How an AI Scored a Perfect IMO Gold and What Its Self‑Correction Loop Reveals for Real‑World Tasks

At IMO 2026, seven human contestants earned perfect 42‑point gold medals, and for the first time an AI model—Xiaohongshu’s dots‑note‑3.0—joined them, receiving a full score on all six problems. In contrast, Google’s Gemini Deep Think in IMO 2025 solved five of six problems for 35 points.

The model reads the original LaTeX statements, expands the reasoning in natural language, and leverages Python‑assisted analysis. It follows a three‑stage loop— Proof , Verify , and Refine —without relying on formal proof systems such as Lean.

Proof generates multiple candidate proofs by exploring different reasoning paths. Verify inspects each draft, looking for missing conditions, logical jumps, or nonexistent theorems, and suggests corrections. Refine incorporates the feedback, revises the flawed sections, and produces a final, submit‑ready proof. The cycle can repeat, allowing the model to iteratively eliminate errors.

Problem 3, a combinatorial two‑player game, illustrates the approach. Human solvers typically convert the game to a graph‑connectivity problem, whereas dots‑note‑3.0 adopts an induction strategy: it designs a set of wooden segments decreasing by multiples, then proves by induction that the total length lost by Liu Bang is always bounded, compressing a complex game into a concise proof chain.

The IMO’s requirement for complete natural‑language proofs forces the model to expose hidden assumptions, edge‑case failures, and even invented theorems—issues that simple answer‑matching benchmarks would miss. This highlights the importance of a self‑checking capability for long‑chain reasoning tasks.

Beyond mathematics, real‑world tasks are longer and less verifiable. The team visualizes tasks on two axes: duration and ease of verification. Short, verifiable tasks like IMO problems contrast with open‑ended activities such as home renovation, travel planning, or job hunting, which may span weeks and lack a single correct answer.

To evaluate agents on such complex scenarios, the team built VibeAgentBench , covering ten life domains, 200 tasks, 22 simulated service back‑ends, and 288 tool interfaces (calendar, email, finance, travel, e‑commerce, recruitment, etc.). The median task duration is 29 days, with a maximum of 111 days, involving 7 453 scripted events and over 12 000 check standards to assess whether an agent can maintain goals, adapt to changes, and refine solutions over extended interactions.

The 42‑point IMO result demonstrates a concrete instance of “recursive self‑improvement” (RSI): the model identifies flaws in its own output, iterates, and converges on a correct proof. This capability is positioned as a prerequisite for agents that must continuously audit their reasoning and adapt to evolving real‑world requirements.