Sketchpad proves 0.8B VLM does exact arithmetic at any length

Qwen3.5-0.8B with a low-rank adapter now comes with a Lean proof that it will perform arithmetic correctly on any input length. Not on average, not on a benchmark sample. On every input the system will ever see. That is the claim of a new arXiv preprint from Mostafa 'Neo' Mohsenvand, who calls the system Sketchpad.

The setup is deliberately strange. Each forward pass reads a three-cell view on a rendered sheet, then emits one step: a digit, a carry or borrow, and the next operation. A fixed runtime moves the view and writes no digit of the result itself. "We prove in Lean that the model is then exact on all inputs of any length if and only if it is exact on the finite set of views the runtime presents," the paper states. A finite check replaces an infinite one.

The author ran that check. "All 2,446 views pass on the deployment device, a laptop GPU running the model in a web browser."

On a pre-registered test, Sketchpad solved 200 of 200 problems. On 220 sums of up to 1,000 digits and products of up to 20 digits, it went 220 of 220; GPT-6.1 Sol, which the paper calls the strongest of ten other models tested, managed 217.

The certified operations are signed addition and subtraction, long multiplication and division, square roots and greatest common divisors. A symbolic runtime built on these solves, expands and factors polynomials with every number computed by the model. A "multiplicative gate on the adapter recovers the base model exactly when the sheet is not in use," so the arithmetic mode is opt-in.

The paper is by a single author, filed on November 3. Independent reproduction of the Lean proof, and of whether the three-cell discipline extends beyond arithmetic, is still to come.