Mechanic: Sorrifier-Driven Formal Decomposition Workflow for Automated Theorem Proving

Recent advances in large language models (LLMs) and LLM-based agents have substantially improved the capabilities of automated theorem proving. However, for problems requiring complex mathematical reasoning, current systems rarely succeed on the first try and must repeatedly modify their proof strategies. Existing approaches for handling failed attempts typically either discard the entire proof and regenerate it from scratch or iteratively fix errors within the proof. The former is inefficient, as it may abandon mostly correct reasoning due to localized errors, while the latter, although preserving prior progress, leads to progressively longer contexts which progressively degrades the model's ability to attend to the remaining unresolved subproblems. To address this dilemma, we propose Mechanic, a novel agent system that employs a sorry-driven formal decomposition strategy. By leveraging the sorry placeholder in Lean to precisely isolate unresolved subgoals while preserving the surrounding verified proof structure, Mechanic extracts each failed subproblem into a clean, self-contained context and resolves it independently. This avoids both the waste of full regeneration and the excessive context length induced by repeated repairs. Experimental results on challenging mathematical competition benchmarks, including IMO 2025 and Putnam 2025, demonstrate that our agent achieves significant advantages in proving efficiency.

Atomic Trajectory Modeling with State Space Models for Biomolecular Dynamics

Understanding the dynamic behavior of biomolecules is fundamental to elucidating biological function and facilitating drug discovery. While Molecular Dynamics (MD) simulations provide a rigorous physical basis for studying these dynamics, they remain computationally expensive for long timescales. Conversely, recent deep generative models accelerate conformation generation but are typically either failing to model temporal relationship or built only for monomeric proteins. To bridge this gap, we introduce ATMOS, a novel generative framework based on State Space Models (SSM) designed to generate atom-level MD trajectories for biomolecular systems. ATMOS integrates a Pairformer-based state transition mechanism to capture long-range temporal dependencies, with a diffusion-based module to decode trajectory frames in an autoregressive manner. ATMOS is trained across crystal structures from PDB and conformation trajectory from large-scale MD simulation datasets including mdCATH and MISATO. We demonstrate that ATMOS achieves state-of-the-art performance in generating conformation trajectories for both protein monomers and complex protein-ligand systems. By enabling efficient inference of atomic trajectory of motions, this work establishes a promising foundation for modeling biomolecular dynamics.

Tele-Omni: a Unified Multimodal Framework for Video Generation and Editing

Recent advances in diffusion-based video generation have substantially improved visual fidelity and temporal coherence. However, most existing approaches remain task-specific and rely primarily on textual instructions, limiting their ability to handle multimodal inputs, contextual references, and diverse video generation and editing scenarios within a unified framework. Moreover, many video editing methods depend on carefully engineered pipelines tailored to individual operations, which hinders scalability and composability. In this paper, we propose Tele-Omni, a unified multimodal framework for video generation and editing that follows multimodal instructions, including text, images, and reference videos, within a single model. Tele-Omni leverages pretrained multimodal large language models to parse heterogeneous instructions and infer structured generation or editing intents, while diffusion-based generators perform high-quality video synthesis conditioned on these structured signals. To enable joint training across heterogeneous video tasks, we introduce a task-aware data processing pipeline that unifies multimodal inputs into a structured instruction format while preserving task-specific constraints. Tele-Omni supports a wide range of video-centric tasks, including text-to-video generation, image-to-video generation, first-last-frame video generation, in-context video generation, and in-context video editing. By decoupling instruction parsing from video synthesis and combining it with task-aware data design, Tele-Omni achieves flexible multimodal control while maintaining strong temporal coherence and visual consistency. Experimental results demonstrate that Tele-Omni achieves competitive performance across multiple tasks.

Numina-Lean-Agent: An Open and General Agentic Reasoning System for Formal Mathematics

Agentic systems have recently become the dominant paradigm for formal theorem proving, achieving strong performance by coordinating multiple models and tools. However, existing approaches often rely on task-specific pipelines and trained formal provers, limiting their flexibility and reproducibility. In this paper, we propose the paradigm that directly uses a general coding agent as a formal math reasoner. This paradigm is motivated by (1) A general coding agent provides a natural interface for diverse reasoning tasks beyond proving, (2) Performance can be improved by simply replacing the underlying base model, without training, and (3) MCP enables flexible extension and autonomous calling of specialized tools, avoiding complex design. Based on this paradigm, we introduce Numina-Lean-Agent, which combines Claude Code with Numina-Lean-MCP to enable autonomous interaction with Lean, retrieval of relevant theorems, informal proving and auxiliary reasoning tools. Using Claude Opus 4.5 as the base model, Numina-Lean-Agent solves all problems in Putnam 2025 (12 / 12), matching the best closed-source system. Beyond benchmark evaluation, we further demonstrate its generality by interacting with mathematicians to successfully formalize the Brascamp-Lieb theorem. We release Numina-Lean-Agent and all solutions at https://github.com/project-numina/numina-lean-agent.

TeleWorld: Towards Dynamic Multimodal Synthesis with a 4D World Model

World models aim to endow AI systems with the ability to represent, generate, and interact with dynamic environments in a coherent and temporally consistent manner. While recent video generation models have demonstrated impressive visual quality, they remain limited in real-time interaction, long-horizon consistency, and persistent memory of dynamic scenes, hindering their evolution into practical world models. In this report, we present TeleWorld, a real-time multimodal 4D world modeling framework that unifies video generation, dynamic scene reconstruction, and long-term world memory within a closed-loop system. TeleWorld introduces a novel generation-reconstruction-guidance paradigm, where generated video streams are continuously reconstructed into a dynamic 4D spatio-temporal representation, which in turn guides subsequent generation to maintain spatial, temporal, and physical consistency. To support long-horizon generation with low latency, we employ an autoregressive diffusion-based video model enhanced with Macro-from-Micro Planning (MMPL)--a hierarchical planning method that reduces error accumulation from frame-level to segment-level-alongside efficient Distribution Matching Distillation (DMD), enabling real-time synthesis under practical computational budgets. Our approach achieves seamless integration of dynamic object modeling and static scene representation within a unified 4D framework, advancing world models toward practical, interactive, and computationally accessible systems. Extensive experiments demonstrate that TeleWorld achieves strong performance in both static and dynamic world understanding, long-term consistency, and real-time generation efficiency, positioning it as a practical step toward interactive, memory-enabled world models for multimodal generation and embodied intelligence.

See More, Change Less: Anatomy-Aware Diffusion for Contrast Enhancement

Image enhancement improves visual quality and helps reveal details that are hard to see in the original image. In medical imaging, it can support clinical decision-making, but current models often over-edit. This can distort organs, create false findings, and miss small tumors because these models do not understand anatomy or contrast dynamics. We propose SMILE, an anatomy-aware diffusion model that learns how organs are shaped and how they take up contrast. It enhances only clinically relevant regions while leaving all other areas unchanged. SMILE introduces three key ideas: (1) structure-aware supervision that follows true organ boundaries and contrast patterns; (2) registration-free learning that works directly with unaligned multi-phase CT scans; (3) unified inference that provides fast and consistent enhancement across all contrast phases. Across six external datasets, SMILE outperforms existing methods in image quality (14.2% higher SSIM, 20.6% higher PSNR, 50% better FID) and in clinical usefulness by producing anatomically accurate and diagnostically meaningful images. SMILE also improves cancer detection from non-contrast CT, raising the F1 score by up to 10 percent.

TempoMaster: Efficient Long Video Generation via Next-Frame-Rate Prediction

We present TempoMaster, a novel framework that formulates long video generation as next-frame-rate prediction. Specifically, we first generate a low-frame-rate clip that serves as a coarse blueprint of the entire video sequence, and then progressively increase the frame rate to refine visual details and motion continuity. During generation, TempoMaster employs bidirectional attention within each frame-rate level while performing autoregression across frame rates, thus achieving long-range temporal coherence while enabling efficient and parallel synthesis. Extensive experiments demonstrate that TempoMaster establishes a new state-of-the-art in long video generation, excelling in both visual and temporal quality.

LeanGeo: Formalizing Competitional Geometry problems in Lean

Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since most geometric proofs rely on intuitive diagrams, verifying geometry problems is particularly challenging. To address these gaps, we introduce LeanGeo, a unified formal system for formalizing and solving competition-level geometry problems within the Lean 4 theorem prover. LeanGeo features a comprehensive library of high-level geometric theorems with Lean's foundational logic, enabling rigorous proof verification and seamless integration with Mathlib. We also present LeanGeo-Bench, a formal geometry benchmark in LeanGeo, comprising problems from the International Mathematical Olympiad (IMO) and other advanced sources. Our evaluation demonstrates the capabilities and limitations of state-of-the-art Large Language Models on this benchmark, highlighting the need for further advancements in automated geometric reasoning. We open source the theorem library and the benchmark of LeanGeo at https://github.com/project-numina/LeanGeo/tree/master.

Kimi K2: Open Agentic Intelligence

We introduce Kimi K2, a Mixture-of-Experts (MoE) large language model with 32 billion activated parameters and 1 trillion total parameters. We propose the MuonClip optimizer, which improves upon Muon with a novel QK-clip technique to address training instability while enjoying the advanced token efficiency of Muon. Based on MuonClip, K2 was pre-trained on 15.5 trillion tokens with zero loss spike. During post-training, K2 undergoes a multi-stage post-training process, highlighted by a large-scale agentic data synthesis pipeline and a joint reinforcement learning (RL) stage, where the model improves its capabilities through interactions with real and synthetic environments. Kimi K2 achieves state-of-the-art performance among open-source non-thinking models, with strengths in agentic capabilities. Notably, K2 obtains 66.1 on Tau2-Bench, 76.5 on ACEBench (En), 65.8 on SWE-Bench Verified, and 47.3 on SWE-Bench Multilingual -- surpassing most open and closed-sourced baselines in non-thinking settings. It also exhibits strong capabilities in coding, mathematics, and reasoning tasks, with a score of 53.7 on LiveCodeBench v6, 49.5 on AIME 2025, 75.1 on GPQA-Diamond, and 27.1 on OJBench, all without extended thinking. These results position Kimi K2 as one of the most capable open-source large language models to date, particularly in software engineering and agentic tasks. We release our base and post-trained model checkpoints to facilitate future research and applications of agentic intelligence.

CombiBench: Benchmarking LLM Capability for Combinatorial Mathematics

Neurosymbolic approaches integrating large language models with formal reasoning have recently achieved human-level performance on mathematics competition problems in algebra, geometry and number theory. In comparison, combinatorics remains a challenging domain, characterized by a lack of appropriate benchmarks and theorem libraries. To address this gap, we introduce CombiBench, a comprehensive benchmark comprising 100 combinatorial problems, each formalized in Lean~4 and paired with its corresponding informal statement. The problem set covers a wide spectrum of difficulty levels, ranging from middle school to IMO and university level, and span over ten combinatorial topics. CombiBench is suitable for testing IMO solving capabilities since it includes all IMO combinatorial problems since 2000 (except IMO 2004 P3 as its statement contain an images). Furthermore, we provide a comprehensive and standardized evaluation framework, dubbed Fine-Eval (for $\textbf{F}$ill-in-the-blank $\textbf{in}$ L$\textbf{e}$an Evaluation), for formal mathematics. It accommodates not only proof-based problems but also, for the first time, the evaluation of fill-in-the-blank questions. Using Fine-Eval as the evaluation method and Kimina Lean Server as the backend, we benchmark several LLMs on CombiBench and observe that their capabilities for formally solving combinatorial problems remain limited. Among all models tested (none of which has been trained for this particular task), Kimina-Prover attains the best results, solving 7 problems (out of 100) under both ``with solution'' and ``without solution'' scenarios. We open source the benchmark dataset alongside with the code of the proposed evaluation method at https://github.com/MoonshotAI/CombiBench/.