is sensitive to sample thermal-history, which calls for careful consideration of sample preparation effects in both experimental and numerical studies of size-effect in MG samples.

preprint2010arXiv

Size-independent Shear Band Formation in Amorphous Nanowires made from Simulated Casting

Molecular dynamics simulations indicate that surfaces strongly influence the strain localization behavior of amorphous nanowires in tension. A sample preparation routine that simulates casting was employed to facilitate the relaxation of the sample surface. Samples as short as 15 nm (7.5 nm in diameter) form dominant shear bands during deformation. The elastic energy release during plastic deformation is sufficient to provide the excess potential energy required for the shear band nucleation at rather small sample sizes. The results show that shear band formation is almost size-independent and is bounded only by its own length scale.