PAIWorld: A 3D-Consistent World Foundation Model for Robotic Manipulation

World foundation models (WFMs) are powerful simulators, yet they predominantly operate in a single-view setting and lack the multi-view 3D consistency required for robotic manipulation. While robotic systems rely on multiple cameras (egocentric, eye-to-hand, and wrist-mounted) for policy learning, current multi-view world models simply concatenate view tokens without explicit geometric reasoning. This causes cross-view object drift, depth inconsistency, and texture misalignment. We trace these failures to two deficiencies: the absence of an explicit inter-view communication mechanism and the lack of a 3D geometric prior. We argue that resolving both simultaneously is necessary and sufficient. To address this, we present PAIWorld, a framework that augments diffusion-transformer world models via three core components: (1) Geometry-Aware Cross-View Attention blocks that establish an explicit pathway across views, (2) Geometric Rotary Position Embedding that encodes camera ray directions and extrinsic poses into the attention mechanism, and (3) Latent 3D-REPA, which distills 3D-aware features from frozen 3D foundation models to ensure 3D consistency. Built upon a DiT-based world foundation model, PAIWorld achieves state-of-the-art multi-view 3D consistency on robotic manipulation benchmarks, ranking 1st on the WorldArena leaderboard and 2nd on the AgiBot-Challenge2026 leaderboard, while enabling downstream applications such as model-based planning, world action models, and multi-view policy post-training.

Leveraging Large Language Models for Automated Proof Synthesis in Rust

Formal verification can provably guarantee the correctness of critical system software, but the high proof burden has long hindered its wide adoption. Recently, Large Language Models (LLMs) have shown success in code analysis and synthesis. In this paper, we present a combination of LLMs and static analysis to synthesize invariants, assertions, and other proof structures for a Rust-based formal verification framework called Verus. In a few-shot setting, LLMs demonstrate impressive logical ability in generating postconditions and loop invariants, especially when analyzing short code snippets. However, LLMs lack the ability to retain and propagate context information, a strength of traditional static analysis. Based on these observations, we developed a prototype based on OpenAI's GPT-4 model. Our prototype decomposes the verification task into multiple smaller ones, iteratively queries GPT-4, and combines its output with lightweight static analysis. We evaluated the prototype with a developer in the automation loop on 20 vector-manipulating programs. The results demonstrate that it significantly reduces human effort in writing entry-level proof code.